CBFEM-MPI: A Parallelized Version of Characteristic Basis Finite Element Method for Extraction of 3-D Interconnect Capacitances

In this paper, we present a novel, non-iterative domain decomposition method, which has been parallelized by using the message passing interface (MPI) library, and used to efficiently extract the capacitance matrixes of 3-D interconnect structures, by employing characteristic basis functions (CBFs) in the context of the finite element method (FEM). In this method, which is called CBFEM-MPI, the computational domain is partitioned into a number of nonoverlapping subdomains in which the CBFs are constructed by employing a procedure that is different from what has been used in the past for generating them. Specifically, the CBFs for the problem at hand are determined by calculating the potentials due to a finite number of point charges located hypothetically along the boundaries of the conductors. Two major advantages of the method are substantial reduction of the matrix size - enabling the use of direct solvers - and the utilization of parallel processing techniques that provide a substantial decrease in the overall computation time. Numerical examples are included to illustrate the application of the proposed approach to a number of representative problems.