In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively. The newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to $Re=O(10^5)$.

1 aHijazi, Saddam1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1907.0990900617nas a2200193 4500008004100000245007100041210006300112100001800175700002300193700001900216700001800235700001700253700002400270700002000294700002400314700002000338700001700358856004800375 2020 eng d00aThe deal.II finite element library: Design, features, and insights0 adealII finite element library Design features and insights1 aArndt, Daniel1 aBangerth, Wolfgang1 aDavydov, Denis1 aHeister, Timo1 aHeltai, Luca1 aKronbichler, Martin1 aMaier, Matthias1 aPelteret, Jean-Paul1 aTurcksin, Bruno1 aWells, David uhttps://doi.org/10.1016/j.camwa.2020.02.02202129nas a2200145 4500008004100000245011600041210006900157520162200226100002001848700002001868700001701888700002101905700002001926856003701946 2020 eng d00aEfficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method0 aEfficient computation of bifurcation diagrams with a deflated ap3 aThe majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work we implemented an elaborated deflated continuation method, that relies on the spectral element method (SEM) and on the reduced basis (RB) one, to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations.

1 aPintore, Moreno1 aPichi, Federico1 aHess, Martin1 aRozza, Gianluigi1 aCanuto, Claudio uhttps://arxiv.org/abs/1912.0608900996nas a2200121 4500008004100000245004100041210003400082260001200116520067500128100001400803700002000817856003700837 2020 eng d00aOn the gauge group of Galois objects0 agauge group of Galois objects c03/20203 aWe study the Ehresmann--Schauenburg bialgebroid of a noncommutative principal bundle as a quantization of the classical gauge groupoid of a principal bundle. When the base algebra is in the centre of the total space algebra, the gauge group of the noncommutative principal bundle is isomorphic to the group of bisections of the bialgebroid. In particular we consider Galois objects (non-trivial noncommutative bundles over a point in a sense) for which the bialgebroid is a Hopf algebra. For these we give a crossed module structure for the bisections and the automorphisms of the bialgebroid. Examples include Galois objects of group Hopf algebras and of Taft algebras.1 aHan, Xiao1 aLandi, Giovanni uhttps://arxiv.org/abs/2002.0609702335nas a2200325 4500008004100000022001400041245014400055210006900199300000800268490000600276520131600282653001801598653002401616653001801640653002301658653001601681653002401697653002501721653002501746100002501771700002101796700002301817700002201840700002101862700002501883700002201908700001701930700001901947856004301966 2020 eng d a2640-350100aMicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales0 aMicroMotility State of the art recent accomplishments and perspe a2300 v23 aMathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research.

10aactive matter10aadhesive locomotion10acell motility10acell sheet folding10aknotted DNA10atopological defects10aunicellular swimmers10aunjamming transition1 aAgostinelli, Daniele1 aCerbino, Roberto1 aDel Alamo, Juan, C1 aDeSimone, Antonio1 aHöhn, Stephanie1 aMicheletti, Cristian1 aNoselli, Giovanni1 aSharon, Eran1 aYeomans, Julia uhttp://dx.doi.org/10.3934/mine.202001100372nas a2200097 4500008004100000245008800041210006900129100002200198700001700220856003700237 2020 eng d00aMultiscale modeling of fiber reinforced materials via non-matching immersed methods0 aMultiscale modeling of fiber reinforced materials via nonmatchin1 aAlzetta, Giovanni1 aHeltai, Luca uhttps://arxiv.org/abs/1906.0388101465nas a2200193 4500008004100000245014700041210006900188260003800257520076900295100001901064700002201083700001701105700002101122700002601143700002401169700002001193700002101213856003701234 2020 eng d00aNon-Intrusive Polynomial Chaos Method Applied to Problems in Computational Fluid Dynamics with a Comparison to Proper Orthogonal Decomposition0 aNonIntrusive Polynomial Chaos Method Applied to Problems in Comp bSpringer International Publishing3 aIn this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

1 aHijazi, Saddam1 aStabile, Giovanni1 aMola, Andrea1 aRozza, Gianluigi1 avan Brummelen, Harald1 aCorsini, Alessandro1 aPerotto, Simona1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0228500384nas a2200097 4500008004100000245010100041210006900142100002100211700001700232856003700249 2020 eng d00aA numerical study of the jerky crack growth in elastoplastic materials with localized plasticity0 anumerical study of the jerky crack growth in elastoplastic mater1 aDal Maso, Gianni1 aHeltai, Luca uhttps://arxiv.org/abs/2004.1270500388nas a2200097 4500008004100000245006200041210006000103100001700163700001500180856009500195 2020 eng d00aA priori error estimates of regularized elliptic problems0 apriori error estimates of regularized elliptic problems1 aHeltai, Luca1 aLei, Wenyu uhttps://www.math.sissa.it/publication/priori-error-estimates-regularized-elliptic-problems01527nas a2200145 4500008004100000245011100041210006900152300001200221490000700233520104500240100001701285700002101302700002101323856003701344 2020 eng d00aReduced Basis Model Order Reduction for Navier-Stokes equations in domains with walls of varying curvature0 aReduced Basis Model Order Reduction for NavierStokes equations i a119-1260 v343 aWe consider the Navier-Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter dependency, the offline-online procedure can be used to compute reduced order solutions for parameter variations. The reduced order space is computed from the steady-state snapshot solutions by a standard POD procedure. The model is discretised with high-order spectral element ansatz functions, resulting in 4752 degrees of freedom. The proposed reduced order model produces accurate approximations of steady-state solutions for a wide range of geometries and kinematic viscosity values. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the valve shape. Through our computational study, we found that the critical Reynolds number for the symmetry breaking increases as the wall curvature increases.

1 aHess, Martin1 aQuaini, Annalisa1 aRozza, Gianluigi uhttps://arxiv.org/abs/1901.0370801869nas a2200181 4500008004100000245012100041210006900162260003800231520122900269100002801498700002201526700001901548700002401567700002101591700001601612700002201628856003701650 2020 eng d00aA Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries0 aReduced Order Approach for the Embedded Shifted Boundary FEM and bSpringer International Publishing3 aA model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined shape-regular background mesh to account for parametrized geometries. In particular, the employed embedded boundary element method is the Shifted Boundary Method (SBM) recently proposed. This approach is based on the idea of shifting the location of true boundary conditions to a surrogate boundary, with the goal of avoiding cut cells near the boundary of the computational domain. This combination of methodologies has multiple advantages. In the first place, since the Shifted Boundary Method always relies on the same background mesh, there is no need to update the discretized parametric domain. Secondly, we avoid the treatment of cut cell elements, which usually need particular attention. Thirdly, since the whole background mesh is considered in the reduced basis construction, the SBM allows for a smooth transition of the reduced modes across the immersed domain boundary. The performances of the method are verified in two dimensional heat transfer numerical examples.

