TY - JOUR

T1 - The 3D wave equation and its Cartesian coordinate stretched perfectly matched embedding - A time-domain Green's function performance analysis

AU - de Hoop, AT

AU - Remis, RF

AU - van den Berg, PM

PY - 2007

Y1 - 2007

N2 - A general class of 3d perfectly matched, i.e. relfectionless, Cartesian embeddings (perfectly matched layers in the three coordinate directions) is analyzed with the aid of a combined time-domain Green's function technique and a time-domain, causality-preserving, Cartesian coordinate stretching procedure. It is shown that, for an unbounded embedding of the specified class, the wavefield is, in any 3-rectangular computational solution domain, reproduced exactly. The spurious reflection caused by a (computationally necessary) trunction of the embedding is analyzed as a function of layer thicknesses and their coordinate stretching relaxation functions. A time-domain uniqueness proof for the solution to the truncated embedding problem is provided and a numerical illustration is given for a test case with known analytical solution. For such cases, the pure space-time discretization errors can be seperated from the disturbance caused by the spurious reflection. For the second-order coordinate stretched wave equation an equivalent system of first-order equations is presented.

AB - A general class of 3d perfectly matched, i.e. relfectionless, Cartesian embeddings (perfectly matched layers in the three coordinate directions) is analyzed with the aid of a combined time-domain Green's function technique and a time-domain, causality-preserving, Cartesian coordinate stretching procedure. It is shown that, for an unbounded embedding of the specified class, the wavefield is, in any 3-rectangular computational solution domain, reproduced exactly. The spurious reflection caused by a (computationally necessary) trunction of the embedding is analyzed as a function of layer thicknesses and their coordinate stretching relaxation functions. A time-domain uniqueness proof for the solution to the truncated embedding problem is provided and a numerical illustration is given for a test case with known analytical solution. For such cases, the pure space-time discretization errors can be seperated from the disturbance caused by the spurious reflection. For the second-order coordinate stretched wave equation an equivalent system of first-order equations is presented.

KW - academic journal papers

KW - CWTS 0.75 <= JFIS < 2.00

U2 - doi10.1016/j.jcp.2006.06.018

DO - doi10.1016/j.jcp.2006.06.018

M3 - Article

VL - 221

SP - 88

EP - 105

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -