Schur Complement-Schwarz DD Preconditioners for Non-stationary Darcy Flow Problems
The paper concerns development of highly parallelizable preconditioners for solving nonstationary Darcy flow problems. The discretization of the solved problem is done by mixed finite elements in space and by first order implicit Euler discretization in time. The systems with generalized saddle point matrices, which appear in each time step of the implicit Euler method, are then solved by FGMRES method with a block type preconditioner. Moreover, highly parallelizable, one-level additive Schwarz method is used for preconditioning of the velocity block. Both analysis and numerical experiment show that this application of the Schwarz method is highly efficient for a class of flow problems with parameters corresponding to many applications in geosciences.
The work was done within the projects LD15105 “Ultrascale computing in geosciences” and LQ1602 “IT4Innovations excellence in science” supported by the Ministry of Education, Youth and Sports of the Czech Republic. The third author acknowledges the support of the Czech Science Foundation (GACR) project no. 15-18274S. Authors would also like to thank the referees for their helpful comments.
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