1 aKaratzas, Efthymios, N.1 aStabile, Giovanni1 aAtallah, Nabib1 aScovazzi, Guglielmo1 aRozza, Gianluigi1 aFehr, Jörg1 aHaasdonk, Bernard uhttps://arxiv.org/abs/1807.0775301165nas a2200109 4500008004100000245004700041210004700088260001200135520085700147100001401004856003701018 2020 eng d00aTwisted Ehresmann Schauenburg bialgebroids0 aTwisted Ehresmann Schauenburg bialgebroids c09/20203 aWe construct an invertible normalised 2 cocycle on the Ehresmann Schauenburg bialgebroid of a cleft Hopf Galois extension under the condition that the corresponding Hopf algebra is cocommutative and the image of the unital cocycle corresponding to this cleft Hopf Galois extension belongs to the centre of the coinvariant subalgebra. Moreover, we show that any Ehresmann Schauenburg bialgebroid of this kind is isomorphic to a 2-cocycle twist of the Ehresmann Schauenburg bialgebroid corresponding to a Hopf Galois extension without cocycle, where comodule algebra is an ordinary smash product of the coinvariant subalgebra and the Hopf algebra (i.e. $\C(B/#_{\sigma}H, H)\simeq \C(B\#H, H)^{\tilde{\sigma}}$). We also study the theory in the case of a Galois object where the base is trivial but without requiring the Hopf algebra to be cocommutative.1 aHan, Xiao uhttps://arxiv.org/abs/2009.0276400891nas a2200277 4500008004100000022001300041245003700054210003000091520010800121100001800229700002300247700002600270700001900296700001800315700002700333700001900360700001800379700001700397700002400414700002500438700002000463700002500483700002000508700001700528856006800545 2019 eng d a1570282000aThe deal.II Library, Version 9.10 adealII Library Version 913 aThis paper provides an overview of the new features of the finite element library deal.II, version 9.1.1 aArndt, Daniel1 aBangerth, Wolfgang1 aClevenger, Thomas, C.1 aDavydov, Denis1 aFehling, Marc1 aGarcia-Sanchez, Daniel1 aHarper, Graham1 aHeister, Timo1 aHeltai, Luca1 aKronbichler, Martin1 aKynch, Ross, Maguire1 aMaier, Matthias1 aPelteret, Jean, Paul1 aTurcksin, Bruno1 aWells, David uhttps://www.math.sissa.it/publication/dealii-library-version-9101648nas a2200121 4500008004100000245009500041210006900136520122200205100002401427700001701451700002101468856003701489 2019 eng d00aDiscontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation0 aDiscontinuous Galerkin Model Order Reduction of Geometrically Pa3 aThe present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order model is based on the discontinuous Galerkin method with an interior penalty formulation. We introduce the broken Sobolev spaces as well as the weak formulation required for an affine parameter dependency. The operators are transformed from a fixed domain to a parameter dependent domain using the affine parameter dependency. The proper orthogonal decomposition is used to obtain the basis of functions of the reduced order model. By using the Galerkin projection the linear system is projected onto the reduced space. During this process, the offline-online decomposition is used to separate parameter dependent operations from parameter independent operations. Finally this technique is applied to an obstacle test problem.The numerical outcomes presented include experimental error analysis, eigenvalue decay and measurement of online simulation time. Keywords: Discontinuous Galerkin method, Stokes flow, Geometric parametrization, Proper orthogonal decomposition.

1 aShah, Nirav, Vasant1 aHess, Martin1 aRozza, Gianluigi uhttps://arxiv.org/abs/1912.0978700459nas a2200133 4500008004100000245009200041210006900133260001600202300001600218490000700234100001700241700001900258856004800277 2019 eng d00aError estimates in weighted Sobolev norms for finite element immersed interface methods0 aError estimates in weighted Sobolev norms for finite element imm bElsevier BV a3586–36040 v781 aHeltai, Luca1 aRotundo, Nella uhttps://doi.org/10.1016/j.camwa.2019.05.02902124nas a2200169 4500008004100000245008400041210006900125300001200194490000800206520160300214100001701817700002101834700002101855700002101876700002001897856003701917 2019 eng d00aA Localized Reduced-Order Modeling Approach for PDEs with Bifurcating Solutions0 aLocalized ReducedOrder Modeling Approach for PDEs with Bifurcati a379-4030 v3513 aReduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional discretizations of partial differential equations (PDEs) that can be used to more efficiently treat problems in control and optimization, uncertainty quantification, and other settings that require multiple approximate PDE solutions. In this work, a ROM is developed and tested for the treatment of nonlinear PDEs whose solutions bifurcate as input parameter values change. In such cases, the parameter domain can be subdivided into subregions, each of which corresponds to a different branch of solutions. Popular ROM approaches such as proper orthogonal decomposition (POD), results in a global low-dimensional basis that does no respect not take advantage of the often large differences in the PDE solutions corresponding to different subregions. Instead, in the new method, the k-means algorithm is used to cluster snapshots so that within cluster snapshots are similar to each other and are dissimilar to those in other clusters. This is followed by the construction of local POD bases, one for each cluster. The method also can detect which cluster a new parameter point belongs to, after which the local basis corresponding to that cluster is used to determine a ROM approximation. Numerical experiments show the effectiveness of the method both for problems for which bifurcation cause continuous and discontinuous changes in the solution of the PDE.

1 aHess, Martin1 aAlla, Alessandro1 aQuaini, Annalisa1 aRozza, Gianluigi1 aGunzburger, Max uhttps://arxiv.org/abs/1807.0885100406nas a2200121 4500008004100000245008200041210006900123300001000192490000700202100001700209700002100226856003700247 2019 eng d00aMultiscale modeling of vascularized tissues via non-matching immersed methods0 aMultiscale modeling of vascularized tissues via nonmatching imme ae32640 v351 aHeltai, Luca1 aCaiazzo, Alfonso uhttps://doi.org/10.1002/cnm.326401397nas a2200193 4500008004100000245006200041210006000103260003800163490000800201520080600209100002101015700002101036700002501057700001801082700001601100700002801116700002201144856003701166 2019 eng d00aA Spectral Element Reduced Basis Method in Parametric CFD0 aSpectral Element Reduced Basis Method in Parametric CFD bSpringer International Publishing0 v1263 aWe consider the Navier-Stokes equations in a channel with varying Reynolds numbers. The model is discretized with high-order spectral element ansatz functions, resulting in 14 259 degrees of freedom. The steady-state snapshot solu- tions define a reduced order space, which allows to accurately evaluate the steady- state solutions for varying Reynolds number with a reduced order model within a fixed-point iteration. In particular, we compare different aspects of implementing the reduced order model with respect to the use of a spectral element discretization. It is shown, how a multilevel static condensation in the pressure and velocity boundary degrees of freedom can be combined with a reduced order modelling approach to enhance computational times in parametric many-query scenarios.

