CVEM-BEM Coupling for the Simulation of Time-Domain Wave Fields Scattered by Obstacles with Complex Geometries

Luca Desiderio, Silvia Falletta, Matteo Ferrari, L. Scuderi

2023Computational Methods in Applied Mathematics14 citationsDOI

Abstract

Abstract In this paper, we present a numerical method based on the coupling between a Curved Virtual Element Method (CVEM) and a Boundary Element Method (BEM) for the simulation of wave fields scattered by obstacles immersed in homogeneous infinite media. In particular, we consider the 2D time-domain damped wave equation, endowed with a Dirichlet condition on the boundary (sound-soft scattering). To reduce the infinite domain to a finite computational one, we introduce an artificial boundary on which we impose a Boundary Integral Non-Reflecting Boundary Condition (BI-NRBC). We apply a CVEM combined with the Crank–Nicolson time integrator in the interior domain, and we discretize the BI-NRBC by a convolution quadrature formula in time and a collocation method in space. We present some numerical results to test the performance of the proposed approach and to highlight its effectiveness, especially when obstacles with complex geometries are considered.

Topics & Concepts

Boundary element methodMathematical analysisDiscretizationSingular boundary methodMathematicsDirichlet boundary conditionMethod of fundamental solutionsBoundary knot methodCollocation (remote sensing)Boundary (topology)Quadrature (astronomy)Gaussian quadratureConvolution (computer science)Boundary value problemNyström methodFinite element methodPhysicsComputer scienceOpticsMachine learningThermodynamicsArtificial neural networkElectromagnetic Simulation and Numerical MethodsAdvanced Numerical Methods in Computational MathematicsNumerical methods for differential equations