Accelerated Direct Solver With Multiscale Compressed Block Decomposition and Multilevel Characteristic Basis Function Method

In this letter, an accelerated fast direct solver based on the multiscale compressed block decomposition (MSCBD) and the multilevel characteristic basis function method (MLCBFM) is presented to analyze electrically large problems. The MSCBD is used to enhance the efficiency of the characteristic basis functions generation to accelerate the process of linear system solving in the MLCBFM. In addition, the MLCBFM can reduce the number of unknowns and improve the efficiency of MSCBD process. That means the MSCBD and MLCBFM can accelerate each other. The correctness and efficiency of the method are demonstrated with numerical results for several perfect electric conducting objects, by comparing with other methods.