1 aHess, Martin, W.1 aRozza, Gianluigi1 aRadu, Florin, Adrian1 aKumar, Kundan1 aBerre, Inga1 aNordbotten, Jan, Martin1 aPop, Iuliu, Sorin uhttps://arxiv.org/abs/1712.0643200414nas a2200109 4500008004100000245010800041210006900149300001100218100002100229700001700250856003700267 2018 eng d00aAccelerating the iterative solution of convection-diffusion problems using singular value decomposition0 aAccelerating the iterative solution of convectiondiffusion probl a1–211 aPitton, Giuseppe1 aHeltai, Luca uhttps://arxiv.org/abs/1807.0946700579nas a2200145 4500008004100000245010500041210006900146300001600215490000700231100001500238700001600253700001700269700001800286856012900304 2018 eng d00aAn authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production0 aauthenticated theoretical modeling of electrified fluid jet in c a1791–18110 v471 aRafiei, S.1 aNoroozi, B.1 aHeltai, Luca1 aHaghi, A., K. uhttps://www.math.sissa.it/publication/authenticated-theoretical-modeling-electrified-fluid-jet-core%E2%80%93shell-nanofibers00586nas a2200133 4500008004100000245010800041210006900149300001200218490000700230100002200237700002200259700002100281856015000302 2018 eng d00aCertified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models0 aCertified Reduced Basis Approximation for the Coupling of Viscou a197-2190 v741 aMartini, Immanuel1 aHaasdonk, Bernard1 aRozza, Gianluigi uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a96400540nas a2200145 4500008004100000245007700041210006900118300001400187490000600201100002100207700002100228700002200249700001700271856010600288 2018 eng d00adeal2lkit: A toolkit library for high performance programming in deal.II0 adeal2lkit A toolkit library for high performance programming in a318–3270 v71 aSartori, Alberto1 aGiuliani, Nicola1 aBardelloni, Mauro1 aHeltai, Luca uhttps://www.math.sissa.it/publication/deal2lkit-toolkit-library-high-performance-programming-dealii-000702nas a2200253 4500008004100000245003700041210003000078100002200108700001800130700001700148700001800165700002100183700001900204700002200223700001800245700001700263700002300280700002400303700002000327700002400347700001700371700001700388856004300405 2018 eng d00aThe deal.II Library, Version 9.00 adealII Library Version 901 aAlzetta, Giovanni1 aArndt, Daniel1 aBangerth, W.1 aBoddu, Vishal1 aBrands, Benjamin1 aDavydov, Denis1 aGassmöller, Rene1 aHeister, Timo1 aHeltai, Luca1 aKormann, Katharina1 aKronbichler, Martin1 aMaier, Matthias1 aPelteret, Jean-Paul1 aTurcksin, B.1 aWells, David uhttps://doi.org/10.1515/jnma-2018-005400547nas a2200145 4500008004100000245013400041210006900175260004400244300001100288490000700299100001900306700002000325700001700345856003900362 2018 eng d00aA distributed lagrange formulation of the finite element immersed boundary method for fluids interacting with compressible solids0 adistributed lagrange formulation of the finite element immersed aChambSpringer International Publishing a1–210 v161 aBoffi, Daniele1 aGastaldi, Lucia1 aHeltai, Luca uhttps://arxiv.org/abs/1712.02545v100590nas a2200133 4500008004100000245012000041210006900161100001900230700001700249700002200266700002400288700002100312856012300333 2018 eng d00aThe Effort of Increasing Reynolds Number in Projection-Based Reduced Order Methods: from Laminar to Turbulent Flows0 aEffort of Increasing Reynolds Number in ProjectionBased Reduced 1 aHijazi, Saddam1 aAli, Shafqat1 aStabile, Giovanni1 aBallarin, Francesco1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/effort-increasing-reynolds-number-projection-based-reduced-order-methods-laminar00612nas a2200169 4500008004100000245015500041210006900196300001100265490000800276100002200284700002000306700002000326700002300346700001700369700001900386856003700405 2018 eng d00aIterative map-making with two-level preconditioning for polarized cosmic microwave background data sets. A worked example for ground-based experiments0 aIterative mapmaking with twolevel preconditioning for polarized a1–140 v6181 aPuglisi, Giuseppe1 aPoletti, Davide1 aFabbian, Giulio1 aBaccigalupi, Carlo1 aHeltai, Luca1 aStompor, Radek uhttps://arxiv.org/abs/1801.0893700437nas a2200121 4500008004100000245010800041210006900149300001400218490000800232100002100240700001700261856003700278 2018 eng d00aNURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces0 aNURBSSEM A hybrid spectral element method on NURBS maps for the a440–4620 v3381 aPitton, Giuseppe1 aHeltai, Luca uhttps://arxiv.org/abs/1804.0827100509nas a2200133 4500008004100000245012700041210006900168300001400237490000600251100002100257700001700278700002200295856005800317 2018 eng d00aPredicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions0 aPredicting and Optimizing Microswimmer Performance from the Hydr a410–4240 v51 aGiuliani, Nicola1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/00970nas a2200145 4500008004100000245005300041210005300094300001200147490000700159520055900166100002800725700001400753700002000767856003700787 2018 eng d00aPrincipal fibrations over noncommutative spheres0 aPrincipal fibrations over noncommutative spheres a18500200 v303 aWe present examples of noncommutative four-spheres that are base spaces of $SU(2)$-principal bundles with noncommutative seven-spheres as total spaces. The noncommutative coordinate algebras of the four-spheres are generated by the entries of a projection which is invariant under the action of $SU(2)$. We give conditions for the components of the Connes–Chern character of the projection to vanish but the second (the top) one. The latter is then a non-zero Hochschild cycle that plays the role of the volume form for the noncommutative four-spheres.1 aDubois-Violette, Michel1 aHan, Xiao1 aLandi, Giovanni uhttps://arxiv.org/abs/1804.0703200501nas a2200121 4500008004100000245013400041210006900175490000700244100002100251700002000272700002100292856006600313 2018 eng d00aReduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings0 aReduced Basis Approximation and A Posteriori Error Estimation Ap0 v151 aHuynh, D., B. P.1 aPichi, Federico1 aRozza, Gianluigi uhttps://link.springer.com/chapter/10.1007/978-3-319-94676-4_800574nas a2200133 4500008004100000245012000041210007000161300001200231490000800243100002100251700001700272700001700289856013400306 2018 eng d00aπ-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods0 aπBEM A flexible parallel implementation for adaptive geometry aw a39–580 v1211 aGiuliani, Nicola1 aMola, Andrea1 aHeltai, Luca uhttps://www.math.sissa.it/publication/%CF%80-bem-flexible-parallel-implementation-adaptive-geometry-aware-and-high-order-boundary01821nas a2200181 4500008004100000024003700041245012000078210006900198520118600267653002301453653002601476100002201502700001901524700002101543700001701564700002101581856003701602 2017 eng d ahttps://arxiv.org/abs/1701.0342400aAdvances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method0 aAdvances in Reduced order modelling for CFD vortex shedding arou3 aVortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

