High Order Accurate Methods for the Evaluation of Layer Heat Potentials
High Order Accurate Methods for the Evaluation of Layer Heat Potentials
复制标题
层热势评估的高阶精确方法
DOI：
10.1137/080732389
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
L. Greengard
中科院分区：
文献类型：
--
作者：
Jing;L. Greengard
本文讨论了二维静止边界和运动边界上的单层和双层热势的数值计算。设计高阶方法的主要困难之一是热核的局部行为，它在时间上是弱奇异的，在空间上是快速衰减的。我们发现，标准的正交计划遭受公认的形式不准确，我们称之为“几何诱导刚度”，但规则的基础上产品集成的全热核时间是强大的。当结合以前开发的快速算法的“历史部分”的层电位的演变，扩散过程中的复杂，移动的几何形状可以准确地计算，并在接近最佳的时间。
We discuss the numerical evaluation of single and double layer heat potentials in two dimensions on stationary and moving boundaries. One of the principal difficulties in designing high order methods concerns the local behavior of the heat kernel, which is both weakly singular in time and rapidly decaying in space. We show that standard quadrature schemes suffer from a poorly recognized form of inaccuracy, which we refer to as “geometrically induced stiffness,” but that rules based on product integration of the full heat kernel in time are robust. When combined with previously developed fast algorithms for the evolution of the “history part” of layer potentials, diffusion processes in complex, moving geometries can be computed accurately and in nearly optimal time.