A Domain Decomposition Finite-Difference Method Utilizing Characteristic Basis Functions for Solving Electrostatic Problems

This paper presents an efficient approach for solving a linear system of equations arising in the domain decomposition finite-difference (DDFD) method, employed for electrostatic problems. This novel approach is based on utilizing characteristic basis functions (CBFs)-special functions defined on macrodomains, or blocks in which the computational domain is discretized by using the DDFD method. The use of the CBFs leads to a significant reduction in the number of unknowns, and results in a substantial size reduction of the DDFD system; this, in turn, enables us to handle the reduced matrix by using an iteration-free direct solver. The reduced sparse matrix system is solved via the Schur complement approach, which reduces the system into many independent smaller subsystems. Two electrostatic problems are used as examples to illustrate the application of the proposed approach. Numerical results that demonstrate the accuracy and efficiency of the method are included.