An Efficient Finite-Element Time-Domain Method via Hierarchical Matrix Algorithm for Electromagnetic Simulation
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An Efficient Finite-Element Time-Domain Method via Hierarchical Matrix Algorithm for Electromagnetic SimulationAbstract
An efficient finite-element timedomain (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.
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