High-order finite difference methods for the Helmholtz equation
High-order finite difference methods for the Helmholtz equation
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DOI：
10.1016/s0045-7825(98)00023-1
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发表时间：
1998-09
影响因子：
7.2
通讯作者：
I. Singer;Eli Turkel
中科院分区：
文献类型：
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作者：
I. Singer;Eli Turkel
高阶有限差分法求解Helmholtz方程的开发和分析，在一个和两个维度上的均匀网格。标准的逐点表示具有二阶精度的局部截断误差。我们还研究了两个具有四阶精度局部截断误差的格式。高阶格式之一是基于Padé近似的推广。第二种方案是基于高阶近似的衍生物计算的亥姆霍兹方程本身。针对诺伊曼边界条件建立了对称的高阶表示。数值结果与发达国家的计划近似的模型问题。
High-order finite difference methods for solving the Helmholtz equation are developed and analyzed, in one and two dimensions on uniform grids. The standard pointwise representation has a second-order accurate local truncation error. We also study two schemes which have a fourth-order accurate local truncation error. One of the high-order schemes is based on generalizations of the Padé approximation. The second scheme is based on high-order approximation to the derivative calculated from the Helmholtz equation itself. A symmetric high-order representation is developed for a Neumann boundary condition. Numerical results are presented on model problems approximated with the developed schemes.