%0 Journal Article
%J COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
%D 2018
%T NURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces
%A Giuseppe Pitton
%A Luca Heltai
%B COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
%V 338
%P 440–462
%G eng
%U https://arxiv.org/abs/1804.08271
%R 10.1016/j.cma.2018.04.039
%0 Journal Article
%J COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
%D 2017
%T A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling
%A Luca Heltai
%A Kiendl, J.
%A Antonio DeSimone
%A Alessandro Reali
%B COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
%V 316
%P 522–546
%G eng
%U http://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H
%R 10.1016/j.cma.2016.08.008
%0 Journal Article
%D 2014
%T Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D
%A Luca Heltai
%A Marino Arroyo
%A Antonio DeSimone
%K Isogeometric Analysis
%X Isogeometric 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.
%I Elsevier
%G en
%U http://hdl.handle.net/1963/6326
%1 6250
%2 Mathematics
%4 1
%# MAT/08 ANALISI NUMERICA
%$ Submitted by Luca Heltai (heltai@sissa.it) on 2012-12-03T08:19:28Z
No. of bitstreams: 1
isogeo_stokes.pdf: 732320 bytes, checksum: 224ef57de6c49f03db0afaccdcb234f9 (MD5)
%R 10.1016/j.cma.2013.09.017
%0 Journal Article
%J Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387
%D 2011
%T Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers
%A François Alouges
%A Antonio DeSimone
%A Luca Heltai
%K Optimal swimming
%X We 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.
%B Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387
%I World Scientific
%G en_US
%U http://hdl.handle.net/1963/3657
%1 648
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-06-23T17:30:51Z\\r\\nNo. of bitstreams: 1\\r\\nSissa33_2009M.pdf: 708341 bytes, checksum: 6134bd52f083488620fb5bb24bcf9b93 (MD5)
%R 10.1142/S0218202511005088