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

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.

Automated summary

In this paper, a numerical method combining Curved Virtual Element Method (CVEM) and Boundary Element Method (BEM) is proposed for simulating wave field scattering by obstacles in homogeneous infinite media. The method considers the 2D time-domain damped wave equation with a Dirichlet condition on the boundary (sound-soft scattering). To handle the infinite domain, an artificial boundary is introduced with a Non-Reflecting Boundary Condition (BI-NRBC). CVEM with Crank-Nicolson time integrator is used in the interior domain, and BI-NRBC is discretized using a convolution quadrature formula in time and a collocation method in space. Numerical results demonstrate the effectiveness of the proposed approach, especially for obstacles with complex geometries.