Systems of PDEs and Block Preconditioning

We consider several systems of PDEs and how block preconditioners can be formulated. Implementation of block preconditioners in Diffpack is in particular explained. We emphasize object-oriented design, where a standard simulator is developed and debugged before being extended with efficient block preconditioners in a derived class. Optimal preconditioners are applied to the Stokes problem, the mixed formulation of the Poisson equation, and the Bidomain model for the electrical activity in the heart.

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