A Parallel Direct Domain Decomposition Solver Based on Schur Complement for Electromagnetic Finite Element Analysis

In this letter, a parallel direct solver for the analysis of electromagnetic problems with minimum memory cost is presented. The solver makes use of the finite element method to perform the analysis dividing the entire computational domain into several subdomains. Then, the partial lower/upper decomposition of each subdomain is performed obtaining the Schur complement matrix of each subdomain. This process is performed one by one using all the computer power available for each decomposition. Subsequently, the original 3-D problem is reduced to a 2-D problem on the interface skeleton through assembling the obtained Schur complement matrices. After obtaining the interface solution by using a dense direct solver, each well-posed subdomain is solved independently. Thus, the resulting parallel solver does not suffer from convergence issues since is based on direct method strategies instead of iterative methodologies. Through comparisons with commonly used parallel direct solvers, the benefits and the accuracy of the proposed solver are demonstrated. Finally, a waveguide wide-edge slot antenna with 14 million tetrahedrons is analyzed showing the power of the presented parallel direct solver.