Algebraic Domain Decomposition Preconditioner for Electromagnetic Computations

Abstract

The solution of large-scale linear equations is a computationally challenging problem in scientific and engineering computing. Due to memory and CPU time constraints, usually only iterative solver can be used. In recent years, many solvers have been built to handle such challenging problems.  In this paper, our main objective is to design a new ADDM preconditioner for finding a method of linear equations which are efficient, robust, and can also be implemented well. We designed and implemented an efficient ADDM preconditioner algebraically without having to know an information of the problem in general and also without any hypothesis on the least-squares matrix except that it is sparse, this and other results showing how our designed preconditioner outperformed other preconditioners are shown in this paper.We discussed how the ADDM preconditioner can be designed using the Matlab and Python codes and the results are analyzed and presented to show the performance of the proposed preconditioner. The ADDM preconditioner designed are very robust and efficient since it outperforms other preconditioners designed in the past in terms of convergence. The problems which could possible arise from a very practical applications are actually used to make a relation in the performance of our new preconditioner and the other related preconditioners designed in the past.