TY - JOUR T1 - Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media Using Compact High Order Schemes AU - Steven Britt, Semyon Tsynkov & Eli Turkel 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 -
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.