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

A hybrid h- and p-Type multiplicative Schwarz (h-p-MUS) preconditioned algorithm is proposed to improve efficiency of higher-order finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) for 3D scattering in this paper. An h-p-MUS precondtioner is first constructed for the FEM matrix obtained by using vector higher-order hierarchical basis functions. Numerical experiments show that this preconditioner can offer a better efficiency both in CPU time and memory requirement than the h-MUS and the p-MUS preconditioners. Then this h-p-MUS preconditioner for the FEM matrix 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 large 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.