Multipole Accelerated Iterative Algorithms for the Rapid Solution of Three Dimensional Integral Equations, Including Adaptive Regridding and Higher-Order Elements

潜在问题的多极加速迭代方法将得到发展，包括自动离散误差控制，特别是：方法，包括高阶边界元素和自动细化低阶和高阶元素。两个具有已知解析解的测试问题，由诺伊曼和狄利克雷边界条件的混合物指定，将用于研究低阶方法并给出直接的数值误差校准。​利用上述结果，将开发几种具有不同“计算成本”的局部化方法，以达到具有指定误差范围的元素精化的目的。

Multipole-accelerated iterative methods for potential problems will be developed to include automatic discretization error control, in particular, methods to include higher-order boundary elements and automatically refine low-and high- order elements. Two test problems with known analytical solutions specified by a mixture of Neuman and Dirichlet boundary conditions will be used to investigate the low-order approach and to give a direct numerical error calibration. Utilizing the above results several localized approached will be developed with different "Computational Cost" for the purpose of element refinements with specified error bounds.