Polynomial time-marching for nonreflecting boundary problems

The newly developed polynomial time-marching technique has been successfully extended to nonperiodic boundary condition cases. In this paper, a special nonperiodic 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.