The deal.II library, version 8.5

Arndt, Daniel; Bangerth, Wolfgang; Davydov, Denis; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Maier, Matthias; Pelteret, Jean Paul; Turcksin, Bruno; Wells, David

doi:10.1515/jnma-2017-0058

Cited by 144 publications

(149 citation statements)

References 12 publications

Supporting

Mentioning

144

Contrasting

Unclassified

Order By: Relevance

“…The algorithm is implemented in the C++ programming language using the object-oriented finite element library deal.II. 36 Our implementation computes all matrix-vector products and right-hand side vectors by matrix-free operator evaluation based on fast integration, using the high-performance framework developed in the works of Kronbichler and Kormann. 9,10 The integrals over cells and faces are computed by sum factorization specialized for quadrilateral and hexahedral cell shapes.…”

Section: Matrix-free Evaluation Of Dg-discretized Operatorsmentioning

confidence: 99%

Efficiency of high‐performance discontinuous Galerkin spectral element methods for under‐resolved turbulent incompressible flows

Fehn

Wall

Kronbichler

2018

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

Summary The present paper addresses the numerical solution of turbulent flows with high‐order discontinuous Galerkin methods for discretizing the incompressible Navier‐Stokes equations. The efficiency of high‐order methods when applied to under‐resolved problems is an open issue in the literature. This topic is carefully investigated in the present work by the example of the three‐dimensional Taylor‐Green vortex problem. Our implementation is based on a generic high‐performance framework for matrix‐free evaluation of finite element operators with one of the best realizations currently known. We present a methodology to systematically analyze the efficiency of the incompressible Navier‐Stokes solver for high polynomial degrees. Due to the absence of optimal rates of convergence in the under‐resolved regime, our results reveal that demonstrating improved efficiency of high‐order methods is a challenging task and that optimal computational complexity of solvers and preconditioners as well as matrix‐free implementations are necessary ingredients in achieving the goal of better solution quality at the same computational costs already for a geometrically simple problem such as the Taylor‐Green vortex. Although the analysis is performed for a Cartesian geometry, our approach is generic and can be applied to arbitrary geometries. We present excellent performance numbers on modern cache‐based computer architectures achieving a throughput for operator evaluation of 3·108 up to 1·109 DoFs/s (degrees of freedom per second) on one Intel Haswell node with 28 cores. Compared to performance results published within the last five years for high‐order discontinuous Galerkin discretizations of the compressible Navier‐Stokes equations, our approach reduces computational costs by more than one order of magnitude for the same setup.

show abstract

Section: Matrix-free Evaluation Of Dg-discretized Operatorsmentioning

confidence: 99%

Efficiency of high‐performance discontinuous Galerkin spectral element methods for under‐resolved turbulent incompressible flows

Fehn

Wall

Kronbichler

2018

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this section we present numerical results that verify the theoretical results from the previous sections. We used deal.II finite element library [5] for the implementation of the method. We consider a homogeneous and isotropic body,…”

Section: Numerical Resultsmentioning

confidence: 99%

A Multipoint Stress Mixed Finite Element Method for Elasticity on Simplicial Grids

Ambartsumyan¹,

Khattatov²,

Nordbotten³

et al. 2020

SIAM J. Numer. Anal.

View full text Add to dashboard Cite

We develop a multipoint stress mixed finite element method for linear elasticity with weak stress symmetry on quadrilateral grids, which can be reduced to a symmetric and positive definite cell centered system. The method is developed on simplicial grids in [4]. The method utilizes the lowest order Brezzi-Douglas-Marini finite element spaces for the stress and the trapezoidal quadrature rule in order to localize the interaction of degrees of freedom, which allows for local stress elimination around each vertex. We develop two variants of the method. The first uses a piecewise constant rotation and results in a cell-centered system for displacement and rotation. The second uses a continuous piecewise bilinear rotation and trapezoidal quadrature rule for the asymmetry bilinear form. This allows for further elimination of the rotation, resulting in a cell-centered system for the displacement only. Stability and error analysis is performed for both methods. First-order convergence is established for all variables in their natural norms. A duality argument is employed to prove second order superconvergence of the displacement at the cell centers. Numerical results are presented in confirmation of the theory.

show abstract

“…The governing equations (5) to (7) are solved numerically with finite-element method (FEM) using a C++ FEM software library deal.II [35,36]. The primary variables are the two velocity components (u r , u z ), pressure p, and structure parameter λ.…”

Section: Methodsmentioning

confidence: 99%

The non-homogeneous flow of a thixotropic fluid around a sphere

Kim

Park

2020

Applied Mathematical Modelling

View full text Add to dashboard Cite

The non-homogeneous flow of a thixotropic fluid around a settling sphere is explored. A four-parameter Moore model is used for a generic thixotropic fluid and discontinuous Galerkin method is employed to solve the structure-kinetics equation coupled with the conservation equations of mass and momentum. Depending on Weissenberg number (Wi), flow solutions are divided into three different regimes, which are attributed to an interplay of three competing factors: Brownian structure recovery, shear-induced structure breakdown, and structure refilling effect due to convection. At small Wi ( 1), where the Brownian structure recovery is predominant, thixotropic effect is negligible and flow solutions are not too dissimilar to that of Newtonian fluid. As Wi increases, a remarkable structural gradient is observed and the structure profile around the settling sphere is determined by the balance of all three competing factors. For large enough Wi ( 1), where the Brownian structure recovery becomes negligible, the balance between shear-induced structure breakdown and refilling effect by convection plays a decisive role in determining flow profile. To quantify the interplay of three factors, the drag coefficient Cs of the sphere is investigated for ranges of Wi. With this framework, the effect of destruction parameter, confinement ratio, and possible nonlinearity in the model-form on the non-homogeneous flow of a thixotropy fluid have been discussed. arXiv:1908.04993v1 [physics.flu-dyn]

show abstract

The deal.II library, version 8.5

Abstract: This paper provides an overview of the new features of the finite element library deal.II version 8.5.

Cited by 144 publications

References 12 publications

Efficiency of high‐performance discontinuous Galerkin spectral element methods for under‐resolved turbulent incompressible flows

Efficiency of high‐performance discontinuous Galerkin spectral element methods for under‐resolved turbulent incompressible flows

A Multipoint Stress Mixed Finite Element Method for Elasticity on Simplicial Grids

The non-homogeneous flow of a thixotropic fluid around a sphere

Contact Info

Product

Resources

About