The optimal relaxation parameter for the SOR method applied to the Poisson equation in any space dimensions
نویسندگان
چکیده
منابع مشابه
The optimal relaxation parameter for the SOR method applied to the Poisson equation in any space dimensions
The finite difference discretization of the Poisson equation with Dirichlet boundary conditions leads to a large, sparse system of linear equations for the solution values at the interior mesh points. This problem is a popular and useful model problem for performance comparisons of iterative methods for the solution of linear systems. To use the successive overrelaxation (SOR) method in these c...
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The successive overrelaxation (SOR) method is an example of a classical iterative method for the approximate solution of a system of linear equations. Its iteration matrix depends on a relaxation parameter. There is no explicit formula for the optimal relaxation parameter in terms of properties of the system matrix of a general system matrix. However, for the classical model problem of a finite...
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15 صفحه اولOptimal relaxation parameter for the Uzawa Method
We consider the Uzawa method to solve the stationary Stokes equations discretized with stable finite elements. An iteration step consists of a velocity update un+1 involving the (augmented Lagrangian) operator −ν − ρ∇div with ρ ≥ 0, followed by the pressure update pn+1 = p − ανdiv un+1, the so-called Richardson update. We prove that the inf-sup constant β satisfies β ≤ 1 and that, if σ = 1 + ρν...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2009
ISSN: 0893-9659
DOI: 10.1016/j.aml.2008.03.028