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首页> 外文期刊>Journal of Computational Physics >An FDTD scheme on a face-centered-cubic (FCC) grid for the solution of the wave equation
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An FDTD scheme on a face-centered-cubic (FCC) grid for the solution of the wave equation

机译：求解波动方程的面心立方（FCC）网格上的FDTD方案

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摘要

A method is proposed to improve the numerical dispersion characteristics for simulations of the scalar wave equation in 3D using the FDTD method. The improvements are realized by choosing a face-centered-cubic (FCC) grid instead of the typical Cartesian (Yee) grid, which exhibits non-physical distortions of the wavefront due to the FD stencil. FCC grids are the logical extension of hexagonal grids in 2D, and have been shown previously to provide optimal sampling of space based on close packing of spheres (highest density). The difference equations are developed for the wave equation on this alternative grid, and the dispersion relationship and stability for grids of equal and non-equal aspect ratios are derived. A comparison is made between FCC and Cartesian formulations, based upon having an equal volume density of gridpoints in each method (i.e. the computational storage requirements of each method would be the same for the same simulated space). The comparison shows that the FCC grid exhibits a much more isotropic dispersion relation than the Cartesian grid of equivalent density. Furthermore, for an equivalent density, the FCC method has a more relaxed stability criterion by a factor of approximately 1.35, resulting in a further reduction in computational resources.
机译：提出了一种改进数字色散特性的方法，用于使用FDTD方法对3D标量波动方程进行仿真。通过选择一个面心立方（FCC）网格而不是典型的笛卡尔（Yee）网格来实现改进，该网格由于FD模板而表现出波前的非物理失真。 FCC网格是2D中六边形网格的逻辑扩展，并且先前已经显示过，它们可以根据球的紧密堆积（最高密度）提供最佳的空间采样。在该替代网格上为波动方程建立了差分方程，并推导了纵横比相等和不相等的网格的色散关系和稳定性。基于在每种方法中网格点的体积密度相等（即，对于相同的模拟空间，每种方法的计算存储需求将是相同的），在FCC和笛卡尔公式之间进行比较。比较表明，与等效密度的笛卡尔网格相比，FCC网格具有更大的各向同性色散关系。此外，对于等效密度，FCC方法具有更宽松的稳定性标准（约为1.35倍），从而导致计算资源的进一步减少。

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