The use of Huygens' equivalence principle for solving 3-D volume integral equation of scattering
The use of Huygens' equivalence principle for solving 3-D volume integral equation of scattering
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DOI：
10.1109/8.384194
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发表时间：
1993-07
影响因子：
5.7
通讯作者：
Caicheng Lu;W. Chew
中科院分区：
文献类型：
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作者：
Caicheng Lu;W. Chew
一个三维（3-D）版本的嵌套等效原理算法（NEPAL）。在3-D中，首先将散射体分解成N个子散射体。然后，球面波函数被用来表示的子散射场。子散射体以嵌套的方式被划分为不同级别的组。例如，每个群由8个子群组成，每个子群又包含8个子群，依此类推，对于每个子群，首先求解散射解，然后利用惠更斯等效原理，用边界子散射体代替内部子散射体，从而减少子群的子散射体数目。因此，当子组被组合以形成更高级别的组时，该组将具有更少数量的子散射体。在最后一层，子散射体的数目与散射体的边界尺寸成正比。该算法在三维空间中对所有激励的计算复杂度为O（N/sup 2/），并具有求解多激励大散射问题的优点。这是在对比高斯消除具有O（N/sup 3/）的计算复杂度。>
A three-dimensional (3-D) version of the nested equivalent principle algorithm (NEPAL) is presented. In 3-D, a scatterer is first decomposed into N subscatterers. Then, spherical wave functions are used to represent the scattered field of the subscatterers. Subscatterers are divided into different levels of groups in a nested manner. For example, each group consists of eight subgroups, and each subgroup contains eight sub-subgroups, and so on. For each subgroup, the scattering solution is first solved and the number of subscatterers of the subgroup is then reduced by replacing the interior subscatterers with boundary subscatterers using Huygens' equivalence principle. As a result, when the subgroups are combined to form a higher level group, the group will have a smaller number of subscatterers. This process is repeated for each level, and in the last level, the number of subscatterers is proportional to that of boundary size of the scatterers. This algorithm has a computational complexity of O(N/sup 2/) in three dimensions for all excitations and has the advantage of solving large scattering problems for multiple excitations. This is in contrast to Gaussian elimination which has a computational complexity of O(N/sup 3/). >