The goals of this research are two-fold: to develop and analyze efficient parallel iterative solvers with effective preconditioners that arise in solid-liquid computational simulations; and to parallelize a solid-liquid computational simulation for the NSF Grand Challenge Particle Simulation Project. In this particle simulation, the motion of solid particles in flowing fluid is carried out using an Arbitrary Lagrangian-Eulerian finite element method with a moving particle-fitted unstructured grid. This formulation results in a nonlinear system of equations that is solved at each time step with a modified-Newton method. Using the modified-Newton method gives rise to nonsymmetric linear systems that are solved with a preconditioned GMRES iterative method. The first focus of this research is to efficiently solve these nonsymmetric linear systems by developing robust and effective parallel preconditioners for iterative solving. Moreover, a library of parallel numerical algorithms will be developed to solve nonlinear algebraic systems using variants of Newton's method and to solve sparse nonsymmetric linear systems using preconditioned iterative methods. The library will be portable across a range of parallel machines and will be placed on the public domain. The parallelization will be carried out using the general methodology and optimization techniques developed in Oplus (Oxford Parallel Library for Unstructured Solvers).
