TY - JOUR
T1 - Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations
AU - N. Anders Petersson & Björn Sjögreen
JO - Communications in Computational Physics
VL - 5
SP - 1074
EP - 1110
PY - 2010
DA - 2010/08
SN - 8
DO - http://doi.org/10.4208/cicp.041109.120210a
UR - https://global-sci.org/intro/article_detail/cicp/7609.html
KW - 
AB - <p style="text-align: justify;">An energy conserving discretization of the elastic wave equation in second
order formulation is developed for a composite grid, consisting of a set of structured
rectangular component grids with hanging nodes on the grid refinement interface. Previously
developed summation-by-parts properties are generalized to devise a stable
second order accurate coupling of the solution across mesh refinement interfaces. The
discretization of singular source terms of point force and point moment tensor type are
also studied. Based on enforcing discrete moment conditions that mimic properties of
the Dirac distribution and its gradient, previous single grid formulas are generalized
to work in the vicinity of grid refinement interfaces. These source discretization formulas
are shown to give second order accuracy in the solution, with the error being
essentially independent of the distance between the source and the grid refinement
boundary. Several numerical examples are given to illustrate the properties of the proposed
method.</p>