Hierarchical LU decomposition‐based direct method with improved solution for 3D scattering problems in FEM

An efficient direct method based on hierarchical LU (H-LU) Decomposition is developed for the solution of large sparse finite element systems.On the basis of hierarchical matrix (H-matrix) technique, H-LU direct method provides a data-sparse way to approximate the LU-factors of a finite element matrix which are dense originally. The approximate LU-factors can be computed and stored in the algebra of H-matrices with logarithmic-linear complexity. The accuracy of this approximation is controllable related to the different choices of the H-matrix parameters. A modification algorithm is proposed to efficiently improve the accuracy of the approximate solution computed by the H-LU-based direct method. Some numerical examples are provided to illustrate the accuracy and efficiency of the proposed method for finite element analysis of three-dimensional (3D) electromagnetic scattering problems. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26122

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