TY - JOUR
T1 - Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media Using Compact High Order Schemes
JO - Communications in Computational Physics
VL - 3
SP - 520
EP - 541
PY - 2011
DA - 2011/03
SN - 9
DO - http://doi.org/10.4208/cicp.091209.080410s
UR - https://global-sci.org/intro/article_detail/cicp/7509.html
KW - 
AB - <p style="text-align: justify;">In many problems, one wishes to solve the Helmholtz equation with variable
coefficients within the Laplacian-like term and use a high order accurate method
(e.g., fourth order accurate) to alleviate the points-per-wavelength constraint by reducing
the dispersion errors. The variation of coefficients in the equation may be due
to an inhomogeneous medium and/or non-Cartesian coordinates. This renders existing
fourth order finite difference methods inapplicable. We develop a new compact
scheme that is provably fourth order accurate even for these problems. We present
numerical results that corroborate the fourth order convergence rate for several model
problems.</p>