A fast method for solving the heat equation by layer potentials

Authors:
Johannes Tausch
Affiliations:
Southern Methodist University, Department of Mathematics, 209A Clements Hall, Dallas, TX 75275-0156, United States
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

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