A fast method for solving the heat equation by layer potentials
A fast method for solving the heat equation by layer potentials
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层位势求解热方程的快速方法
DOI：
10.1016/j.jcp.2006.11.001
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
J. Tausch
中科院分区：
文献类型：
--
作者：
J. Tausch
热方程的边界积分公式除了表面势之外还涉及时间卷积。如果M是时间步的数目，N是空间离散化的自由度的数目，则热势的直接计算涉及阶N2M2操作。本文介绍了一种基于时空热核切比雪夫插值的三维热势快速计算方法。计算复杂度为p4q2NM阶运算，其中p和q是空间和时间上多项式逼近的阶数。
Boundary integral formulations of the heat equation involve time convolutions in addition to surface potentials. If M is the number of time steps and N is the number of degrees of freedom of the spatial discretization then the direct computation of a heat potential involves order N2M2operations. This article describes a fast method to compute three-dimensional heat potentials which is based on Chebyshev interpolation of the heat kernel in both space and time. The computational complexity is order p4q2NM operations, where p and q are the orders of the polynomial approximation in space and time.