Abstract
The newly developed polynomial time-marching technique has been successfully extended to nonperiodic boundary condition cases. In this paper, a special non-periodic boundary condition, nonreflecting or absorbing boundary condition, is incorporated into the pseudospectral polynomial time-marching scheme. Thus, this accurate and stable time-dependent PDE solver can be applied to some open domain or free space problems. The balanced overall spectral accuracy is illustrated by some numerical experiments in the one-dimensional case. The error goes to zero at a rate faster than many fixed orders of the finite-difference scheme. The order of the absorbing boundary approximation is addressed in one-dimension. Also, in the two-dimensional case, a 2nd-order absorbing approximation has been incorporated into the polynomial time-marching scheme with Chebyshev collocation in space. Comparison with the previous finite-difference implementation indicates that the high stability and efficiency of the polynomial time-marching remains. The overall accuracy is mainly limited by the 2nd-order absorbing approximation.
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Luo, Y., Yedlin, M.J. Polynomial Time-Marching for Nonreflecting Boundary Problems. Journal of Scientific Computing 12, 31–50 (1997). https://doi.org/10.1023/A:1025654303349
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DOI: https://doi.org/10.1023/A:1025654303349