Polynomial time-marching for nonreflecting boundary problems (Q1387812)

A special nonperiodic boundary condition is incorporated into the pseudospectral polynomial time-marching scheme, including nonreflecting or absorbing boundary conditions. Based on this principle an accurate and stable time-dependent solver for partial differential equations in an open domain and free space environment can be applied. The balanced overall spectral accuracy is illustrated by some numerical experiments in the one-dimensional case, where the order of the absorbing boundary condition is addressed. In the two-dimensional case a 2nd-order absorbing approximation is incorporated into the polynomial time-marching scheme with Chebyshev collocation in space. Comparison with a 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.