Customized Coarse Models for Highly Heterogeneous Materials

Dodwell, Tim; Sandhu, Anhadjeet; Scheichl, Robert

doi:10.1007/978-3-319-56397-8_72

Cited by 2 publications

(2 citation statements)

References 3 publications

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“…In fact, the GenEO coarse space provides and natural multiscale method. Current research [36] is aiming to provide this functionality as an embedded solution scheme within dune-composites.…”

Section: Discussion and Future Developmentsmentioning

confidence: 99%

High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites

Butler

Dodwell

Reinarz

et al. 2020

Computer Physics Communications

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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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Section: Discussion and Future Developmentsmentioning

confidence: 99%

High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites

Butler

Dodwell

Reinarz

et al. 2020

Computer Physics Communications

Self Cite

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“…The robustness is due to its good approximation properties for problems with highly heterogeneous material parameters. This is in fact of independent interest [2,11]. Details of our specific implementation of GenEO in DUNE are given in [25].…”

Section: Efficiency Of Dune-composites: Robust Iterative Solversmentioning

confidence: 99%

Dune-composites – A new framework for high-performance finite element modelling of laminates

Reinarz

Dodwell

Fletcher

et al. 2018

Composite Structures

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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.

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Customized Coarse Models for Highly Heterogeneous Materials

Cited by 2 publications

References 3 publications

High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites

High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites

Dune-composites – A new framework for high-performance finite element modelling of laminates

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