Postdoc: To Develop and Analyze Efficient Parallel Iterative Solvers with Effective Preconditioners that Arise in Solid-Liquid Computational Simulations

本研究的目标有两个：开发和分析在固液计算模拟中出现的具有有效前置条件的高效并行迭代求解器；并为NSF大挑战粒子模拟项目并行化固体-液体计算模拟。在颗粒模拟中，固体颗粒在流动流体中的运动采用任意拉格朗日-欧拉有限元方法，并采用运动颗粒拟合的非结构网格。这个公式的结果是一个非线性方程组，在每个时间步用修正牛顿法求解。采用修正牛顿法得到非对称线性系统，用预条件GMRES迭代法求解。本研究的第一个重点是通过开发鲁棒和有效的并行预条件来迭代求解这些非对称线性系统。此外，将开发一个并行数值算法库，以使用牛顿方法的变体来求解非线性代数系统，并使用预置迭代方法来求解稀疏非对称线性系统。该图书馆将在一系列并行机器上便携，并将放在公共领域。并行化将使用Oplus （Oxford Parallel Library for Unstructured Solvers）中开发的通用方法和优化技术进行。

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).