Hybrid h- and p-Type Multiplicative Schwarz (h-p-MUS) Preconditioned Algorithm of Higher-Order FE-BI-MLFMA for 3D Scattering

摘要

The key to design algorithms of higher-order finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is how to construct preconditioners for the FEM matrix part in the FE-BI matrix equation. A hybrid h- and p-Type multiplicative Schwarz (h-p-MUS) preconditioner is proposed for 3D scattering in this paper. First, the hierarchical higher-order FEM matrix is rewritten by classifying unknowns into different groups corresponding to different FEM orders. Then a preconditioner is constructed by the p-type multiplicative Schwarz method (p-MUS). To further improve efficiency in the p-MUS construction, an h-type multiplicative Schwarz preconditioner is employed for different submatrices. Numerical experiments show that this preconditioning scheme can offer a better efficiency both in CPU time and memory requirement than previous algorithms. This h-p-MUS preconditioner for the FEM matrices is applied to different algorithms of FE-BI-MLMFA. Analysis and Numerical results show that the h-p-MUS preconditioned conventional algorithm (h-p-MUS-CA) has a better efficiency over other h-p-MUS preconditioned algorithms. A variety of numerical experiments are performed for complex objects in this paper, demonstrating that this h-p-MUS-CA exhibits superior efficiency in the CPU time and memory, and greatly improves the capability of the higher-order FE-BI-MLFMA.