1990/12/01 by Leslie Greengard, John Strain · 9 citations
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Model Reduction and Neural Networks #Numerical methods in engineering
paper · doi:10.1002/cpa.3160430802
Abstract Numerical methods for solving the heat equation via potential theory have been hampered by the high cost of evaluating heat potentials. When M points are used in the discretization of the boundary and N time steps are computed, an amount of work of the order O ( N 2 M 2 ) has traditionally been required. In this paper, we present an algorithm which requires an amount of work of the order O ( NM ), and we observe speedups of five orders of magnitude for large‐scale problems. Thus, the method makes it possible to solve the heat equation by potential theory in practical situations.