Zulian Patrick, Kopaničáková Alena, Nestola Maria Giuseppina Chiara, Fink Andreas, Fadel Nur Aiman, VandeVondele Joost, Krause Rolf
Euler Institute, Università della Svizzera italiana, Via la Santa 1, 6962 Lugano-Viganello, Switzerland.
Institute of Geochemistry and Petrology, ETH Zurich, Clausiusstrasse 25, 8092 Zurich, Switzerland.
CCF Trans High Perform Comput. 2021;3(4):407-426. doi: 10.1007/s42514-021-00069-6. Epub 2021 Jun 29.
Non-linear phase field models are increasingly used for the simulation of fracture propagation problems. The numerical simulation of fracture networks of realistic size requires the efficient parallel solution of large coupled non-linear systems. Although in principle efficient iterative multi-level methods for these types of problems are available, they are not widely used in practice due to the complexity of their parallel implementation. Here, we present Utopia, which is an open-source C++ library for parallel non-linear multilevel solution strategies. Utopia provides the advantages of high-level programming interfaces while at the same time a framework to access low-level data-structures without breaking code encapsulation. Complex numerical procedures can be expressed with few lines of code, and evaluated by different implementations, libraries, or computing hardware. In this paper, we investigate the parallel performance of our implementation of the recursive multilevel trust-region (RMTR) method based on the Utopia library. RMTR is a globally convergent multilevel solution strategy designed to solve non-convex constrained minimization problems. In particular, we solve pressure-induced phase-field fracture propagation in large and complex fracture networks. Solving such problems is deemed challenging even for a few fractures, however, here we are considering networks of realistic size with up to 1000 fractures.
非线性相场模型越来越多地用于模拟裂缝扩展问题。对实际尺寸的裂缝网络进行数值模拟需要高效并行求解大型耦合非线性系统。尽管原则上有适用于这类问题的高效迭代多级方法，但由于其并行实现的复杂性，它们在实际中并未得到广泛应用。在此，我们介绍Utopia，它是一个用于并行非线性多级求解策略的开源C++库。Utopia提供了高级编程接口的优势，同时提供了一个在不破坏代码封装的情况下访问底层数据结构的框架。复杂的数值过程可以用几行代码来表达，并由不同的实现、库或计算硬件进行评估。在本文中，我们研究了基于Utopia库的递归多级信赖域（RMTR）方法实现的并行性能。RMTR是一种全局收敛的多级求解策略，旨在解决非凸约束最小化问题。特别是，我们求解大型复杂裂缝网络中压力诱导的相场裂缝扩展问题。即使对于少数裂缝，解决此类问题也被认为具有挑战性，然而，在此我们考虑的是具有多达1000条裂缝的实际尺寸的网络。
