Toward an Optimized Global-in-Time Schwarz Algorithm for Diffusion Equations with Discontinuous and Spatially Variable Coefficients, Part 1: The Constant Coefficients Case
نویسندگان
چکیده
In this paper we present a global-in-time non-overlapping Schwarz method applied to the one dimensional unsteady diffusion equation. We address specifically the problem with discontinuous diffusion coefficients, our approach is therefore especially designed for subdomains with heterogeneous properties. We derive efficient interface conditions by solving analytically the minmax problem associated with the search for optimized conditions in a Robin-Neumann case and in a two-sided Robin-Robin case. The performance of the proposed schemes are illustrated by numerical experiments.
منابع مشابه
Toward an Optimized Global-in-Time Schwarz Algorithm for Diffusion Equations with Discontinuous and Spatially Variable Coefficients, Part 2: the Variable Coefficients Case
This paper is the second part of a study dealing with the application of a global-in-time Schwarz method to a one dimensional diffusion problem defined on two non-overlapping subdomains. In the first part, we considered that the diffusion coefficients were constant and possibly discontinuous. In the present study, we address the problem for spatially variable coefficients with a discontinuity a...
متن کاملOptimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients
In this report we present a global-in-time non-overlapping Schwarz method applied to the one dimensional unsteady diffusion equation. We address specifically the problem with discontinuous diffusion coefficients, our approach is therefore especially designed for subdomains with heterogeneous properties. We derive efficient interface conditions by solving analytically the minmax problem associat...
متن کاملFinite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients
In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...
متن کاملOptimized Schwarz Waveform Relaxation for Porous Media Applications
Far field simulations of underground nuclear waste disposal involve a number of 11 challenges for numerical simulations: widely differing lengths and time-scales, 12 highly variable coefficients and stringent accuracy requirements. In the site under 13 consideration by the French Agency for Nuclear Waste Management (ANDRA), the 14 repository would be located in a highly impermeable geological l...
متن کاملAnalytical Solutions for Spatially Variable Transport-Dispersion of Non-Conservative Pollutants
Analytical solutions have been obtained for both conservative and non-conservative forms of one-dimensional transport and transport-dispersion equations applicable for pollution as a result of a non-conservative pollutant-disposal in an open channel with linear spatially varying transport velocity and nonlinear spatially varying dispersion coefficient on account of a steady unpolluted lateral i...
متن کامل