A Geometry-Aware Domain Decomposition Preconditioning for Hybrid Finite Element-Boundary Integral Method

Abstract

Fast, scalable, and robust solution of the hybrid finite element-boundary integral (FE-BI) linear system of equations is traditionally considered a challenge due to multifaceted technical difficulties. This paper proposes a nonoverlapping geometry-aware domain decomposition (DD) preconditioning technique for iteratively solving hybrid FE-BI equation. The technique ingredients include a volume-based Schwarz FE DD method and a surface-based interior penalty BI DD method. Compared with previous algorithms, the work has two major benefits: 1) it results in a robust and cost-effective preconditioning technique for the solution of the FE-BI linear system of equations and 2) it provides a flexible and natural way to set up the mathematical models, to create the problem geometries, and to discretize the computational domain. The capability and performance of the computational algorithms are illustrated and validated through numerical experiments.