Accelerated generation of Characteristic Basis Functions using randomized Singular Value Decomposition

Abstract

It has been demonstrated in the literature on Characteristic Basis Function Method (CBFM) that higher compression rate can be achieved by using larger blocks while carrying out domain decomposition in the context of CBFM [1]. However, the increased degrees of freedom (DOFs) in large domains make the generation of the Characteristic Basis Functions (CBFs) very time- and memory-consuming for the following reasons: (a) Impedance matrices for each domain need to be calculated; (b) Singular Value Decomposition (SVD) must be carried out to remove the redundancy between the CBFs. To mitigate the above problem, Multilevel CBFM (MLCBFM) has been proposed. Also, similar to MLCBFM, a hybrid approach namely the hybrid CBFM/ACA/UV method has been developed recently to address the same issue [2]. By using the UV technique, the computational time and memory complexity required by the matrix filling process can be decreased from O(BN RWG 2) to O(BN RWG logN RWG ), where B is the number of blocks andN RWG is the average number of RWGs in each block. Compared to MLCBFM, the hybrid CBFM/ACA/UV has the advantage that it does not require the generation of either the CBFs or the reduced matrix at the lower level (two-level domain decomposition policy is normally adopted for MLCBFM).