10afinite volume, CFD10aReduced order methods1 aStabile, Giovanni1 aHijazi, Saddam1 aLorenzi, Stefano1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1701.0342400585nas a2200217 4500008004100000245003700041210003000078300001400108490000700122100001800129700001700147700001900164700001800183700001700201700002400218700002000242700002400262700001700286700001700303856004700320 2017 eng d00aThe deal.II Library, Version 8.50 adealII Library Version 85 a137–1450 v251 aArndt, Daniel1 aBangerth, W.1 aDavydov, Denis1 aHeister, Timo1 aHeltai, Luca1 aKronbichler, Martin1 aMaier, Matthias1 aPelteret, Jean-Paul1 aTurcksin, B.1 aWells, David uhttps://www.dealii.org/deal85-preprint.pdf01991nas a2200157 4500008004100000245002800041210002800069260002200097300000900119520158000128100002401708700002001732700002101752700001901773856004101792 2017 eng d00aModel Reduction Methods0 aModel Reduction Methods bJohn Wiley & Sons a1-363 aThis chapter presents an overview of model order reduction – a new paradigm in the field of simulation-based engineering sciences, and one that can tackle the challenges and leverage the opportunities of modern ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, a number of challenging problems remain intractable. These problems are of different nature, but are common to many branches of science and engineering. Among them are those related to high-dimensional problems, problems involving very different time scales, models defined in degenerate domains with at least one of the characteristic dimensions much smaller than the others, model requiring real-time simulation, and parametric models. All these problems represent a challenge for standard mesh-based discretization techniques; yet the ability to solve these problems efficiently would open unexplored routes for real-time simulation, inverse analysis, uncertainty quantification and propagation, real-time optimization, and simulation-based control – critical needs in many branches of science and engineering. Model order reduction offers new simulation alternatives by circumventing, or at least alleviating, otherwise intractable computational challenges. In the present chapter, we revisit three of these model reduction techniques: proper orthogonal decomposition, proper generalized decomposition, and reduced basis methodologies.} preprint = {http://preprints.sissa.it/xmlui/bitstream/handle/1963/35194/ECM_MOR.pdf?sequence=1&isAllowed=y

1 aChinesta, Francisco1 aHuerta, Antonio1 aRozza, Gianluigi1 aWillcox, Karen uhttps://www.math.sissa.it/node/1294900506nas a2200145 4500008004100000245009700041210006900138300001400207490000800221100001700229700001500246700002200261700002200283856005500305 2017 eng d00aA natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling0 anatural framework for isogeometric fluidstructure interaction ba a522–5460 v3161 aHeltai, Luca1 aKiendl, J.1 aDeSimone, Antonio1 aReali, Alessandro uhttp://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H00603nas a2200169 4500008004100000245012600041210006900167260003400236300001400270490000600284100002200290700001900312700001700331700002100348700002100369856004300390 2017 eng d00aPOD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder0 aPODGalerkin reduced order methods for CFD using Finite Volume Di bWalter de Gruyter {GmbH}cdec a210–2360 v81 aStabile, Giovanni1 aHijazi, Saddam1 aMola, Andrea1 aLorenzi, Stefano1 aRozza, Gianluigi uhttps://doi.org/10.1515/caim-2017-001101540nas a2200133 4500008004100000245006000041210005900101520111900160100001301279700002401292700001901316700002301335856004801358 2017 en d00aTime quasi-periodic gravity water waves in finite depth0 aTime quasiperiodic gravity water waves in finite depth3 aWe prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water wave solutions - namely periodic and even in the space variable x - of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a Borel set of asymptotically full measure. This is a small divisor problem. The main difficulties are the quasi-linear nature of the gravity water waves equations and the fact that the linear frequencies grow just in a sublinear way at infinity. We overcome these problems by first reducing the linearized operators obtained at each approximate quasi-periodic solution along the Nash-Moser iteration to constant coefficients up to smoothing operators, using pseudo-differential changes of variables that are quasi-periodic in time. Then we apply a KAM reducibility scheme which requires very weak Melnikov non-resonance conditions (losing derivatives both in time and space), which we are able to verify for most values of the depth parameter using degenerate KAM theory arguments.1 aBaldi, P1 aBerti, Massimiliano1 aHaus, Emanuele1 aMontalto, Riccardo uhttp://preprints.sissa.it/handle/1963/3529602562nas a2200145 4500008004100000245012400041210006900165300001100234490000700245520198000252100001702232700001702249700002202266856012802288 2017 eng d00aWet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations0 aWet and Dry Transom Stern Treatment for Unsteady and Nonlinear P a1–140 v613 aWe present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/wet-and-dry-transom-stern-treatment-unsteady-and-nonlinear-potential-flow-model-naval00494nas a2200181 4500008004100000245003700041210003000078300001100108490000600119100001700125700001800142700001700160700001700177700002400194700002000218700001700238856005700255 2016 eng d00aThe deal.II Library, Version 8.30 adealII Library Version 83 a1–110 v41 aBangerth, W.1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B. uhttp://nbn-resolving.de/urn:nbn:de:bsz:16-ans-23122600573nas a2200205 4500008004100000245003700041210003000078300001400108490000700122100001700129700001900146700001800165700001700183700001700200700002400217700002000241700001700261700001700278856007200295 2016 eng d00aThe deal.II library, Version 8.40 adealII library Version 84 a135–1410 v241 aBangerth, W.1 aDavydov, Denis1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B.1 aWells, David uhttps://www.math.clemson.edu/ heister/preprints/deal84-preprint.pdf00590nas a2200157 4500008004100000245009800041210006900139300001400208490000700222100001600229700001700245700001400262700001700276700001400293856012500307 2016 eng d00aError Estimates of B-spline based finite-element method for the wind-driven ocean circulation0 aError Estimates of Bspline based finiteelement method for the wi a430–4590 v691 aRotundo, N.1 aKim, T., -Y.1 aJiang, W.1 aHeltai, Luca1 aFried, E. uhttps://www.math.sissa.it/publication/error-estimates-b-spline-based-finite-element-method-wind-driven-ocean-circulation01409nas a2200145 4500008004100000245011900041210006900160260007700229520081900306100002501125700002401150700001701174700002101191856005101212 2016 en d00aIsogeometric analysis-based reduced order modelling for incompressible linear viscous flows in parametrized shapes0 aIsogeometric analysisbased reduced order modelling for incompres bSpringer, AMOS Advanced Modelling and Simulation in Engineering Sciences3 aIn this work we provide a combination of isogeometric analysis with reduced order modelling techniques, based on proper orthogonal decomposition, to guarantee computational reduction for the numerical model, and with free-form deformation, for versatile geometrical parametrization. We apply it to computational fluid dynamics problems considering a Stokes flow model. The proposed reduced order model combines efficient shape deformation and accurate and stable velocity and pressure approximation for incompressible viscous flows, computed with a reduced order method. Efficient offine-online computational decomposition is guaranteed in view of repetitive calculations for parametric design and optimization problems. Numerical test cases show the efficiency and accuracy of the proposed reduced order model.1 aSalmoiraghi, Filippo1 aBallarin, Francesco1 aHeltai, Luca1 aRozza, Gianluigi uhttp://urania.sissa.it/xmlui/handle/1963/3519900522nas a2200133 4500008004100000245008200041210006900123300001100192490000700203100002000210700002200230700001700252856011900269 2016 eng d00aLinearOperator – a generic, high-level expression syntax for linear algebra0 aLinearOperator a generic highlevel expression syntax for linear a1–240 v721 aMaier, Matthias1 aBardelloni, Mauro1 aHeltai, Luca uhttps://www.math.sissa.it/publication/linearoperator-%E2%80%93-generic-high-level-expression-syntax-linear-algebra00391nas a2200133 4500008004100000245003600041210003500077260001000112100002400122700002000146700002100166700001900187856005100206 2016 en d00aModel Order Reduction: a survey0 aModel Order Reduction a survey bWiley1 aChinesta, Francisco1 aHuerta, Antonio1 aRozza, Gianluigi1 aWillcox, Karen uhttp://urania.sissa.it/xmlui/handle/1963/3519400651nas a2200157 4500008004100000245009600041210006900137260005800206300001400264490000600278100001700284700001700301700002200318700002400340856012900364 2016 eng d00aShip Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model0 aShip Sinkage and Trim Predictions Based on a CAD Interfaced Full bInternational Society of Offshore and Polar Engineers a511–5180 v31 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/ship-sinkage-and-trim-predictions-based-cad-interfaced-fully-nonlinear-potential-model01454nas a2200157 4500008004100000245007300041210006900114260003500183300001100218490000700229520093500236100002201171700002501193700002201218856005601240 2016 eng d00aTowards a gauge theory interpretation of the real topological string0 aTowards a gauge theory interpretation of the real topological st bAmerican Physical SocietycMar a0660010 v933 aWe consider the real topological string on certain noncompact toric Calabi-Yau three-folds $\mathbb{X}$, in its physical realization describing an orientifold of type IIA on $\mathbb{X}$ with an O4-plane and a single D4-brane stuck on top. The orientifold can be regarded as a new kind of surface operator on the gauge theory with 8 supercharges arising from the singular geometry. We use the M-theory lift of this system to compute the real Gopakumar-Vafa invariants (describing wrapped M2-brane Bogomol’nyi-Prasad-Sommerfield (BPS) states) for diverse geometries. We show that the real topological string amplitudes pick up certain signs across flop transitions, in a well-defined pattern consistent with continuity of the real BPS invariants. We further give some preliminary proposals of an intrinsically gauge theoretical description of the effect of the surface operator in the gauge theory partition function.

