arXiv subjects

Karen Stengel

Publications and source records attributed to Karen Stengel.

3 recordsLinked to original sources

arXiv2026

Matrix-free phase-field modeling of fracture in micromechanical testing simulations of inelastic materials

Resolving steep damage gradients across diffuse cracks in the phase-field modeling of fracture favors the use of high-order finite elements, for which matrix-free methods can provide superior performance and scalability. Here, we implement the Peric & Dettmer constitutive framework for visco-elastoplastic materials in an open source solid mechanics library supporting matrix-free operators for high-order finite elements with p-multigrid preconditioning on GPUs. We introduce a rheological fracture element assembled in series so that inelastic and fracture properties can appear to affect each other only at homogenization length scales. Numerical simulations of tensile and compressive tests are conducted for synthetic particle-matrix microstructures on an El Capitan high performance computing prototype. Results are shown to reproduce characteristic inelastic responses and crack propagation patterns.

physics.comp-ph↗

arXiv2022

Performance Portable Solid Mechanics via Matrix-Free $p$-Multigrid

Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models and numerical experiments to demonstrate that high-order methods greatly reduce the costs to reach engineering tolerances while enabling effective use of GPUs; these data structures also offer up to 2x benefit for linear elements. We demonstrate the reliability, efficiency, and scalability of matrix-free $p$-multigrid methods with algebraic multigrid coarse solvers through large deformation hyperelastic simulations of multiscale structures. We investigate accuracy, cost, and execution time on multi-node CPU and GPU systems for moderate to large models (millions to billions of degrees of freedom) using AMD MI250X (OLCF Crusher), NVIDIA A100 (NERSC Perlmutter), and V100 (LLNL Lassen and OLCF Summit), resulting in order of magnitude efficiency improvements over a broad range of model properties and scales. We discuss efficient matrix-free representation of Jacobians and demonstrate how automatic differentiation enables rapid development of nonlinear material models without impacting debuggability and workflows targeting GPUs. The methods are broadly applicable and amenable to common workflows, presented here via open source libraries that encapsulate all GPU-specific aspects and are accessible to both new and legacy code, allowing application code to be GPU-oblivious without compromising end-to-end performance on GPUs.

cs.MS↗

arXiv2021

Adversarial sampling of unknown and high-dimensional conditional distributions

Many engineering problems require the prediction of realization-to-realization variability or a refined description of modeled quantities. In that case, it is necessary to sample elements from unknown high-dimensional spaces with possibly millions of degrees of freedom. While there exist methods able to sample elements from probability density functions (PDF) with known shapes, several approximations need to be made when the distribution is unknown. In this paper the sampling method, as well as the inference of the underlying distribution, are both handled with a data-driven method known as generative adversarial networks (GAN), which trains two competing neural networks to produce a network that can effectively generate samples from the training set distribution. In practice, it is often necessary to draw samples from conditional distributions. When the conditional variables are continuous, only one (if any) data point corresponding to a particular value of a conditioning variable may be available, which is not sufficient to estimate the conditional distribution. This work handles this problem using an a priori estimation of the conditional moments of a PDF. Two approaches, stochastic estimation, and an external neural network are compared here for computing these moments; however, any preferred method can be used. The algorithm is demonstrated in the case of the deconvolution of a filtered turbulent flow field. It is shown that all the versions of the proposed algorithm effectively sample the target conditional distribution with minimal impact on the quality of the samples compared to state-of-the-art methods. Additionally, the procedure can be used as a metric for the diversity of samples generated by a conditional GAN (cGAN) conditioned with continuous variables.

stat.ML↗