On the generic parallelisation of iterative solvers for the finite element method

The numerical solution of partial differential equations frequently requires solving large and sparse linear systems. When using the Finite Element Method these systems exhibit a natural block structure that is exploited for efficiency in the “Iterative Solver Template Library” (ISTL). Based on existing sequential preconditioned iterative solvers we present an abstract parallelisation approach which clearly separates the parallelisation aspects from the data structures and solver algorithms by imposing an abstract consistency model onto the building blocks of the iterative solver components. This allows for supporting overlapping and non-overlapping domain decompositions as well as data parallel implementations of standard linear solvers.