Speeding up parallel performance of porous media flow simulations using multiscale preconditioners

Recent studies in numerical simulations are directed to the development of optimized approximations in fluid dynamics, aiming at solving larger and more detailed problems. The Multiscale Robin Coupled Method (MRCM), a multiscale domain decomposition technique based on the imposition of Robin-type boundary condition on each subdomain, has shown accurate solutions taking advantage of parallel computing for modeling flows in petroleum reservoirs with high contrast in heterogeneity. MRCM allows a flexible choice of parameters and approximation spaces, and it shows excellent scalability in modern multicore architectures. In view of these advantages, we investigate MRCM as a preconditioner in the context of well-known iterative linear solvers, namely the Preconditioned Conjugate Gradient method. Numerical results demonstrate that, when combined with different smoothing methods, the MRCM preconditioner significantly reduces the number of iterations, providing a competitive, scalable alternative to algebraic multigrid to solve challenging problems.