We 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-algebra00651nas 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-model01510nas 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-001640nas 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/1963/3446602449nas 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-about01202nas 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/1963/723601660nas 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/1963/566900824nas 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/1963/646200977nas 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/1963/392901810nas 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/1963/393000754nas 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/1963/3700