An Efficient Finite-Element Time-Domain Method via Hierarchical Matrix Algorithm for Electromagnetic Simulation

作者：Wan Ting^*; Chen Rushan; She Jianjian; Ding Dazhi; Fan Zhenhong

来源：Applied Computational Electromagnetics Society Journal, 2011, 26(7): 584-595.

• Direct solution
• finite-element time-domain (FETD) method
• H-matrix algorithm
• reduced complexity

An efficient finite-element time-domain (FETD) method based on the hierarchical (H-) matrix algorithm is presented. The FETD method is on the basis of the second-order vector wave equation, obtained by eliminating one of the field variables from Maxwell's equations. The time-dependent formulation employs the Newmark-beta method which is known as an unconditional stable time-integration method. H-matrix algorithm is introduced for the direct solution of a large sparse linear system at each time step, which is a serious handicap in conventional FETD method. H-matrix algorithm provides a data-sparse way to approximate the LU triangular factors of the FETD system matrix. Using the H-matrix arithmetic, the computational complexity and memory requirement of H-LU decomposition can be significantly reduced to almost logarithmic-linear. Once the H-LU factors are obtained, the FETD method can be computed very efficiently at each time step by the H-matrix formatted forward and backward substitution (H-FBS). Numerical examples are provided to illustrate the accuracy and efficiency of the proposed FETD method for the simulation of three-dimension (3D) electromagnetic problems.

• 出版日期2011-7
• 单位南京理工大学