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Santiago Badia, "On highly scalable implicit solvers for multiphysics"
The simulation of many problems in computational mechanics and physics require the use of implicit solvers. Implicit solvers can deal with steady problems and can solve transient problems without the need to reduce the time step size in order to satisfy a stringent CFL condition. This last situation is particularly important when dealing with multiphysics problems involving very different time scales but one is only interested in slow time scales. Irremediably, implicit solvers require to solve linear systems. Increasingly more realistic simulations of complex physics and engineering three-dimensional phenomena end up with very large linear systems, which can easily reach 1010 unknowns. And some other applications, like full grid-based direct numerical simulations of plasma physics via kynetic models, are still out of the reach. The only way to deal with these large scale simulations is to make use of distributed-memory platforms in an efficient way. Current petascale supercomputers involve tens of thousands of interconnected processors. The design of robust linear solvers in these ranges and in the forthcoming exascale machines of the future pose a complicated problem in terms of mathematics and implementation issues.
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