1 aHayashi, Hirotaka1 aPiazzalunga, Nicolò1 aUranga, Angel, M. uhttps://link.aps.org/doi/10.1103/PhysRevD.93.06600101510nas a2200121 4500008004100000245009300041210006900134520100200203100001701205700001701222700002401239856012501263 2015 en d00aBenchmarking the Immersed Finite Element Method for Fluid-Structure Interaction Problems0 aBenchmarking the Immersed Finite Element Method for FluidStructu3 aWe present an implementation of a fully variational formulation of an immersed methods for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use of approximate Dirac delta distributions, fully variational formulations of the method do not require the use of said distributions. In our implementation the immersed solid is general in the sense that it is not required to have the same mass density and the same viscous response as the surrounding fluid. We assume that the immersed solid can be either viscoelastic of differential type or hyperelastic. Here we focus on the validation of the method via various benchmarks for fluid-structure interaction numerical schemes. This is the first time that the interaction of purely elastic compressible solids and an incompressible fluid is approached via an immersed method allowing a direct comparison with established benchmarks.1 aSaswati, Roy1 aHeltai, Luca1 aCostanzo, Francesco uhttps://www.math.sissa.it/publication/benchmarking-immersed-finite-element-method-fluid-structure-interaction-problems-001368nam a2200229 4500008004100000020002200041022001400063245008400077210006900161250000600230260002600236300000800262520053600270653003000806653002800836653004800864653004500912100002200957700002100979700002001000856011801020 2015 eng d a978-3-319-22469-5 a2191-820100aCertified Reduced Basis Methods for Parametrized Partial Differential Equations0 aCertified Reduced Basis Methods for Parametrized Partial Differe a1 aSwitzerlandbSpringer a1353 aThis book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

10aa posteriori error bounds10aempirical interpolation10aparametrized partial differential equations10areduced basis methods, greedy algorithms1 aHesthaven, Jan, S1 aRozza, Gianluigi1 aStamm, Benjamin uhttps://www.math.sissa.it/publication/certified-reduced-basis-methods-parametrized-partial-differential-equations01640nas a2200145 4500008004100000245007700041210006900118260001000187520116500197100002101362700002101383700002201404700001701426856005101443 2015 en d00aDeal2lkit: a Toolkit Library for High Performance Programming in deal.II0 aDeal2lkit a Toolkit Library for High Performance Programming in bSISSA3 aWe present version 1.0.0 of the deal2lkit (deal.II ToolKit) library. deal2lkit is a collection of modules and classes for the general purpose finite element library deal.II. Its principal aim is to provide a high level interface, controlled via parameter files, for those steps that are common in all finite element programs: mesh generation, selection of the finite element type, application of boundary conditions and many others. Each module can be used as a building block independently on the others, and can be integrated in existing finite element codes based on deal.II, drastically reducing the size of programs, rendering their use automatically parametrised, and reducing the overall time-to-market of finite element programming. Moreover, deal2lkit features interfaces with the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) and ASSIMP (Open Asset Import Library) libraries. Some examples are provided which show the aim and scopes of deal2lkit. The deal2lkit library is released under the GNU Lesser General Public License (LGPL) and can be retrieved from the deal2lkit repository https://github.com/mathLab/deal2lkit.1 aSartori, Alberto1 aGiuliani, Nicola1 aBardelloni, Mauro1 aHeltai, Luca uhttp://urania.sissa.it/xmlui/handle/1963/3500600596nas a2200181 4500008004100000245003700041210003000078520010700108100001700215700001800232700001700250700001700267700002400284700002000308700001700328700001800345856005100363 2015 en d00aThe deal.II Library, Version 8.20 adealII Library Version 823 aThis paper provides an overview of the new features of the finite element library deal.II version 8.21 aBangerth, W.1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B.1 aYoung, T., D. uhttp://urania.sissa.it/xmlui/handle/1963/3446401899nas a2200133 4500008004300000245010100043210006900144520142800213100002101641700001701662700001701679700001801696856005101714 2015 en_Ud 00aFEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows0 aFEM SUPG stabilisation of mixed isoparametric BEMs application t3 aIn finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally more tractable. In this framework, the Galerkin method and the stabilisation may still be used to successfully apply boundary conditions and resolve instabilities that are frequently observed in transport dominated problems. We apply this technique to an adaptive collocation boundary element method for the solution of stationary potential flows, where we solve a mixed Poisson problem in boundary integral form, with the addition of linearised free surface boundary conditions. We use a mixed boundary element formulation to allow for different finite dimensional spaces describing the flow potential and its normal derivative, and we validate our method simulating the flow around both a submerged body and a surface piercing body. The coupling of mixed surface finite elements and strongly consistent stabilisation techniques with boundary elements opens up the possibility to use non conformal unstructured grids with local refinement, without introducing the inconsistencies of other stabilisation techniques based on up-winding and finite difference schemes.

