AI 中文总结
QBMAX通过将核的渐近衰减行为纳入泰勒展开，扩展QBX框架，在二维和三维大参数情形下精度提升达四位数字，且计算成本相当。
AI 中文摘要
在存在边界层的情况下，评估具有快速衰减核的层势在计算上变得具有挑战性，例如具有大虚波数的亥姆霍兹层势。我们引入了匹配渐近展开求积（QBMAX），这是一种高阶方法，通过将核的渐近衰减行为直接纳入势的泰勒展开中，扩展了展开求积（QBX）框架。在二维和三维中的数值结果表明，对于所测试的大参数情况，与QBX相比，精度提升可达四位数字，而对于较小参数或曲率更强的几何形状，两种方法的性能可能相似。一个符号加权操作计数模型表明，形成两个展开核的成本相当。泰勒展开具有相同的正式阶数，而QBMAX在平坦边界模型中减少了截断误差常数，并且在所报告的实验中通常表现出更少的收敛退化。
英文摘要
Evaluating layer potentials with rapidly decaying kernels becomes computationally challenging in the presence of boundary layers, as occurs for Helmholtz layer potentials with large imaginary wavenumbers. We introduce Quadrature by Matched Asymptotic Expansion (QBMAX), a high-order method that extends the Quadrature by Expansion (QBX) framework by incorporating the kernel's asymptotic decay behavior directly into the Taylor expansion of the potential. Numerical results in both 2D and 3D show improvements of up to four digits over QBX for the tested large-parameter cases, while the methods can perform similarly for smaller parameters or more strongly curved geometries. A symbolic weighted operation-count model indicates comparable costs for forming the two expansion kernels. The Taylor expansions have the same formal order, while QBMAX reduces the truncation-error constants in the flat-boundary model and generally exhibits less convergence degradation in the reported experiments.
Comments38 pages, 21 figures, 3 tables
