An accelerated time domain finite difference simulation scheme for three‐dimensional transient electromagnetic modeling using geometric multigrid concepts
An accelerated time domain finite difference simulation scheme for three‐dimensional transient electromagnetic modeling using geometric multigrid concepts
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DOI：
10.1029/2005rs003413
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发表时间：
2006-06
期刊：
影响因子：
1.6
通讯作者：
M. Commer;G. Newman
中科院分区：
文献类型：
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作者：
M. Commer;G. Newman
瞬态电磁 (TEM) 场随时间在空间中逐渐平滑，这一事实允许降低 EM 场的空间采样率。基于多重网格方法中已知的概念，我们开发了一种限制算子，以便在使用显式时间步进方案的正向场模拟过程中将电磁场和材料属性从精细有限差分网格映射到较粗糙的有限差分网格。接下来有两个优点。首先，可以减小网格尺寸。场限制涉及将每个笛卡尔方向的网格节点数量减少 2 倍。其次，从 Courant-Friedrichs-Levy 条件可以看出，较大的网格间距允许按比例增大时间步长。场限制后，采用材料平均方案来计算粗模拟网格上的底层有效介质。示例结果显示，与使用恒定网格的方案相比，解决方案运行时间最多减少 5 倍。该方法准确性的关键是了解限制字段的适当时间范围。在运行时决定何时进行限制的适当标准涉及对细网格上的字段与受限字段之间的感兴趣位置的误差测量。
The fact that the transient electromagnetic (TEM) field is smoothed gradually in space with time allows for a reduced spatial sampling rate of the EM field. On the basis of concepts known from multigrid methods, we have developed a restriction operator in order to map the EM field and the material properties from a fine to a coarser finite difference mesh during a forward field simulation with an explicit time‐stepping scheme. Two advantages follow. First, the grid size can be reduced. Field restriction involves reducing the number of grid nodes by a factor of 2 for each Cartesian direction. Second, as can be seen from the Courant‐Friedrichs‐Levy condition, the larger grid spacing allows for proportionally larger time step sizes. After field restriction, a material averaging scheme is employed in order to calculate the underlying effective medium on the coarse simulation grid. Example results show a factor of up to 5 decrease in solution run time, compared to a scheme that uses a constant grid. Key to the accuracy of the approach is knowledge of the proper time range to restrict the fields. An adequate criterion to decide during run time when to restrict involves an error measure for the locations of interest between the fields on the fine mesh and the restricted fields.