In this thesis we study efficient parallel iterative solution algorithms for multiphysics problems. In particular, we consider fluid structure interaction (FSI) problems, a type of multiphysics problem in which a fluid and a deformable solid interact.All computations were performed in OomphLib, a finite element library for the simulation of multiphysics problems. In OomphLib, the constituent problems in a multiphysics problem are coupled monolithically, and the resulting system of nonlinear equations solved with Newton's method. This requires the solution of sequences of large, sparse linear systems, for which optimal solvers are essential. The linear systems arising from the monolithic discretisation of multiphysics problems are natural candidates for solution with blockpreconditioned Krylov subspace methods.We developed a generic framework for the implementation of block preconditioners within OomphLib. Furthermore the framework is parallelised to facilitate the efficient solution of very large problems. This framework enables the reuse of all of OomphLib's existing linear algebra infrastructure and preconditioners (including block preconditioners). We will demonstrate that a wide range of block preconditioners can be seamlessly implemented in this framework, leading to optimal iterative solvers with good parallel scaling.We concentrate on the development of an effective preconditioner for a FSI problem formulated in an arbitrary Lagrangian Eulerian (ALE) framework with pseudosolid node updates (for the deforming fluid mesh). We begin by considering the pseudosolid subsidiary problem; the deformation of a solid governed by equations of large displacement elasticity, subject to a prescribed boundary displacement imposed with Lagrange multiplier. We present a robust, optimal, augmentedLagrangian type preconditioner for the resulting saddlepoint linear system and prove analytically tight bounds for the spectrum of the preconditioned operator with respect to the discrete problem size.This pseudosolid preconditioner is incorporated into a block preconditioner for the full FSI problem. One key feature of the FSI preconditioner is that existing optimal single physics preconditioners (such as the well known NavierStokes Least Squares Commutator preconditioner) can be employed to approximately solve the linear systems associated with the constituent subproblems. We evaluate its performance on selected 2D and 3D problems. The preconditioner is optimal for most problems considered. In cases when suboptimality is detected, we explain the reasons for such behavior and suggest potential improvements.
Date of Award  31 Dec 2011 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Matthias Heil (Supervisor) & Milan Mihajlovic (Supervisor) 

 block preconditioners
 preconditioners
 parallel computations
 multiphysics problems
 fluidstructure interaction problems
Parallel Block Preconditioning for MultiPhysics Problems
Muddle, R. (Author). 31 Dec 2011
Student thesis: Phd