Efficient multilevel solvers and high performance computing techniques for the finite element simulation of large-scale elasticity problems

Hilmar Wobker, Technische Universität Dortmund, Technische Universität Dortmund
In the simulation of realistic solid mechanical problems, linear equation systems with hundreds of million unknowns can arise. For the efficient solution of such systems, parallel multilevel methods are mandatory that are able to exploit the capabilities of modern hardware technologies. The finite element and solution toolbox FEAST, which is designed to solve scalar equations, pursues exactly this goal. It combines hardware-oriented implementation techniques with a multilevel domain
more » ... domain decomposition method called ScaRC that achieves high numerical and parallel efficiency. In this thesis a concept is developed to solve multivariate elasticity problems based on the FEAST library. The general strategy is to reduce the solution of multivariate problems to the solution of a series of scalar problems. This approach facilitates a strict separation of 'low level' scalar kernel functionalities (in the form of the FEAST library) and 'high level' multivariate application code (in the form of the elasticity problem), which is very attractive from a software-engineering point of view: All efforts to improve hardware-efficiency and adaptations to future technology trends can be restricted to scalar operations, and the multivariate application automatically benefits from these enhancements. In the first part of the thesis, substantial improvements of the scalar ScaRC solvers are developed, which are then used as essential building blocks for the efficient solution of multivariate elasticity problems. Extensive numerical studies demonstrate how the efficiency of the scalar FEAST library transfers to the multivariate solution process. The solver strategy is then applied to treat nonlinear problems of finite deformation elasticity. A line-search method is used to significantly increase the robustness of the Newton-Raphson method, and different strategies are compared how to choose the accuracy of the linear system solves within the nonlinear iteration. In order to treat the important class of (nearly) incompressible material, a mixed [...]
doi:10.17877/de290r-497 fatcat:77ah3ualdverxdvv6l3asogpmq