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IGA-Energetic BEM for the numerical solution of 2D wave scattering problems in the space-time domain

Ariel S. Boiardi
Monday, November 14, 2022 - 18:45
Hybrid: in presence and online

The Energetic Boundary Element Method (BEM) was proposed in 2009 for the numerical solution of 2D exterior wave propagation problems. Compared to other space-time discretizations of the wave equation, the energetic weak form offers desirable accuracy and stability properties.

Isogeometric Analysis (IGA), proposed by T. J. R. Hughes and collaborators in the context of the FEM to bridge the gap between design and analysis using B-splines and NURBS as shape functions, naturally fits into BEMs, allowing an exact representation of curvilinear boundaries.

In this talk I will discuss some recent advances in the use of an isogeometric approach in Energetic BEM for what concerns discretization in space variables. Numerical issues for an efficient integration of the singular kernel related to the fundamental solution of the wave operator, will be described, highlighting the new challenges posed by the presence of curvilinear boundaries.

Extensive numerical experiments will show, 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, based on lagrangian shape functions. Simulations on long time intervals allow to observe the consistency of the proposed method with the stationary IGA-BEM.

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