TY - JOUR
T1 - A fast algorithm for the evaluation of heat potentials
AU - Greengard, Leslie
AU - Strain, John
PY - 1990/12
Y1 - 1990/12
N2 - 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(N2M2) 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.
AB - 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(N2M2) 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.
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U2 - 10.1002/cpa.3160430802
DO - 10.1002/cpa.3160430802
M3 - Article
AN - SCOPUS:84990587865
VL - 43
SP - 949
EP - 963
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
SN - 0010-3640
IS - 8
ER -