解耦势积分方程的高阶Galerkin格式
High-order $L^2$-Galerkin schemes for the decoupled potential integral equations
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中文总结 AI 辅助
该研究针对解耦势积分方程，证明其Sobolev空间适定性，提出含不连续基函数或逐元素切向连续性的高阶Galerkin格式，该格式条件数更优且与波数等因素几乎无关。
中文摘要 AI 辅助
我们证明了解耦势积分方程在Sobolev空间中的适定性。利用基本的伪微分技术，得到了标准L²配对的离散稳定性，进而推导出采用不连续基函数或在系统向量部分施加额外逐元素切向连续性的高阶格式的谱收敛性。结果表明，该格式的条件数远优于成熟的商业EFIE/CFIE求解器，在许多情况下几乎与波数、网格密度及阶数无关。
英文摘要
We prove Sobolev space well-posedness of the decoupled potential integral equations. Using basic pseudo-differential techniques, discrete stability is obtained for the standard $L^2$-pairing, and we deduce spectral convergence for a high-order scheme employing discontinuous basis functions, or with additional element-wise tangential continuity imposed in the vectorial part of the system. The scheme is shown to be much better conditioned than a mature commercial EFIE/CFIE solver. In many cases appearing almost independent of wavenumber, mesh density, and the order.
发表机构
- DTU（丹麦技术大学）
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