Abstract
A Krylov space based time domain method for wave propagation problems is introduced. The proposed method uses the Arnoldi algorithm to obtain broad-band frequency domain solutions. This method is especially advantageous in cases where slow convergence is observed when using traditional time domain methods. The efficiency of the method is examined in several test cases to show its fast convergence in such problems.
Highlights
Wave equations can be generally solved using two categories of methods: time-domain and frequency-domain methods
The proposed method uses the Arnoldi algorithm to obtain broadband frequency domain solutions. This method is especially advantageous in cases where slow convergence is observed when using traditional time domain methods
The efficiency of the method is examined in several test cases to show its fast convergence in such problems
Summary
Wave equations can be generally solved using two categories of methods: time-domain and frequency-domain methods. Finite-difference time-domain (FDTD) methods have been widely adopted for solving different kinds of wave propagation problems. In these methods, the field is discretized into a series of uniform hexahedral volumes. The time domain methods, have been found to suffer from convergence problems for physical models that include locally resonant structures. Such structures may be the result of large material mismatches, or complex geometries. Different from existing work, the proposed algorithm is derived directly from discrete Fourier transform of time domain data, by which the corresponding frequency domain solutions of a wide range can be obtained with negligible computational costs once the projection of the time domain solution onto the Krylov subspace is obtained. Several numerical cases are examined to demonstrate the efficiency of the method, in which cases the spatial discretization is done with finite element methods
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