Finite element (FE) analysis has the potential to offset much of the expensive experimental testing currently required to certify aerospace laminates. However, large numbers of degrees of freedom are necessary to model entire aircraft components whilst accurately resolving micro-scale defects. The new module dune-composites, implemented within DUNE by the authors, provides a tool to efficiently solve large-scale problems using novel iterative solvers. The key innovation is a preconditioner that guarantees a constant number of iterations regardless of the problem size. Its robustness has been shown rigorously in Spillane et al. (Numer. Math. 126, 2014) for isotropic problems. For anisotropic problems in composites it is verified numerically for the first time in this paper. The parallel implementation in DUNE scales almost optimally over thousands of cores. To demonstrate this, we present an original numerical study, varying the shape of a localised wrinkle and the effect this has on the strength of a curved laminate. This requires a high-fidelity mesh containing at least four layers of quadratic elements across each ply and interface layer, underlining the need for dunecomposites, which can achieve run times of just over 2 minutes on 2048 cores for realistic composites problems with 173 million degrees of freedom.
Scientists and engineers frequently rely on mathematical and numerical models to interpret observational data, forecast system behavior, and make decisions. However, unknown and neglected physics, limited and noisy data, and numerical error result in uncertain model predictions. The MIT Uncertainty Quantification library (MUQ) is a modular software framework for defining and solving uncertainty quantification problems involving complex models. MUQ is written in C++ but uses pybind11 (Jakob et al., 2017) to provide a nearly comprehensive Python interface. Users can access nearly all of MUQ's capabilities from either language.MUQ provides users many commonly used UQ tools and its modular design allows developers to easily modify, extend, and advance existing algorithms. For example, MUQ allows exact sampling of non-Gaussian distributions (e.g., Markov chain Monte Carlo and importance sampling), approximating computationally intensive forward models (e.g., polynomial chaos expansions and Gaussian process regression), working with integral covariance operators (e.g., Gaussian processes and Karhunen-Loève decompositions), and characterizing predictive uncertainties. The software is designed to support algorithm developers who want to easily construct new algorithms by exploiting a wide variety of existing algorithmic building blocks. Many UQ algorithms are model agnostic: Different physics-based or statistical models can be substituted into the algorithm based on the application. Therefore, MUQ enables users to quickly implement new models and exploit state-of-the art UQ algorithms.A suite of documented examples, including Gaussian process regression of Mauna Loa C02 observations, global sensitivity analysis of an Euler-Bernoulli beam, and a hierarchical Bayesian model of groundwater pump-test data, are provided to guide users through the process of implementing their own models and leveraging MUQ's UQ algorithms on quasi-realistic applications.
The key innovation in this paper is an open-source, high-performance iterative solver for high contrast, strongly anisotropic elliptic partial differential equations implemented within dune-pdelab. The iterative solver exploits a robust, scalable two-level additive Schwarz preconditioner, GenEO (Spillane et al. 2014). The development of this solver has been motivated by the need to overcome the limitations of commercially available modeling tools for solving structural analysis simulations in aerospace composite applications. Our software toolbox dune-composites encapsulates the mathematical complexities of the underlying packages within an efficient C++ framework, providing an application interface to our new high-performance solver. We illustrate its use on a range of industrially motivated examples, which should enable other scientists to build on and extend dune-composites and the GenEO preconditioner for use in their own applications. We demonstrate the scalability of the solver on more than 15,000 cores of the UK national supercomputer Archer, solving an aerospace composite problem with over 200 million degrees of freedom in a few minutes. This scale of computation brings composites problems that would otherwise be unthinkable into the feasible range. To demonstrate the wider applicability of the new solver, we also confirm the robustness and scalability of the solver on SPE10, a challenging benchmark in subsurface flow/reservoir simulation. Nature of problem:dune-composites is designed to solve anisotropic linear elasticity equations for anisotropic, heterogeneous materials, e.g. composite materials. To achieve this, our contribution also implements a new preconditioner in dune-pdelab. Solution method:The anisotropic elliptic partial differential equations are solved via the finite element method. The resulting linear system is solved via an iterative solver with a robust, scalable two-level overlapping Schwarz preconditioner: GenEO.
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