Browsing by Author "Dupont, T.F."

Now showing 1 - 3 of 3
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    A Finite Difference Domain Decomposition Algorithm for Numerical Solution of the Heat Equation
    (1990-10) Dawson, Clint N.; Du, Qiang; Dupont, T.F.
    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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    Several Procedures for Operator-Based Averaging for Elliptic Equations
    (1992-08) Dawson, C.N.; Dupont, T.F.
    Numerical procedures are discussed for constructing averaged coefficients for elliptic differential operators. These procedures are intended for problems where the coefficients vary on a scale finer than can be resolved by a reasonable computational grid. Numerical methods for calculating locally averaged coefficients using mixed and Galerkin finite elements are presented. These methods involve solving local elliptic problems either to determine a pseudo-coefficient or as part of the overall solution procedure. The local problems are independent and can be solved in parallel. The procedures are formulated and numerical results demonstrating their performance are presented.
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