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Parallel multilevel solvers for coupled interface problems

用于耦合接口问题的并行多级求解器

基本信息

批准号：
237098861
负责人：
Professor Dr. Arnold Reusken
金额：
--
依托单位：
Institute of Computational Science
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2013
资助国家：
德国
起止时间：
2012-12-31 至 2017-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/237098861?language=en
关键词：
Parallel multilevel solvers coupled interface

项目摘要

Although during the last decades tremendous progress has been achieved in the area of parallel finite element simulations, the parallel solution of complex and constrained problems in, e. g., mechanics and fluid mechanics, still remains a challenging task. Usually, good scalability can be achieved relatively straightforwardly for homogeneous problems and structured meshes. Parallel simulations involving unstructured and adaptive meshes have also been successfully carried out, using a wide variety of solution methods, ranging from Krylov subspace methods to domain decomposition approaches or multilevel methods. The parallel treatment of constrained or heterogeneous problems, however, is still far from trivial.This is caused by the more complex mathematical structure of the discrete systems to be solved and by the more advanced data structures employed for assembling, solving, and parallel data exchange.An additional and up to now only scarcely addressed difficulty arises if time dependent interfaces have to be resolved, as is the case in, e.g., droplets impacting on a wall (liquid-gas flow) or crack propagation. These interfaces do not only influence the discretization, but also the robustness of iterative solution methods. Moreover, the special treatment of the interface poses a challenge for the parallel distribution of geometric objects across large scale machines.Efficient solution methods for these problems and their scalable and flexible implementations put a high demand not only on underlying methodology but also on the software used. In this project we will develop and implement parallel multilevel solvers for saddle point problems which are able to deal with time dependent interfaces in a robust manner. To this end, we will employ a new approach for the construction of multilevel hierarchies, which is based on non-standard transfer operators and solution dependent coarse grid spaces. As a basis for this work, one central goal of this project is the development and implementation of a stand-alone high level library for the management of distributed geometric objects. In order to foster the broad applicability of this library, we will use it within two different software and application environments, namely DROPS at RWTH and ObsLib++ at USI. Despite the seemingly different application fields, RWTH with two-phase flow and USI with computational mechanics and crack propagation, both applications lead to large saddle point problems, additionally complicated by the numerical treatment of time dependent interfaces. For this project strong expertise in the handling of time dependent interfacial constraints, multilevel methods and solvers for saddle point problems, non-standard transfer operators, and HPC software for efficient parallel data management is mandatory. The applicants at RWTH and USI together provide in a complementary manner this expertise, which motivated the formation of this research team and the Swiss-German cooperation.

虽然在过去的几十年里，并行有限元模拟领域取得了巨大的进展，但复杂约束问题的并行求解，例如，例如，在一个实施例中，力学和流体力学，仍然是一个具有挑战性的任务。通常，对于均匀问题和结构化网格，可以相对直接地实现良好的可扩展性。涉及非结构化和自适应网格的并行模拟也已成功地进行，使用各种各样的解决方案的方法，从Krylov子空间方法到区域分解方法或多级方法。然而，约束或异构问题的并行处理仍然远非微不足道。这是由待求解的离散系统的更复杂的数学结构以及用于组装、求解和并行数据交换的更高级的数据结构引起的。如果必须解决与时间相关的接口，则会出现另外的并且到目前为止几乎没有解决的困难，例如，液滴撞击壁（液-气流）或裂纹扩展。这些界面不仅影响离散化，而且影响迭代求解方法的鲁棒性。此外，接口的特殊处理对几何对象在大规模机器上的并行分布提出了挑战，这些问题的有效解决方法及其可扩展性和灵活性的实现不仅对底层方法学而且对所使用的软件提出了很高的要求。在这个项目中，我们将开发和实现并行多级求解鞍点问题，能够处理时间相关的接口，在一个强大的方式。为此，我们将采用一种新的方法来构建多级层次结构，这是基于非标准的传输算子和解决方案相关的粗网格空间。作为这项工作的基础，这个项目的一个中心目标是开发和实现一个独立的高层次库的分布式几何对象的管理。为了促进这个库的广泛适用性，我们将在两个不同的软件和应用程序环境中使用它，即RWTH的DROPS和USI的ObsLib++。尽管表面上不同的应用领域，RWTH与两相流和USI与计算力学和裂纹扩展，这两个应用程序导致大鞍点问题，另外复杂的数值处理的时间依赖接口。对于这个项目的强大的专业知识，在处理时间相关的界面约束，多层次的方法和鞍点问题，非标准传输运营商，高性能计算软件的解决方案，有效的并行数据管理是强制性的。RWTH和USI的申请人以互补的方式共同提供这种专业知识，这促使了该研究团队的形成和瑞士-德国合作。