Improvement of efficiency of Conjugate Gradient method with extracting GEbE-SSOR preconditioner

Abstract

Large scale analysis with Finite Element Method (FEM) needs much memory because of construction of a global matrix. This motivates us to employ Element by Element (EbE) scheme, which does not require to construct global matrix. However, in the EbE scheme, general useful preconditioners for global matrix cannot be applied. To enhance effectiveness of the EbE scheme, variants of the EbE schemes, such as Grouped EbE, Clustered EbE, and preconditionings for them have been proposed by many researchers. In the Grouped EbE scheme, parallel implementation of the EbE scheme becomes easier. The clustered EbE scheme, which is regarded as a generalization of standard EbE scheme, can decrease number of iterations. Therefore, in this paper, we propose an efficient Eisenstat SSOR preconditioning used in the Grouped EbE scheme, and demonstrate its effectiveness.