Fast Direct Error-Controlled Solution of Scattering Problems via ℋ-matrix Acceleration of Locally Corrected Nyström Method
Fast Direct Error-Controlled Solution of Scattering Problems via ℋ-matrix Acceleration of Locally Corrected Nyström Method
复制标题
通过局部校正 Nyström 方法的 ℋ 矩阵加速快速直接误差控制解决散射问题
DOI：
10.23919/eucap51087.2021.9411057
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
V. Okhmatovski
中科院分区：
文献类型：
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作者：
R. Gholami;Zhuotong Chen;M. Shafieipour;V. Okhmatovski
提出了使用局部校正 Nyström (LCN) 方法在完美导电 (PEC) 球体存在的情况下快速直接高阶解决辐射问题。使用误差控制的分层 (ℋ) 矩阵框架获得加速解决方案。与传统 LCN 所需的时间相比，矩阵填充时间和直接求解时间显着缩短。解的误差是通过与解析米氏级数解进行比较来计算的。所开发的计算框架被证明可以产生更高阶的解决方案，同时保持相应ℋ-矩阵块的高可压缩性。分析了内存成本和 CPU 时间复杂度随问题规模的变化。
The fast direct high-order solution of radiation problems in the presence of perfect electrically conducting (PEC) sphere with the Locally Corrected Nyström (LCN) method is presented. Accelerated solution is obtained using error-controlled hierarchical (ℋ)-matrix framework. Matrix fill time and direct solution time are shown to be substantially reduced compared to those needed by conventional LCN. The error of solution is computed via comparison against the analytical Mie series solution. Developed computational framework is shown to produce the higher order solution while preserving high compressibility of the corresponding ℋ-matrix blocks. The memory cost and CPU time complexity scaling with the size of the problem is analyzed.