Parallel Computation of Stochastic Groundwater Flow
If a stochastic model is used to describe uncertainties, the physical system may be described by a stochastic partial differential equation (SPDE). A discretisation by a Galerkin ansatz with tensor-products of finite element functions and stochastic ansatz functions yields a large system of equations that can be efficiently solved by iterative methods. Due to its sheer size, parallel techniques are required, and we have implemented a ``hierarchical parallel solver'' for this: our solver uses a (possibly parallel) deterministic solver for the spatial discretisation. Coarser grained levels of parallelism are implemented by distributing the unknowns over the processors and by running different instances of the (possibly parallel) deterministic solver in parallel.