Parallel 3D Finite Element Analysis of Coupled Problems

Abstract

Steady advances in computer power have enabled researchers to consider tackling increasingly complex problems. In the academic community, current focus is on multiscale modelling and multiphysics. The aim is for simulation to be more realistically representative of real world processes. This paper considers the simulation of coupled problems involving more than one physical process, multiphysics. In particular, the authors present some ideas and experiences regarding the use of the finite element method and parallel computers to solve 3D coupled problems. In the literature, two main approaches have been used to solve coupled problems. These are sometimes referred to as (i) fully coupled modelling and (ii) un-coupled multi-physics. Both methods have their advantages and disadvantages. In the paper, the authors discuss some of the issues that should be considered when selecting a particular strategy, to ensure computational efficiency. Particular attention is given to an example from the field of magnetohydrodynamics: three dimensional steady state flow in a perfectly insulated rectangular duct. The magnetohydrodynamics example involves solving a system in which both magnetic and hydrodynamic forces influence the behaviour of the fluid. Visualisation of the problem, using streamlines to represent fluid flow (Figure 1) shows that a three dimensional representation is essential to capture the full complexity of the flow. A fully coupled solution strategy is presented in which the full system is represented by a single “stiffness” matrix and solved by a single computer program. A parallel implementation of an element-by-element variant of BiCGStab(l) is used to solve the equations, demonstrating the efficient use of up to 128 processors.