Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media Using Compact High Order Schemes (Communications in Computational Physics, 2011)
In many problems, one wishes to solve the Helmholtz equation with variablecoefficients 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 reducingthe dispersion errors. The variation of coefficients in the equation may be dueto an inhomogeneous medium and/or non-Cartesian coordinates. This renders existingfourth order finite difference methods inapplicable. We develop a new compactscheme that is provably fourth order accurate even for these problems. We presentnumerical results that corroborate the fourth order convergence rate for several modelproblems.