Highly efficient parallel direct solver for solving dense complex matrix equations from method of moments

Abstract

Based on the vectorised and cache optimised kernel, a parallel lower upper decomposition with a novel communication avoiding pivoting scheme is developed to solve dense complex matrix equations generated by the method of moments. The fine-grain data rearrangement and assembler instructions are adopted to reduce memory accessing times and improve CPU cache utilisation, which also facilitate vectorisation of the code. Through grouping processes in a binary tree, a parallel pivoting scheme is designed to optimise the communication pattern and thus reduces the solving time of the proposed solver. Two large electromagnetic radiation problems are solved on two supercomputers, respectively, and the numerical results demonstrate that the proposed method outperforms those in open source and commercial libraries.

Keywords

• parallel processing
• cache storage
• matrix decomposition
• method of moments
• parallel direct solver
• dense complex matrix equations
• method of moments
• vectorised optimised kernel
• cache optimised kernel
• parallel lower upper decomposition
• communication avoiding pivoting scheme
• data rearrangement
• assembler instructions
• memory accessing time
• CPU cache utilisation
• binary tree
• communication pattern optimisation
• electromagnetic radiation problems