An Isogeometric approach to the Energetic Boundary Element Method.
The project for my M.Sc. Thesis in Mathematics at University of Parma was to adapt the energetic boundary element method, developed by the Numerical Analysis group, to the IGA framework. After I graduated, I had the opportunity to publish these findings in a research paper (Aimi & Boiardi, 2022).
References
2022
M.Sc. Thesis
IGA-Energetic BEM: An Effective Tool for the Numerical Solution of Wave Propagation Problems in Space-Time Domain
The Energetic Boundary Element Method (BEM) is a recent discretization technique for the numerical solution of wave propagation problems, inside bounded domains or outside bounded obstacles. The differential model problem is converted into a Boundary Integral Equation (BIE) in the time domain, which is then written into an energy-dependent weak form successively discretized by a Galerkin-type approach. Taking into account the space-time model problem of 2D soft-scattering of acoustic waves by obstacles described by open arcs by B-spline (or NURBS) parametrizations, the aim of this paper is to introduce the powerful Isogeometric Analysis (IGA) approach into Energetic BEM for what concerns discretization in space variables. The same computational benefits already observed for IGA-BEM in the case of elliptic (i.e., static) problems, is emphasized here because it is gained at every step of the time-marching procedure. Numerical issues for an efficient integration of weakly singular kernels, related to the fundamental solution of the wave operator and dependent on the propagation wavefront, will be described. Effective numerical results will be given and discussed, showing, from a numerical point of view, convergence and accuracy of the proposed method, as well as the superiority of IGA-Energetic BEM compared to the standard version of the method, which employs classical Lagrangian basis functions.
@article{aimi_iga-energetic_2022,title={{IGA}-Energetic {BEM}: An Effective Tool for the Numerical Solution of Wave Propagation Problems in Space-Time Domain},volume={10},rights={http://creativecommons.org/licenses/by/3.0/},issn={2227-7390},url={https://www.mdpi.com/2227-7390/10/3/334},doi={10.3390/math10030334},shorttitle={{IGA}-Energetic {BEM}},pages={334},number={3},journal={Mathematics},author={Aimi, Alessandra and Boiardi, Ariel Surya},year={2022},langid={english},keywords={energetic {BEM}, Isogeometric Analysis, soft-scattering, wave propagation},}
