Abstract
As a continuation of the efficient and accurate polynomial interpolation time-marching technique in one-dimensional and two-dimensional cases, this paper proposes a method to extend it to three-dimensional problems. By stacking all two-dimensional (x, y) slice matrices along Z direction, three-dimensional derivative matrices are constructed so that the polynomial interpolation time-marching can be performed in the same way as one-dimensional and two-dimensional cases. Homogeneous Dirichlet and Neumann boundary conditions are also incorporated into the matrix operators in a similar way as in one- and two-dimensional problems. A simple numerical example of scalar wave propagation in a closed-cube has validated this extended method.
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REFERENCES
Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. (1988). Spectral Methods in Fluid Dynamics, Springer-Verlag, Berlin.
Gottlieb, D., Hussaini, M. Y., and Orzarg, S. A. (1984). Introduction: Theory and Applications of Spectral Methods, SIAM, Philadelphia.
Luo, Y. (1994). Simulating Wave Scattering Problems by Pseudospectral Time-marching on Supercomputers, Ph.D. Thesis, The University of British Columbia, Vancouver.
Luo, Y., and Yedlin, M. J. (1994). Polynomial Time-Marching for Nonperiodic Boundary Value Problems, J. Sci. Comput. 9, 123–136.
Luo, Y., and Yedlin, M. J. (1995). Pseudospectral polynomial time-marching for nonreflecting boundary problems, J. Sci. Comput. 12, 31–50.
Morse, P. M., and Freshbach, H. (1953). Methods of Theoretical Physics, McGraw-Hill Book, New York.
Tal-Ezer, H. (1986). Spectral Methods in Time for Hyperbolic Equations. SIAM J. Numer. Anal. 23, 11–26.
Tal-Ezer, H. (1989). Polynomial Approximation of Functions of Matrices and Applications, J. Sci. Comput. 4, 25–60.
Tal-Ezer, H. (1991). High Degree Polynomial Interpolation in Newton Form, SIAM J. Sci. Stat. Comput. 12, 648–667.
Zhao, S. (1993). Chebyshev Spectral Methods for Potential Field Computation, Ph.D. Thesis, The University of British Columbia, Vancouver.
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Luo, Y. Polynomial Time-Marching for Three-Dimensional Wave Equations. Journal of Scientific Computing 12, 465–477 (1997). https://doi.org/10.1023/A:1025633130781
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DOI: https://doi.org/10.1023/A:1025633130781