Finite element analysis with tens of billions of degrees of freedom in a high-frequency electromagnetic field

Abstract

This paper deals with finite element analysis involving tens of billions of degrees of freedom (DOF) in a high-frequency electromagnetic field. The iterative substructuring method has been considered to be an efficient parallel computing method. To show the possibility of analyzing electromagnetic field problems with complex numbers and tens of billions of DOF, problems with up to 30 billion DOF are analyzed by all nodes of an Oakleaf-FX supercomputer. As a result, the human model has been successfully solved in approximately 10 minutes, and the simple hyperthermia applicator model with 30 billion DOF has been successfully solved in approximately 19 minutes. There is a problem in the output analysis results, and bugs relating to the limits of the 32-bit integer data type have been found and fixed through actual analysis of problems with tens of billions of DOF. Key words : Parallel computing, Supercomputer, Finite element method, Iterative substructuring method, Domain decomposition method, Tens of billions of degrees of freedom, High-frequency electromagnetic field problem, Symmetric matrix with complex numbers, Conjugate orthogonal conjugate gradient method, Conjugate orthogonal conjugate residual method