三维高阶Nyström边界积分方程方法的全自动自适应参数选择
Fully Automated Adaptive Parameter Selection for 3-D High-order Nyström Boundary Integral Equation Methods
AI总结：
本文提出了一种全自动自适应参数选择的三维高阶Nyström边界积分方程求解器，通过自适应求积策略和计算方法，实现了高精度和鲁棒性，适用于复杂几何问题。
摘要：
我们提出了一种自适应Chebyshev基于边界积分方程（CBIE）求解器，用于电磁散射从光滑完美电导体（PEC）物体。所提出的方法通过引入（i）统一的自适应求积策略，自动选择近奇异相互作用距离，以及（ii）使用Gauss-Kronrod（h自适应）或Clenshaw-Curtis（p自适应）规则和奇异解消变量变换，自适应计算所有自奇异和近奇异预计算积分，以达到指定精度。在该框架内，探索了h自适应和p自适应方案，确保在广泛几何范围内保持高阶精度和鲁棒性，而不损失效率。对于典型和复杂CAD几何的数值结果表明，自适应求解器在精度和收敛率上与最优调优的固定网格CBIE实现相当，同时为电大、几何复杂的电磁问题提供了自动化和可扩展性。
英文摘要：
We present an adaptive Chebyshev-based Boundary Integral Equation (CBIE) solver for electromagnetic scattering from smooth perfect electric conductor (PEC) objects. The proposed approach eliminates manual parameter tuning by introducing (i) a unified adaptive quadrature strategy for automatic selection of the near-singular interaction distance and (ii) an adaptive computation of all self- and near-singular precomputation integrals to a prescribed accuracy using Gauss-Kronrod (h-adaptive) or Clenshaw-Curtis (p-adaptive) rules and singularity-resolving changes of variables. Both h-adaptive and p-adaptive schemes are explored within this framework, ensuring high-order accuracy and robustness across a broad range of geometries without loss of efficiency. Numerical results for canonical and complex CAD geometries demonstrate that the adaptive solver achieves accuracy and convergence rates comparable to optimally tuned fixed-grid CBIE implementations, while offering automation and scalability to electrically large, geometrically complex problems.
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