Large scale simulation of pressure induced phase-field fracture propagation using Utopia

Abstract

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.

GQCP: The Ghent Quantum Chemistry Package

“…GQCP's focus has been to identify reusable software objects and, as a consequence, we have not attempted any forms of deliberate (i.e., hand-coded) parallelization, or targeted heterogeneous architectures specifically. By designing components that specifically separate the model (i.e., the abstract formulation of a solution) from computation (i.e., how the specifics are implemented under the hood), 5,17 we focus on the implementation of the high-level characteristics of the problem at hand, while delegating the optimization and hardware acceleration to experts in their respective fields. 4,17,61 Currently, we rely on underlying libraries such as Eigen 62 (with interfaces to BLAS implementations) or Libint2 22 (for molecular integral calculations) for achieving parallelization in particular subcalculations.…”

“…By designing components that specifically separate the model (i.e., the abstract formulation of a solution) from computation (i.e., how the specifics are implemented under the hood), 5,17 we focus on the implementation of the high-level characteristics of the problem at hand, while delegating the optimization and hardware acceleration to experts in their respective fields. 4,17,61 Currently, we rely on underlying libraries such as Eigen 62 (with interfaces to BLAS implementations) or Libint2 22 (for molecular integral calculations) for achieving parallelization in particular subcalculations. By relying on lower-level adapter-like modules, 61,[63][64][65][66][67][68][69][70] our APIs can, in principle, proceed to scale to the exascale regime.…”

“…5 Many software libraries are currently targeting modularity, 4,6-13 but with it comes the requirement of interoperability between different modules. In an attempt to overcome this obstacle, there has been a recent focus on providing programmatic communication through APIs (application programming interfaces) that specify instructions and transmit data, 4,11,[13][14][15][16][17][18][19][20][21] and some libraries have adopted support for custom-written plug-ins. 14,18,20,21 Another recent trend is allowing access to lower-level intermediates, which are typically the matrix representations of one-and two-electron integrals.…”

Nonlinear Field-split Preconditioners for Solving Monolithic Phase-field Models of Brittle Fracture

“…As a remedy, preconditioning strategies [39], such as multilevel or domain decomposition methods, can be employed. In the case of phase-field fracture simulations, the efficiency of various linear and nonlinear multilevel methods has been demonstrated by several authors, see for example [22,35,40,41,42,43,44]. In the context of domain decomposition methods, standard linear (block) Jacobi and additive Schwarz methods have been investigated in [40,44].…”

Globally Convergent Multilevel Training of Deep Residual Networks

“…In this work, we utilize the RMTR method, which is designed for solving non-convex optimization problems, as the ones considered in this work. By now, several variants of the RMTR method were proposed and investigated in the literature [53,75,68,48,50,15,49,76], but, to the best of our knowledge, the method has not been extended into stochastic settings nor it has been applied for training of deep neural networks.…”