Iterative methods

Abstract

AbstractAn in-depth treatment of iterative methods in linear algebra will not be given, because this is a huge subject, that would require a seprate volume. Instead, only a bird’s eye view of the subject will be given, providing ample references to the literature, paying particular attention to difficulties that are peculiar to the incompressible Navier-Stokes equations. The uninitiated reader who wants to use these methods is advised to consult the reference that we will quote. The algebraic systems that arise by finite volume discretization are extremely sparse, and also very large, beacause many gird points are required for accuracy. Therefore iterative methods are more efficient and demand far less storage than direct methods, especially in three dimensions. In two dimensions, direct methods using sparse matrix techniques can still be useful. Hence, we will confine ourselves to iterative methods, with one exception: the equation for the pressure correction can often be solved very efficiently by so-called fast Poission solvers, based on Fourier transformation and/or cyclic reduction.KeywordsFluid DynamicsComputational Fluid DynamicsIterative MethodFinite VolumeAlgebraic SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.