1 aGiuliani, Nicola1 aMola, Andrea1 aHeltai, Luca1 aFormaggia, L. uhttp://urania.sissa.it/xmlui/handle/1963/3446602042nas a2200217 4500008004100000022001400041245010200055210006900157490003500226520122900261653002501490653002101515653002501536653002701561653002501588653001601613100002201629700002101651700002201672856013001694 2015 eng d a1019-716800aReduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system0 aReduced basis approximation and aposteriori error estimation for0 vspecial issue for MoRePaS 20123 aThe coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

10aDomain decomposition10aError estimation10aNon-coercive problem10aPorous medium equation10aReduced basis method10aStokes flow1 aMartini, Immanuel1 aRozza, Gianluigi1 aHaasdonk, Bernard uhttps://www.math.sissa.it/publication/reduced-basis-approximation-and-posteriori-error-estimation-coupled-stokes-darcy-system02449nas a2200121 4500008004100000245012900041210006900170520189900239100002002138700002502158700001702183856012702200 2015 en d00aReduced Basis Isogeometric Methods (RB-IGA) for the real-time simulation of potential flows about parametrized NACA airfoils0 aReduced Basis Isogeometric Methods RBIGA for the realtime simula3 aWe present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.We present a Reduced Basis (RB) method based on Isogeometric Analysis (IGA) for the rapid and reliable evaluation of PDE systems characterized by complex geometrical features. At the current state of the art, this is the first case of coupling between RB and IGA methods. The construction of the RB method relies on an Isogeometric Boundary Element Method (IGA-BEM) as the high-fidelity technique, allowing a direct interface with Computer Aided Design (CAD) tools. A suitable Empirical Interpolation Method (EIM) ensures an efficient offline/online decomposition between the construction and the evaluation of the RB method. We consider the real-time simulation of potential flows past airfoils, parametrized with respect to the angle of attack and the NACA number identifying their shape, and we provide a validation of our methodology with respect to experimental data and reference numerical codes, showing in both cases a very good agreement.1 aManzoni, Andrea1 aSalmoiraghi, Filippo1 aHeltai, Luca uhttps://www.math.sissa.it/publication/reduced-basis-isogeometric-methods-rb-iga-real-time-simulation-potential-flows-about01351nas a2200133 4500008004100000245008400041210007000125260003900195520087300234100001901107700001901126700002101145856005101166 2014 en d00aFinite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians0 aFinite dimensional KadomtsevPetviashvili τfunctions I Finite Gra bAmerican Institute of Physics Inc.3 aWe study τ-functions of the Kadomtsev-Petviashvili hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal, and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Plücker coordinates appearing as coefficients in the Schur function expansion of the τ-function.1 aBalogh, Ferenc1 aFonseca, Tiago1 aHarnad, John, P. uhttp://urania.sissa.it/xmlui/handle/1963/3495201202nas a2200145 4500008004100000245010600041210006900147260001000216520062900226653002300855100001700878700001700895700002200912856012200934 2014 en d00aA fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures0 afully nonlinear potential model for ship hydrodynamics directly bSISSA3 aWe present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed.10aship hydrodynamics1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/fully-nonlinear-potential-model-ship-hydrodynamics-directly-interfaced-cad-data02051nas a2200145 4500008004100000245007600041210006900117260001300186520158600199653002601785100001701811700001901828700002201847856003601869 2014 en d00aNonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D0 aNonsingular Isogeometric Boundary Element Method for Stokes Flow bElsevier3 aIsogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM.10aIsogeometric Analysis1 aHeltai, Luca1 aArroyo, Marino1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/632600655nas a2200157 4500008004100000245010000041210006900141260005800210300001400268490000600282100001700288700001700305700002200322700002400344856012900368 2014 eng d00aPotential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures0 aPotential Model for Ship Hydrodynamics Simulations Directly Inte bInternational Society of Offshore and Polar Engineers a815–8220 v41 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/potential-model-ship-hydrodynamics-simulations-directly-interfaced-cad-data-structures00604nas a2200193 4500008004100000245003700041210003000078260001000108520010800118100001700226700001800243700001700261700001700278700002400295700002000319700001700339700001800356856003600374 2013 en d00aThe deal.II Library, Version 8.10 adealII Library Version 81 bSISSA3 aThis paper provides an overview of the new features of the finite element library deal.II version 8.0.1 aBangerth, W.1 aHeister, Timo1 aHeltai, Luca1 aKanschat, G.1 aKronbichler, Martin1 aMaier, Matthias1 aTurcksin, B.1 aYoung, T., D. uhttp://hdl.handle.net/1963/723602183nas a2200145 4500008004100000245015300041210006900194260001300263520163200276653003401908100002101942700001801963700002001981856003602001 2013 en d00aReduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants0 aReduced basis approximation and a posteriori error estimation fo bSpringer3 aIn this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in a ffinely parametrized geometries, focusing on the role played by the Brezzi\\\'s and Babu ska\\\'s stability constants. The crucial ingredients of the methodology are a Galerkin projection onto a low-dimensional space of basis functions properly selected, an a ne parametric dependence enabling to perform competitive Off ine-Online splitting in the computational\\r\\nprocedure and a rigorous a posteriori error estimation on eld variables.\\r\\nThe combination of these three factors yields substantial computational savings which are at the basis of an e fficient model order reduction, ideally suited for real-time simulation and many-query contexts (e.g. optimization, control or parameter identi cation). In particular, in this work we focus on i) the stability of the reduced basis approximation based on the Brezzi\\\'s saddle point theory and the introduction of a supremizer operator on the pressure terms, ii) a rigorous a posteriori error estimation procedure for velocity and pressure elds based on the Babu ska\\\'s inf-sup constant (including residuals calculations), iii) the computation of a lower bound of the stability constant, and iv) di erent options for the reduced basis spaces construction. We present some illustrative results for both\\r\\ninterior and external steady Stokes flows in parametrized geometries representing two parametrized classical Poiseuille and Couette \\r\\nflows, a channel contraction and a simple flow control problem around a curved obstacle.10aparametrized Stokes equations1 aRozza, Gianluigi1 aHuynh, Phuong1 aManzoni, Andrea uhttp://hdl.handle.net/1963/633901660nas a2200145 4500008004100000245010800041210006900149260001000218520115900228653003501387100001701422700001701439700002201456856003601478 2013 en d00aA stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions0 astable and adaptive semiLagrangian potential model for unsteady bSISSA3 aWe present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

10aUnsteady ship-wave interaction1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/566901152nas a2200145 4500008004100000245009700041210006900138260001000207520067600217100002200893700001500915700002000930700002000950856003600970 2012 en d00aA Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group.0 aCodazzilike equation and the singular set for C1 smooth surfaces bSISSA3 aIn this paper, we study the structure of the singular set for a C 1 smooth surface in the 3-dimensional Heisenberg group ℍ 1. We discover a Codazzi-like equation for the p-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify the Codazzi-like equation by proving a fundamental theorem for local surfaces in ℍ 11 aMalchiodi, Andrea1 aYang, Paul1 aCheng, Jih-Hsin1 aHwang, JennFang uhttp://hdl.handle.net/1963/655600824nas a2200169 4500008004100000020001800041245006300059210006300122260001300185520030800198653002400506100002200530700001700552700002300569700002600592856003600618 2012 en d a978146143996700aComputing optimal strokes for low reynolds number swimmers0 aComputing optimal strokes for low reynolds number swimmers bSpringer3 aWe discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

