Browsing by Author "Du, Qiang"
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Item A Domain Decomposition Method for Parabolic Equations Based on Finite Elements(1990-10) Dawson, Clint N.; Du, QiangA domain decomposition procedure for solving parabolic partial differential equations is presented. In this scheme, a Galerkin finite element discretization on a rectangular mesh is used. Boundary values at subdomain interfaces are calculated by an implicit/explicit procedure. This solution serves as boundary data for fully implicit subdomain problems, which can be solved simultaneously. Thus, the scheme is non-iterative, and requires non-overlapping subdomains. Numerical results are presented for problems in two space dimensions.Item 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.Item A Finite Element Domain Decomposition Method for Parabolic(1990-10) Dawson, Clint N.; Du, Qiang