Domain Decomposition Method
The domain decomposition method for the solution of differential problems consists of dividing the computational domain into a set of subdomains in which the solution is calculated by taking into account some transmission conditions at the interfaces between the subdomains. This chapter addresses some usual Chebyshev domain decomposition methods for elliptic problems: influence matrix, iterative Dirichlet/Neumann, and spectral-element methods. The effect of the decomposition on the stability of time-dependent problems will be discussed. The application of the influence matrix method to the multidomain solution of the Stokes problem will be considered for both formulations: vorticity-streamfunction and velocity-pressure. Lastly, examples of application to the Navier-Stokes equations will be presented.
KeywordsDomain Decomposition Collocation Point Stokes Problem Domain Decomposition Method Homogeneous Boundary Condition
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