PETSc Users Manual Revision 3.8

Balay, Satish; Abhyankar, Shrirang; Adams, Mark F.; Brown, Jeremy; Brune, Peter; Buschelman, K.; Dalcín, Lisandro; Eijkhout, Victor; Gropp, William; Kaushik, D.; Knepley, Matthew G.; May, Dave; McInnes, Lois Curfman; Munson, Todd; Rupp, Karl; Sanan, Patrick; Smith, Braeton J.; Zampini, Stefano; Zhang, H.

doi:10.2172/1409218

Cited by 404 publications

(397 citation statements)

References 0 publications

Supporting

Mentioning

392

Contrasting

Unclassified

Order By: Relevance

“…Instead, the minimization step with respect to α ∈ [α i−1 , 1] requires a box-constrained minimization algorithm. The code has been written using the FEniCS library [48,8] for finite elements and PETSc [15,13,14] for linear algebra and bound-constrained solvers. Of course, as the total energy is non convex, one cannot expect convergence of Algo.…”

Section: Numerical Solution Algorithmmentioning

confidence: 99%

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

Alessi

Marigo

Maurini

et al. 2018

International Journal of Mechanical Sciences

113

View full text Add to dashboard Cite

Plasticity and damage are two fundamental phenomena in nonlinear solid mechanics associated to the development of inelastic deformations and the reduction of the material stiffness. Alessi et al. [4] have recently shown, through a variational framework, that coupling a gradient-damage model with plasticity can lead to macroscopic behaviours assimilable to ductile and cohesive fracture. Here, we further expand this approach considering specific constitutive functions frequently used in phase-field models of brittle fracture. A numerical solution technique of the coupled elastodamage-plasticity problem, based on an alternate minimisation algorithm, is proposed and tested against semi-analytical results. Considering a one-dimensional traction test, we illustrate the properties of four different regimes obtained by a suitable tuning of few key constitutive parameters. Namely, depending on the relative yield stresses and softening behaviours of the plasticity and the damage criteria, we obtain macroscopic responses assimilable to (i) brittle fracturè a la Griffith, (ii) cohesive fractures of the Barenblatt or Dugdale type, and (iii) a sort of cohesive fracture including a depinning energy contribution. The comparisons between numerical and analytical results prove the accuracy of the proposed numerical approaches in the considered quasi-static time-discrete setting, but they also emphasise some subtle issues occurring during time-discontinuous evolutions.

show abstract

Section: Numerical Solution Algorithmmentioning

confidence: 99%

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

Alessi

Marigo

Maurini

et al. 2018

International Journal of Mechanical Sciences

113

View full text Add to dashboard Cite

show abstract

“…To evaluate the values at the cell surfaces, the Green-Gauss method is used and the momentum interpolation scheme (Murthy and Mathur, 1997) is applied. The code is parallelized with MPI (Message Passing Interface), and PETSc (Portable, Extensible Toolkit for Scientific Computation) (Balay et al, 2016) is used for standard solver functions (e.g., the stabilized version of the biconjugate gradient squared method with preconditioning by the block Jacobi method). The developed code has been verified by the method of manufactured solutions (further details provided in Jeon, 2015).…”

Section: Governing Equationsmentioning

confidence: 99%

Comparing thixotropic and Herschel–Bulkley parameterizations for continuum models of avalanches and subaqueous debris flows

Jeon

Hodges

2018

Nat. Hazards Earth Syst. Sci.

View full text Add to dashboard Cite

Abstract. Avalanches and subaqueous debris flows are two cases of a wide range of natural hazards that have been previously modeled with non-Newtonian fluid mechanics approximating the interplay of forces associated with gravity flows of granular and solid-liquid mixtures. The complex behaviors of such flows at unsteady flow initiation (i.e., destruction of structural jamming) and flow stalling (restructuralization) imply that the representative viscositystress relationships should include hysteresis: there is no reason to expect the timescale of microstructure destruction is the same as the timescale of restructuralization. The nonNewtonian Herschel-Bulkley relationship that has been previously used in such models implies complete reversibility of the stress-strain relationship and thus cannot correctly represent unsteady phases. In contrast, a thixotropic nonNewtonian model allows representation of initial structural jamming and aging effects that provide hysteresis in the stress-strain relationship. In this study, a thixotropic model and a Herschel-Bulkley model are compared to each other and to prior laboratory experiments that are representative of an avalanche and a subaqueous debris flow. A numerical solver using a multi-material level-set method is applied to track multiple interfaces simultaneously in the simulations. The numerical results are validated with analytical solutions and available experimental data using parameters selected based on the experimental setup and without post hoc calibration. The thixotropic (time-dependent) fluid model shows reasonable agreement with all the experimental data. For most of the experimental conditions, the HerschelBulkley (time-independent) model results were similar to the thixotropic model, a critical exception being conditions with a high yield stress where the Herschel-Bulkley model did not initiate flow. These results indicate that the thixotropic relationship is promising for modeling unsteady phases of debris flows and avalanches, but there is a need for better understanding of the correct material parameters and parameters for the initial structural jamming and characteristic time of aging, which requires more detailed experimental data than presently available.

show abstract

“…Our finite element code relies on the PETSc library [14] for the solution of linear systems of equations. Amongst other features, the PETSc library allows to solve saddle point problems like the incompressible Navier-Stokes equations by building block preconditioners, in what are called field split preconditioners.…”

Section: Solve For An Intermediate Velocityû N+1mentioning

confidence: 99%

An adaptive Fixed-Mesh ALE method for free surface flows

Baiges

Codina

Pont

et al. 2017

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain. This mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required. Some of the main ingredients of the formulation are the use of an Arbitrary-Lagrangian-Eulerian formulation for computing temporal derivatives, the use of stabilization terms for stabilizing convection, stabilizing the lack of compatibility between velocity and pressure interpolation spaces, and stabilizing the ill-conditioning introduced by the cuts on the background finite element mesh, and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments. Algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved. The method is tested in several numerical examples. The expected convergence rates both in space and time are observed. Smooth solution fields for both velocity and pressure are obtained (as a result of the contribution of the stabilization terms). Finally, a good agreement between the numerical results and the reference experimental data is obtained.

show abstract

PETSc Users Manual Revision 3.8

Abstract: vii

Cited by 404 publications

References 0 publications

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

Comparing thixotropic and Herschel–Bulkley parameterizations for continuum models of avalanches and subaqueous debris flows

An adaptive Fixed-Mesh ALE method for free surface flows

Contact Info

Product

Resources

About