10aNumerical analysis.1 aDeSimone, Antonio1 aHeltai, Luca1 aAlouges, François1 aAline, Lefebvre-Lepot uhttp://hdl.handle.net/1963/644501763nas a2200169 4500008004100000245010700041210006900148260001000217520118200227653002601409653002901435653003501464100001701499700001701516700002401533856003601557 2012 en d00aA Fully Coupled Immersed Finite Element Method for Fluid Structure Interaction via the Deal.II Library0 aFully Coupled Immersed Finite Element Method for Fluid Structure bSISSA3 aWe present the implementation of a solution scheme for fluid-structure\\r\\ninteraction problems via the finite element software library deal.II. The\\r\\nsolution scheme is an immersed finite element method in which two independent discretizations are used for the fluid and immersed deformable body. In this type of formulation the support of the equations of motion of the fluid is extended to cover the union of the solid and fluid domains. The equations of motion over the extended solution domain govern the flow of a fluid under the action of a body force field. This body force field informs the fluid of the presence of the immersed solid. The velocity field of the immersed solid is the restriction over the immersed domain of the velocity field in the extended equations of motion. The focus of this paper is to show how the determination of the motion of the immersed domain is carried out in practice. We show that our implementation is general, that is, it is not dependent on a specific choice of the finite element spaces over the immersed solid and the extended fluid domains. We present some preliminary results concerning the accuracy of the proposed method.10aFinite Element Method10aImmersed Boundary Method10aImmersed Finite Element Method1 aHeltai, Luca1 aRoy, Saswati1 aCostanzo, Francesco uhttp://hdl.handle.net/1963/625502076nas a2200145 4500008004100000245004700041210004700088520166300135653001801798100001901816700001701835700002001852700002201872856003601894 2012 en d00aReverse engineering the euglenoid movement0 aReverse engineering the euglenoid movement3 aEuglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.10amicroswimmers1 aArroyo, Marino1 aHeltai, Luca1 aMillán, Daniel1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/644400518nas a2200109 4500008004100000245011900041210006900160100001700229700001700246700002200263856012300285 2012 eng d00aA stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves0 astable semilagrangian potential method for the simulation of shi1 aMola, Andrea1 aHeltai, Luca1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/stable-semi-lagrangian-potential-method-simulation-ship-interaction-unsteady-and02171nas a2200133 4500008004100000245006600041210006600107260001300173520175500186653001901941100001701960700002401977856003602001 2012 en d00aVariational implementation of immersed finite element methods0 aVariational implementation of immersed finite element methods bElsevier3 aDirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

10aTurbulent flow1 aHeltai, Luca1 aCostanzo, Francesco uhttp://hdl.handle.net/1963/646200490nas a2200145 4500008004100000245008500041210006900126260002500195300001200220490000700232100001700239700001900256700002300275856004600298 2011 eng d00aMulti-physics modelling and sensitivity analysis of olympic rowing boat dynamics0 aMultiphysics modelling and sensitivity analysis of olympic rowin bSpringer Naturecnov a85–940 v141 aMola, Andrea1 aGhommem, Mehdi1 aHajj, Muhammad, R. uhttps://doi.org/10.1007/s12283-011-0075-200977nas a2200145 4500008004300000245007900043210006900122260002100191520050000212653002100712100002300733700002200756700001700778856003600795 2011 en_Ud 00aNumerical Strategies for Stroke Optimization of Axisymmetric Microswimmers0 aNumerical Strategies for Stroke Optimization of Axisymmetric Mic bWorld Scientific3 aWe propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms.10aOptimal swimming1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca uhttp://hdl.handle.net/1963/365701187nas a2200145 4500008004300000245004000043210004000083520078100123100002300904700002200927700001700949700002000966700001900986856003601005 2010 en_Ud 00aOptimally swimming Stokesian Robots0 aOptimally swimming Stokesian Robots3 aWe study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca1 aLefebvre, Aline1 aMerlet, Benoit uhttp://hdl.handle.net/1963/392900902nas a2200169 4500008004100000020002200041245007700063210006900140260003600209300001200245520028600257100002200543700001800565700002200583700001700605856011000622 2010 eng d a978-90-481-9195-600aA Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena0 aPhase Field Approach to Wetting and Contact Angle Hysteresis Phe aDordrechtbSpringer Netherlands a51–633 aWe discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

