Many applications benefit from an efficient Discrete Fourier Transform (DFT) between arbitrarily spaced points. The Non Uniform Fast Fourier Transform reduces the computational cost of such operation from O(N2) to O(NlogN) exploiting gridding algorithms and a standard Fast Fourier Transform on an equi-spaced grid. The parallelization of the NUFFT of type 3 (between arbitrary points in space and frequency) still poses some challenges: we present a novel and flexible hybrid parallelization in a MPI-multithreaded environment exploiting existing HPC libraries on modern architectures. To ensure the reliability of the developed library, we exploit continuous integration strategies using Travis CI. We present performance analyses to prove the effectiveness of our implementation, possible extensions to the existing library, and an application of NUFFT type 3 to MRI image processing. Program summary Program Title: BlackNUFFT Program Files doi: http://dx.doi.org/10.17632/vxfj6x2p8x.1 Licensing provisions: LGPL Programming language: C++ External routines/libraries: deal.II , FFTW, PFFT Nature of problem: Provide a modular and extensible implementation of a parallel Non Uniform Fast Fourier Transform of type 3. Solution method: Use of hybrid shared distributed memory paradigm to achieve high level of efficiency. We exploit existing HPC library following best practices in scientific computing (as continuous integration via TravisCI) to reach higher complexities and guarantee the accuracy of the solution proposed.

%B Computer Physics Communications %V 235 %P 324 - 335 %G eng %U http://www.sciencedirect.com/science/article/pii/S0010465518303539 %R https://doi.org/10.1016/j.cpc.2018.10.005 %0 Journal Article %J SOFTWAREX %D 2018 %T deal2lkit: A toolkit library for high performance programming in deal.II %A Alberto Sartori %A Nicola Giuliani %A Mauro Bardelloni %A Luca Heltai %B SOFTWAREX %V 7 %P 318–327 %G eng %R 10.1016/j.softx.2018.09.004 %0 Journal Article %J SOFT ROBOTICS %D 2018 %T Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions %A Nicola Giuliani %A Luca Heltai %A Antonio DeSimone %B SOFT ROBOTICS %V 5 %P 410–424 %G eng %U https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6094362/ %R 10.1089/soro.2017.0099 %0 Journal Article %J Advances in Engineering Software %D 2018 %T π-BEM : A flexible parallel implementation for adaptive , geometry aware , and high order boundary element methods %A Nicola Giuliani %A Andrea Mola %A Luca Heltai %B Advances in Engineering Software %V 121 %P 39–58 %G eng %0 Journal Article %D 2015 %T Deal2lkit: a Toolkit Library for High Performance Programming in deal.II %A Alberto Sartori %A Nicola Giuliani %A Mauro Bardelloni %A Luca Heltai %X We 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. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35006 %1 35235 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by asartori@sissa.it (asartori@sissa.it) on 2015-11-13T13:12:29Z No. of bitstreams: 1 paper_deal2lkit.pdf: 1085486 bytes, checksum: 1dc7e9b9790fe38d2ced7b5328633cd8 (MD5) %0 Journal Article %J Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22 %D 2015 %T FEM SUPG stabilisation of mixed isoparametric BEMs: application to linearised free surface flows %A Nicola Giuliani %A Andrea Mola %A Luca Heltai %A L. Formaggia %XIn 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.

%B Engineering Analysis with Boundary Elements 59 (2015), pp. 8-22 %G en_US %U http://urania.sissa.it/xmlui/handle/1963/34466 %1 34640 %2 Mathematics %4 1 %# MAT/08 %$ Submitted by ngiuliani@sissa.it (ngiuliani@sissa.it) on 2015-05-04T12:32:04Z No. of bitstreams: 1 paper-free-surface.pdf: 888763 bytes, checksum: 68366266786e84b78a356acd6de50840 (MD5) %R 10.1016/j.enganabound.2015.04.006