Efficient Parallel Scalable Matrix-Free 3D High-Order Finite Element Simulation of Neo-Hookean Compressible Hyperelasticity at Finite Strain

Mehraban, Arash; Brown, Jed; Tufo, Henry M.; Thompson, Jeremy; Shakeri, Rezgar; Regueiro, Richard A.

doi:10.1115/imece2021-70768

Cited by 2 publications

(3 citation statements)

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“…Nonetheless, we recall that the reduction strategy, acting at the algebraic level, works irrespectively of the chosen FE degree and type. On the other hand, matrix‐free methods, largely adopted in fluid mechanics, have been successfully applied in the context of cardiac electrophysiology, 68 as well as to problems arising in finite‐strain solid mechanics 69,70 . However, the investigation of these methods is beyond the scope of this work.…”

Section: Numerical Resultsmentioning

confidence: 99%

Efficient approximation of cardiac mechanics through reduced‐order modeling with deep learning‐based operator approximation

Cicci,

Fresca,

Manzoni

et al. 2023

Numer Methods Biomed Eng

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Reducing the computational time required by high‐fidelity, full‐order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient‐specific simulations into clinical practice. Indeed, while FOMs, such as those based on the finite element method, provide valuable information on the cardiac mechanical function, accurate numerical results can be obtained at the price of very fine spatio‐temporal discretizations. As a matter of fact, simulating even just a few heartbeats can require up to hours of wall time on high‐performance computing architectures. In addition, cardiac models usually depend on a set of input parameters that are calibrated in order to explore multiple virtual scenarios. To compute reliable solutions at a greatly reduced computational cost, we rely on a reduced basis method empowered with a new deep learning‐based operator approximation, which we refer to as Deep‐HyROMnet technique. Our strategy combines a projection‐based POD‐Galerkin method with deep neural networks for the approximation of (reduced) nonlinear operators, overcoming the typical computational bottleneck associated with standard hyper‐reduction techniques employed in reduced‐order models (ROMs) for nonlinear parametrized systems. This method can provide extremely accurate approximations to parametrized cardiac mechanics problems, such as in the case of the complete cardiac cycle in a patient‐specific left ventricle geometry. In this respect, a 3D model for tissue mechanics is coupled with a 0D model for external blood circulation; active force generation is provided through an adjustable parameter‐dependent surrogate model as input to the tissue 3D model. The proposed strategy is shown to outperform classical projection‐based ROMs, in terms of orders of magnitude of computational speed‐up, and to return accurate pressure‐volume loops in both physiological and pathological cases. Finally, an application to a forward uncertainty quantification analysis, unaffordable if relying on a FOM, is considered, involving output quantities of interest such as, for example, the ejection fraction or the maximal rate of change in pressure in the left ventricle.

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Section: Numerical Resultsmentioning

confidence: 99%

Efficient approximation of cardiac mechanics through reduced‐order modeling with deep learning‐based operator approximation

Cicci,

Fresca,

Manzoni

et al. 2023

Numer Methods Biomed Eng

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“…For a domain Ω 0 ⊂ R 3 with boundary ∂Ω 0 and the finite element space V ⊂ H 1 (Ω 0 ), the variational problem finds a solution u ∈ V such that [10], [21…”

Section: Mathematical Model a Variational Form For Hyperelasticitymentioning

confidence: 99%

“…In order to solve (2) using a Newton iteration algorithm, we need the Jacobian form of a (u, v) as [21] da (v, du; u)…”

Section: Mathematical Model a Variational Form For Hyperelasticitymentioning

confidence: 99%

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

Brown¹,

Barra²,

Beams³

et al. 2022

Preprint

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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 highorder methods greatly reduce the costs to reach engineering tolerances while enabling effective use of GPUs. 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 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.

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Efficient Parallel Scalable Matrix-Free 3D High-Order Finite Element Simulation of Neo-Hookean Compressible Hyperelasticity at Finite Strain

Cited by 2 publications

References 0 publications

Efficient approximation of cardiac mechanics through reduced‐order modeling with deep learning‐based operator approximation

Efficient approximation of cardiac mechanics through reduced‐order modeling with deep learning‐based operator approximation

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

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