Block preconditioning of systems of PDEs
In this chapter, we describe the implementation of block preconditioned Krylov solvers for systems of partial differential equations (PDEs) using CBC.Block and the Python interfaces of DOLFIN and Trilinos. We start by reviewing the abstract theory of constructing preconditioners by considering the differential operators as mappings in properly chosen Sobolev spaces, before giving a short overview of CBC.Block. We then present several examples, namely the Poisson problem, the Stokes problem, the time-dependent Stokes problem and finally a mixed formulation of the Hodge Laplacian.
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