Domain Imbedding Methods for the Stokes Equations

Summary. We study direct and iterative domain imbedding methods for the Stokes equations on certain non-rectangular domains in two space dimensions. We analyze a continuous analog of numerical domain imbedding for bounded, smooth domains, and give an example of a simple numerical algorithm suggested by the continuous analysis. This algorithm is applicable for simply connected domains which can be covered by rectangular grids, with uniformly spaced grid lines in at least one coordinate direction. We also discuss a related FFT-based fast solver for Stokes problems with physical boundary conditions on rectangles, and present some numerical results. Subject Classifications: AMS(MOS) 65N20, 65F10; CR: G1.3, G1.8.

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