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Mathematics of Computation

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A finite difference domain decomposition algorithm for numerical solution of the heat equation

Authors: Clint N. Dawson, Qiang Du and Todd F. Dupont
Journal: Math. Comp. 57 (1991), 63-71
MSC: Primary 65N06; Secondary 65N55
MathSciNet review: 1079011
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Abstract: A domain decomposition algorithm for numerically solving the heat equation in one and two space dimensions is presented. In this procedure, interface values between subdomains are found by an explicit finite difference formula. Once these values are calculated, interior values are determined by backward differencing in time. A natural extension of this method allows for the use of different time steps in different subdomains. Maximum norm error estimates for these procedures are derived, which demonstrate that the error incurred at the interfaces is higher order in the discretization parameters.

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Keywords: Domain decomposition, parabolic equations, finite differences, parallel computing, spatially varying time step
Article copyright: © Copyright 1991 American Mathematical Society

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