An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: Formulation, analysis, algorithm, and simulation

• Published in: Journal of computational physics 2020-02, Vol.403, p.109052, Article 109052
• Main Authors: Domínguez, V., Ganesh, M., Sayas, F.J.
• Format: Article
• Language: English
• Subjects: Acoustic propagation; Algorithms; Computational physics; Computer simulation; Decomposition; Electromagnetic radiation; Equivalence; Finite element method; Finite/boundary element methods; Free boundaries; Helmholtz equations; Heterogeneous; Mathematical analysis; Mathematical models; Model accuracy; Propagation; Refractivity; Smooth boundaries; Two dimensional models; Unbounded; Wave propagation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2019.109052

•A novel framework to simulate wave propagation in heterogeneous and unbounded media.•Mathematical analysis establishes equivalence of the framework and the wave model.•The framework facilitates retaining a key radiating property in computational model.•Developed a high-order algorithm using decomposition framework and FEM-BEM coupling.•Demonstration of FEM-BEM wave simulation in complex heterogeneous and unbounded media. A natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free-space. Frequency-domain wave propagation models in the medium, such as the variable coefficient Helmholtz equation, include a faraway decay radiation condition (RC). It is desirable to develop algorithms that incorporate the full physics of the heterogeneous and unbounded medium wave propagation model, and avoid an approximation of the RC. In this work we first present and analyze an overlapping decomposition framework that is equivalent to the full-space heterogeneous-homogenous continuous model, governed by the Helmholtz equation with a spatially dependent refractive index and the RC. Our novel overlapping framework allows the user to choose two free boundaries, and gain the advantage of applying established high-order finite and boundary element methods (FEM and BEM) to simulate an equivalent coupled model. The coupled model comprises auxiliary interior bounded heterogeneous and exterior unbounded homogeneous Helmholtz problems. A smooth boundary can be chosen for simulating the exterior problem using a spectrally accurate BEM, and a simple boundary can be used to develop a high-order FEM for the interior problem. Thanks to the spectral accuracy of the exterior computational model, the resulting coupled system in the overlapping region is relatively very small. Using the decomposed equivalent framework, we develop a novel overlapping FEM-BEM algorithm for simulating the acoustic or electromagnetic wave propagation in two dimensions. Our FEM-BEM algorithm for the full-space model incorporates the RC exactly. Numerical experiments demonstrate the efficiency of the FEM-BEM approach for simulating smooth and non-smooth wave fields, with the latter induced by a complex heterogeneous medium and a discontinuous refractive index.