Abstract
A fully explicit marching-on-in-time (MOT) scheme for solving the time domain Kirchhoff (surface) integral equation to analyze transient acoustic scattering from rigid objects is presented. A higher-order Nyström method and a PE(CE)m-type ordinary differential equation integrator are used for spatial discretization and time marching, respectively. The resulting MOT scheme uses the same time step size as its implicit counterpart (which also uses Nyström method in space) without sacrificing from the accuracy and stability of the solution. Numerical results demonstrate the accuracy, efficiency, and applicability of the proposed explicit MOT solver.
Highlights
IntroductionDespite the advantages of the time domain surface integral equation (TDSIE) solvers listed in the first paragraph, use of the MOT-TDSIE solvers in analyzing transient acoustic scattering has been rather limited
time domain surface integral equation (TDSIE) solvers have several advantages over differential equation solvers.4 (i) They require only a twodimensional discretization of the scatterer surface as opposed to a three-dimensional discretization of the whole computation domain. (ii) They are free from numerical dispersion since they do not discretize spatial/temporal derivatives using finite differences or finite elements. (iii) They do not need approximate absorbing boundary conditions to truncate the unbounded physical domain into the computation domain
Despite the advantages of the TDSIE solvers listed in the first paragraph, use of the MOT-TDSIE solvers in analyzing transient acoustic scattering has been rather limited
Summary
Despite the advantages of the TDSIE solvers listed in the first paragraph, use of the MOT-TDSIE solvers in analyzing transient acoustic scattering has been rather limited. This can be attributed to the difficulty of obtaining a stable solution as well as the high cost of computing the discretized spatio-temporal convolution. The former bottleneck has been alleviated with the development of new temporal basis functions and testing schemes, as well as accurate integration methods.. The former bottleneck has been alleviated with the development of new temporal basis functions and testing schemes, as well as accurate integration methods. To reduce the high computational cost, plane wave time domain (PWTD) algorithm and the fast Fourier transform (FFT)-based acceleration schemes have been developed
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