On the Computational efficiency and implementation of block-iterative algorithms for nonlienar coupled problems

Abstract

In this paper we outline a general methodology for the solution of the system of algebraic equations arising from the discretization of the field equations governing coupled problems. In our examples, we shall consider that this discrete problem is obtained from the finite element discretization in space and the finite difference discretization in time. Our motivation is to preserve software modularity, to be able to use existing single field codes to solve more complex problems, and to exploit computer resources optimally, emulating parallel processing. To this end we deal with two well-known coupled problems of computational mechanics – the fluid-structure interaction problem and thermally driven flows of incompressible fluids. The possibility of coupling the block-iterative loop with the nonlinearity of the problems is demonstrated through numerical experiments, which suggest that even a mild nonlinearity drives the convergence rate of the complete iterative scheme, at least for the two problems considered here. The paper discusses the implementation of this alternative to the direct coupled solution, stating advantages and disadvantages. The need for on-line synchronized communication between the different codes used is also explained, together with the description of the master code who will control overall algorithm.