Incomplete LU Preconditioning for Large Scale Dense Complex Linear Systems

Jeonghwa Lee

Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science, University of Kentucky
Lexington, KY 40506--0046, USA

Jun Zhang
Cai-Cheng Lu


Abstract

The main purpose of this study is to evaluate the efficiency of a class of incomplete LU (ILU) factorization preconditioners for solving a complex valued matrix arising from discretizing the integral equation of electromagnetic scattering. We solve the electromagnetic wave equations using the BiCG method with an ILU preconditioner in the context of a multilevel fast multipole algorithm (MLFMA). The novelty of this work is that the ILU preconditioner is constructed using the near part block diagonal submatrices generated from the MLFMA. Experimental results show that the ILU preconditioner reduces the number of BiCG iterations substantially, compared to the block diagonal preconditioner. The preconditioned iteration scheme also maintains the computational complexity of the MLFMA, and consequently reduces the total CPU time.