1 aDeSimone, Antonio1 aFedeli, Livio1 aTurco, Alessandro1 aHackl, Klaus uhttps://www.math.sissa.it/publication/phase-field-approach-wetting-and-contact-angle-hysteresis-phenomena01810nas a2200121 4500008004300000245007000043210006600113520141500179100001901594700002201613700001701635856003601652 2010 en_Ud 00aThe role of membrane viscosity in the dynamics of fluid membranes0 arole of membrane viscosity in the dynamics of fluid membranes3 aFluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.1 aArroyo, Marino1 aDeSimone, Antonio1 aHeltai, Luca uhttp://hdl.handle.net/1963/393000554nas a2200145 4500008004100000245010200041210006900143260005400212300001400266490000800280100001700288700002500305700002300330856005500353 2009 eng d00aLow-Frequency Variations of Force Coefficients on Square Cylinders with Sharp and Rounded Corners0 aLowFrequency Variations of Force Coefficients on Square Cylinder bAmerican Society of Civil Engineers ({ASCE})cjul a828–8350 v1351 aMola, Andrea1 aBordonaro, Giancarlo1 aHajj, Muhammad, R. uhttps://doi.org/10.1061/(asce)st.1943-541x.000003400754nas a2200121 4500008004300000245007200043210006900115520035700184100002200541700001600563700001700579856003600596 2009 en_Ud 00aStratos: a code for 3D free surface flows with floating constraints0 aStratos a code for 3D free surface flows with floating constrain3 aThis report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers......1 aDeSimone, Antonio1 aBianchi, B.1 aHeltai, Luca uhttp://hdl.handle.net/1963/370100841nas a2200121 4500008004300000245007600043210006900119520043200188100002200620700001700642700002400659856003600683 2009 en_Ud 00aTools for the Solution of PDEs Defined on Curved Manifolds with deal.II0 aTools for the Solution of PDEs Defined on Curved Manifolds with 3 aThe deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.1 aDeSimone, Antonio1 aHeltai, Luca1 aManigrasso, Cataldo uhttp://hdl.handle.net/1963/370000645nas a2200121 4500008004300000245011200043210006900155520019600224100002300420700002200443700002200465856003600487 2007 en_Ud 00aAsymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy0 aAsymptotic behaviour of smooth solutions for partially dissipati3 aWe study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition.1 aBianchini, Stefano1 aHanouzet, Bernard1 aNatalini, Roberto uhttp://hdl.handle.net/1963/178001165nas a2200109 4500008004300000245005900043210005900102520081400161100002200975700002200997856003601019 2006 en_Ud 00aReflection symmetries for multiqubit density operators0 aReflection symmetries for multiqubit density operators3 aFor multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing rotations. While one-qubit reflections correspond to antiunitary symmetries, as is known for example from the partial transposition criterion, reflections on the joint density of two or more qubits are not accounted for by the Wigner Theorem and are well-posed only for sufficiently mixed states. One example of such nonlocal reflections is the unconditional NOT operation on a multiparty density, i.e., an operation yelding another density and such that the sum of the two is the identity operator. This nonphysical operation is admissible only for sufficiently mixed states.1 aAltafini, Claudio1 aHavel, Timothy F. uhttp://hdl.handle.net/1963/212100554nas a2200145 4500008004100000022001400041245008800055210006900143300001400212490000800226100001900234700001500253700001500268856012500283 2006 eng d a0010-361600aSemiclassical orthogonal polynomials, matrix models and isomonodromic tau functions0 aSemiclassical orthogonal polynomials matrix models and isomonodr a401–4370 v2631 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://www.math.sissa.it/publication/semiclassical-orthogonal-polynomials-matrix-models-and-isomonodromic-tau-functions01043nas a2200109 4500008004300000245005700043210005400100520069600154100001600850700003100866856003600897 2006 en_Ud 00aSemistability vs. nefness for (Higgs) vector bundles0 aSemistability vs nefness for Higgs vector bundles3 aAccording to Miyaoka, a vector bundle E on a smooth projective curve is semistable if and only if a certain numerical class in the projectivized bundle PE is nef. We establish a similar criterion for the semistability of Higgs bundles: namely, such a bundle is semistable if and only if for every integer s between 0 and the rank of E, a suitable numerical class in the scheme parametrizing the rank s locally-free Higgs quotients of E is nef. We also extend this result to higher-dimensional complex projective varieties by showing that the nefness of the above mentioned classes is equivalent to the semistability of the Higgs bundle E together with the vanishing of the discriminant of E.1 aBruzzo, Ugo1 aHernandez Ruiperez, Daniel uhttp://hdl.handle.net/1963/223701933nas a2200145 4500008004100000245004900041210004900090260002900139520150600168100002001674700002001694700002201714700001501736856003601751 2005 en d00aMinimal surfaces in pseudohermitian geometry0 aMinimal surfaces in pseudohermitian geometry bScuola Normale Superiore3 aWe consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. We interpret the p-mean curvature not only as the tangential sublaplacian of a defining function, but also as the curvature of a characteristic curve, and as a quantity in terms of calibration geometry. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set, we formulate some {\em extension} theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the $xy$-plane) in the Heisenberg group $H_1$. In $H_{1}$, identified with the Euclidean space $R^{3}$, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also prove a uniqueness theorem for the Dirichlet problem under a condition on the size of the singular set in two dimensions, and generalize to higher dimensions without any size control condition. We also show that there are no closed, connected, $C^{2}$ smoothly immersed constant p-mean curvature or p-minimal surfaces of genus greater than one in the standard $S^{3}.$ This fact continues to hold when $S^{3}$ is replaced by a general spherical pseudohermitian 3-manifold.1 aCheng, Jih-Hsin1 aHwang, JennFang1 aMalchiodi, Andrea1 aYang, Paul uhttp://hdl.handle.net/1963/457901445nas a2200121 4500008004300000245006200043210006200105260001300167520106100180100002801241700001801269856003601287 2005 en_Ud 00aStability of solutions of quasilinear parabolic equations0 aStability of solutions of quasilinear parabolic equations bElsevier3 aWe bound the difference between solutions $u$ and $v$ of $u_t = a\\\\Delta u+\\\\Div_x f+h$ and $v_t = b\\\\Delta v+\\\\Div_x g+k$ with initial data $\\\\phi$ and $ \\\\psi$, respectively, by $\\\\Vert u(t,\\\\cdot)-v(t,\\\\cdot)\\\\Vert_{L^p(E)}\\\\le A_E(t)\\\\Vert \\\\phi-\\\\psi\\\\Vert_{L^\\\\infty(\\\\R^n)}^{2\\\\rho_p}+ B(t)(\\\\Vert a-b\\\\Vert_{\\\\infty}+ \\\\Vert \\\\nabla_x\\\\cdot f-\\\\nabla_x\\\\cdot g\\\\Vert_{\\\\infty}+ \\\\Vert f_u-g_u\\\\Vert_{\\\\infty} + \\\\Vert h-k\\\\Vert_{\\\\infty})^{\\\\rho_p} \\\\abs{E}^{\\\\eta_p}$. Here all functions $a$, $f$, and $h$ are smooth and bounded, and may depend on $u$, $x\\\\in\\\\R^n$, and $t$. The functions $a$ and $h$ may in addition depend on $\\\\nabla u$. Identical assumptions hold for the functions that determine the solutions $v$. Furthermore, $E\\\\subset\\\\R^n$ is assumed to be a bounded set, and $\\\\rho_p$ and $\\\\eta_p$ are fractions that depend on $n$ and $p$. The diffusion coefficients $a$ and $b$ are assumed to be strictly positive and the initial data are smooth.1 aCoclite, Giuseppe Maria1 aHolden, Helge uhttp://hdl.handle.net/1963/289201246nas a2200121 4500008004100000245005100041210005100092260001800143520089000161100001701051700002001068856003601088 2004 en d00aFredholm modules for quantum euclidean spheres0 aFredholm modules for quantum euclidean spheres bSISSA Library3 aThe quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\\\\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres $S_q^{N-1}$. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i. e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra $A(S^{N-1}_q)$.1 aHawkins, Eli1 aLandi, Giovanni uhttp://hdl.handle.net/1963/163600596nas a2200145 4500008004100000022001400041245012600055210006900181300001400250490000800264100001900272700001500291700001500306856012900321 2003 eng d a0010-361600aDifferential systems for biorthogonal polynomials appearing in 2-matrix models and the associated Riemann-Hilbert problem0 aDifferential systems for biorthogonal polynomials appearing in 2 a193–2400 v2431 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://www.math.sissa.it/publication/differential-systems-biorthogonal-polynomials-appearing-2-matrix-models-and-associated00524nas a2200145 4500008004100000022001400041245007400055210006900129300001600198490000700214100001900221700001500240700001500255856010800270 2003 eng d a0305-447000aPartition functions for matrix models and isomonodromic tau functions0 aPartition functions for matrix models and isomonodromic tau func a3067–30830 v361 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://www.math.sissa.it/publication/partition-functions-matrix-models-and-isomonodromic-tau-functions00492nas a2200145 4500008004100000022001400041245006200055210006000117300001300177490000800190100001900198700001500217700001500232856009900247 2002 eng d a0010-361600aDuality, biorthogonal polynomials and multi-matrix models0 aDuality biorthogonal polynomials and multimatrix models a73–1200 v2291 aBertola, Marco1 aEynard, B.1 aHarnad, J. uhttps://www.math.sissa.it/publication/duality-biorthogonal-polynomials-and-multi-matrix-models00851nas a2200145 4500008004300000245005500043210005500098260001000153520041100163100002200574700001600596700003100612700002600643856003600669 2002 en_Ud 00aRelatively stable bundles over elliptic fibrations0 aRelatively stable bundles over elliptic fibrations bWiley3 aWe consider a relative Fourier-Mukai transform defined on elliptic fibrations over an arbitrary normal base scheme. This is used to construct relative Atiyah sheaves and generalize Atiyah\\\'s and Tu\\\'s results about semistable sheaves over elliptic curves to the case of elliptic fibrations. Moreover we show that this transform preserves relative (semi)stability of sheaves of positive relative degree.1 aBartocci, Claudio1 aBruzzo, Ugo1 aHernandez Ruiperez, Daniel1 aMunoz Porras, Jose M. uhttp://hdl.handle.net/1963/3132