The deal.II library, Version 9.1

Arndt, Daniel; Bangerth, Wolfgang; Clevenger, Thomas C.; Davydov, Denis; Fehling, Marc; García-Sánchez, Daniel; Harper, Graham; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Kynch, Ross; Maier, Matthias; Pelteret, Jean-Paul; Turcksin, Bruno; Wells, David

doi:10.1515/jnma-2019-0064

Cited by 143 publications

(101 citation statements)

References 36 publications

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“…For the performance of the matrix‐free operator evaluation, it is crucial to find a good intermediate point between precomputing everything (caching) and evaluating all the quantities on‐the‐fly. In order to obtain the gradients with respect to the current configuration, which appear in the tangent operator of the finite‐strain elasticity problem derived with a Lagrangian formulation, we use the MappingQEulerian class from the deal.II library. In addition to the standard mapping from the reference (isoparametric) element to the element in real space, this class computes the mapping to the current configuration given a displacement field.…”

Section: Matrix‐free Operator Evaluationmentioning

confidence: 99%

“…Note that the single instruction, multiple data (SIMD) vectorization in deal.II is applied at the finite element level, that is, the matrix‐free operator is applied simultaneously on several elements (called “blocks”). The main reason is that, apart from the point‐wise computation of the stresses and corresponding tangent operators, the operations are typically the same on all elements, as opposed to the operations within an element.For a given quadrature point, we simultaneously perform tensor evaluations and contractions on all elements.…”

Section: Matrix‐free Operator Evaluationmentioning

confidence: 99%

“…The discretized system of linear equations formulated in Section 3, in conjunction with the constitutive model described in Section 2.3, has been implemented usingdeal.II version 9.1, an open‐source finite element library. This library offers a number of paradigms by which to parallelize a finite‐element code, and as a member of the xSDK (Extreme‐scale Scientific Software Development Kit) ecosystem aims to support exascale computing.…”

Section: Description Of the Utilized Numerical Frameworkmentioning

confidence: 99%

“…Particular emphasis is on the tradeoff between computations at quadrature points versus precomputation with a higher memory access in terms of the representation of the tangent operator. The deal.II finite element library, which provides Message Passing iInterface (MPI) parallelization together with a generalized matrix‐free framework that incorporates SIMD vectorization and an interface to high‐performance MPI‐distributed matrix‐based libraries, is used for this study. In order to improve the convergence of iterative solvers, we also propose a method by which to construct level matrix‐free tangent operators and employ them to define a geometric multigrid preconditioner.…”

Section: Introductionmentioning

confidence: 99%

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A matrix‐free approach for finite‐strain hyperelastic problems using geometric multigrid

Davydov

Pelteret

Arndt

et al. 2020

Numerical Meth Engineering

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The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower than performing the arithmetic operations when solving the problem. In order to improve the performance of iterative solvers within the high-performance computing context, so-called matrix-free methods are widely adopted in the fluid mechanics community, where matrix-vector products are computed on-the-fly.To date, there have been few (if any) assessments into the applicability of the matrix-free approach to problems in solid mechanics. In this work, we perform an initial investigation on the application of the matrix-free approach to problems in quasi-static finite-strain hyperelasticity to determine whether it is viable for further extension. Specifically, we study different numerical implementations of the finite element tangent operator, and determine whether generalized methods of incorporating complex constitutive behavior might be feasible. In order to improve the convergence behavior of iterative solvers, we also propose a method by which to construct level tangent operators and employ them to define a geometric multigrid preconditioner. The performance of the matrix-free operator and the ge- * Corresponding author. ometric multigrid preconditioner is compared to the matrix-based implementation with an algebraic multigrid preconditioner on a single node for a representative numerical example of a heterogeneous hyperelastic material in two and three dimensions. We conclude that the application of matrix-free methods to finite-strain solid mechanics is promising, and that is it possible to develop numerically efficient implementations that are independent of the hyperelastic constitutive law.

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Section: Matrix‐free Operator Evaluationmentioning

confidence: 99%

Section: Matrix‐free Operator Evaluationmentioning

confidence: 99%

Section: Description Of the Utilized Numerical Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A matrix‐free approach for finite‐strain hyperelastic problems using geometric multigrid

Davydov

Pelteret

Arndt

et al. 2020

Numerical Meth Engineering

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“…In this section, we confirm our theoretical results with several numerical tests. We use the open-source finite element library deal.II [1] and specifically an adaptation of the multiphysics template [22].…”

Section: Numerical Examplesmentioning

confidence: 99%

Mathematical theory and simulations of thermoporoelasticity

Duijn

Mikelić

Wick

2020

Computer Methods in Applied Mechanics and Engineering

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Diffuse domain method for needle insertion simulations

Jerg

Austermühl

Roth

et al. 2020

Numer Methods Biomed Eng

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We present a new strategy for needle insertion simulations without the necessity of meshing. A diffuse domain approach on a regular grid is applied to overcome the need for an explicit representation of organ boundaries. A phase field function captures the transition of tissue parameters and boundary conditions are imposed implicitly. Uncertainties of a volume segmentation are translated in the width of the phase field, an approach that is novel and overcomes the problem of defining an accurate segmentation boundary. We perform a convergence analysis of the diffuse elastic equation for decreasing phase field width, compare our results to deformation fields received from conforming mesh simulations and analyze the diffuse linear elastic equation for different widths of material interfaces. Then, the approach is applied to computed tomography data of a patient with liver tumors. A three‐class U‐Net is used to automatically generate tissue probability maps serving as phase field functions for the transition of elastic parameters between different tissues. The needle tissue interaction forces are approximated by the absolute gradient of a phase field function, which eliminates the need for explicit boundary parameterization and collision detection at the needle‐tissue interface. The results show that the deformation field of the diffuse domain approach is comparable to the deformation of a conforming mesh simulation. Uncertainties of tissue boundaries are included in the model and the simulation can be directly performed on the automatically generated voxel‐based probability maps. Thus, it is possible to perform easily implementable patient‐specific elastomechanical simulations directly on voxel data.

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The deal.II library, Version 9.1

Abstract: Abstract This paper provides an overview of the new features of the finite element library deal.II, version 9.1.

Cited by 143 publications

References 36 publications

A matrix‐free approach for finite‐strain hyperelastic problems using geometric multigrid

A matrix‐free approach for finite‐strain hyperelastic problems using geometric multigrid

Mathematical theory and simulations of thermoporoelasticity

Diffuse domain method for needle insertion simulations

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