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Numerical solution of elliptic partial differential equations on parallel systems. (English) Zbl 1130.65106

Summary: The numerical solution of two-dimensional, linear and non-linear elliptic partial differential equations (PDEs) using two parallel algorithms namely Lawrie Sameh and domain decomposition is computed on three parallel architectures. The PDEs considered here describe the diffusion of a pollutant released from a constant source, variable source, and a point source.
In addition, an example with diffusion and chemical removal modelled by a non-linear PDE and three-dimensional diffusion equation is given. The parallel algorithms are implemented on three different systems (i) SUNFIRE (ii) IBM and (iii) PARAM. The scalability analysis is done to analyze the performance of both the algorithms on all three parallel systems.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J65 Nonlinear boundary value problems for linear elliptic equations
92D40 Ecology
65Y20 Complexity and performance of numerical algorithms
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