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Simulating wave scattering problems by pseudospectral time-marching on supercomputers

University of British Columbia

In this thesis, a new time-marching scheme for time-dependent PDEs with periodic and non-periodic boundary conditions is introduced and implemented. The new time-marching scheme is based on the polynomial interpolation of the symbolic solution of the original PDEs. The approximation of the space derivatives is performed by pseudospectral methods. The marching of the solution in the time domain is done by the polynomial expansion or the Newton-form polynomial interpolation, depending on the properties of the space derivatives. The boundary conditions are properly represented by a suitable pseudospectral approximation and some technical manipulations of the collocated operators. This technique can efficiently provide balanced spectral accuracy in both the space and time dimensions. The numerical stability and resolution are also improved by the new polynomial time-marching scheme. In the periodic boundary case, the spatial approximation generally can be done by Fourier collocation and the time-marching sometimes can be easily implemented by Chebyshev polynomial series. In the non-periodic case, the spatial operator should be approximated by a Chebyshev collocation, which can include different non-periodic boundary conditions through careful manipulations of the boundary conditions. In this case and the complicated periodic case, the time-marching has to rely on the more general Newton-form interpolation based on Fejér points. Based on the new polynomial time-marching scheme, a two-dimensional, SH-seismic reflection model is simulated by full implementation of the new time-marching scheme with the approximated absorbing boundary conditions. Some scattering phenomena such as diffraction are illustrated through the visualization. The simulation of the physical model is accomplished on two supercomputers: the TMC Connection Machine CM-5 and the Fujitsu VPX240/10. The parallel programming (CM-Fortran on CM-5 and Fortran 77/VP on the VPX240/10) and optimization issues on the two supercomputers are also discussed in this thesis.

Thesis/Dissertation

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2009-06-09

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http://hdl.handle.net/2429/8870

Electrical and Computer Engineering

University of British Columbia

UBCV

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