Non-overlapping domain-decomposition multiscale preconditioners for flows in porous media
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With the increasing computational power available in multicore distributed systems, the demand for high-resolution models for porous media flows, especially for reservoir simulation, is ever-increasing. This is an opportunity for the development of high-performance methods to speed up computations with great scalability. We present the development of preconditioners for iterative CG solvers applied to porous media flows in reservoir simulations. Our method is based on the Multiscale Robin Coupled Method (MRCM), which is a domain decomposition two-level finite element method based on the imposition of Robin-type boundary conditions in the skeleton of the decomposition. The method can asymptotically recover the solution of other well-known multiscale methods while introducing flexibility over the choice of interface spaces and Robin parameter adaptability. The proposed preconditioner is based on an algebraic version of the MRCM, which is combined with smoothing operators to yield a symmetric positive definite preconditioner, suitable for CG solvers when applied to the solution of pressure systems discretized by standard two-point flux approximation finite volume method. The preconditioner is implemented in a parallel high-performance code, taking advantage of the domain decomposition to compute multiscale basis functions in parallel that are further used inside the CG iterations. Robustness and scalability are assessed by simulating different porous-media flow benchmark problems, with results compared to consolidated preconditioning techniques such as the Algebraic Multigrid method. Weak and strong scaling tests demonstrate the performance of this newly proposed preconditioner.