A fast method for solving the heat equation by layer potentials

✍ Scribed by Johannes Tausch

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 282 KB
• Volume: 224
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2006.11.001

✦ Synopsis

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 N 2 M 2 operations. 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 p 4 q 2 NM operations, where p and q are the orders of the polynomial approximation in space and time.