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Page 4807 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
flow via discretely divergence-free finite element models.  ...  In this paper linear velocity and linear pressure elements are described for both two- and three- dimensional flow that always produce stable solutions provided the elements are assembled into simple macroelements  ... 

Bifurcation Analysis for Timesteppers [chapter]

Laurette S. Tuckerman, Dwight Barkley
2000 IMA Volumes in Mathematics and its Applications  
preconditioning.  ...  A collection of methods is presented to adapt a pre-existing time-stepping code to perform various bifurcation-theoretic tasks.  ...  t 0 and evolves it forward under the linear flow to give the perturbation at time t 0 + T .  ... 
doi:10.1007/978-1-4612-1208-9_20 fatcat:4d5nt7vh2fbubmxa23babdfjdy

Laplacian Preconditioning for the Inverse Arnoldi Method

Laurette S. Tuckerman
2015 Communications in Computational Physics  
We incorporate Laplacian preconditioning into the inverse Arnoldi method, using BiCGSTAB to solve the large linear systems.  ...  In addition, it is also readily available in most scientific calculations in the form of a Poisson solver or an implicit diffusive timestep.  ...  Stable and unstable steady states were previously obtained [24] by adapting a timestepping code to carry out Newton's method, using Laplacian preconditioning and BiCGSTAB to solve the resulting linear  ... 
doi:10.4208/cicp.281114.290615a fatcat:2lxua4s3jffllendjaeybgwhjy

Adaptive Time-Stepping for Incompressible Flow Part II: Navier–Stokes Equations

David A. Kay, Philip M. Gresho, David F. Griffiths, David J. Silvester
2010 SIAM Journal on Scientific Computing  
We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and  ...  In these experiments the accuracy of the linearized TR-AB2 algorithm is almost identical to a fully implicit version of the TR-AB2 algorithm.  ...  The time step sequence that resulted using this nonlinear approach turned out to be almost identical to that generated by our linearized method.  ... 
doi:10.1137/080728032 fatcat:os6lhbigxbfxraciawi23qy2ru

A framework for the development of implicit solvers for incompressible flow problems

David J. Silvester, Alex Bespalov, