Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes
Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes
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DOI：
10.4208/cicp.091209.080410s
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发表时间：
2011-03
影响因子：
3.7
通讯作者：
S. Britt;S. Tsynkov;Eli Turkel
中科院分区：
文献类型：
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作者：
S. Britt;S. Tsynkov;Eli Turkel
在许多问题中，人们希望求解具有类拉普拉斯项内的可变系数的亥姆霍兹方程，并使用高阶精确方法（例如四阶精确）通过减少色散误差来减轻每波长点的约束。方程中系数的变化可能是由于非均匀介质和/或非笛卡尔坐标造成的。这使得现有的四阶有限差分方法不再适用。我们开发了一种新的紧凑方案，即使对于这些问题，该方案也被证明具有四阶精度。我们提出的数值结果证实了几个模型问题的四阶收敛速度。
In many problems, one wishes to solve the Helmholtz equation with vari- able 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 re- ducing the dispersion errors. The variation of coefficients in the equation may be due to an inhomogeneous medium and/or non-Cartesian coordinates. This renders exist- ing 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.