Andreas Keese

Hierarchical parallel solution of stochastic systems

Publisher Summary Uncertainty in a physical system can be described by a stochastic model, resulting in a stochastic partial differential equation (SPDE). Discretization by a Galerkin “ansatz” with tensor products of finite elements and stochastic “ansatz” functions yields a large system of equations that can be efficiently solved by iterative methods, which can take advantage of parallel techniques. The parallel solver uses the spatial discretization by a (possibly parallel) deterministic solver. A coarser-grained level of parallelism is achieved by distributing the unknowns and by running a set of deterministic solvers in parallel. The chapter concludes that the framework implemented discretizes only the stochastic dimension and uses deterministic software in a black-box fashion for the discretization of the spatial problem.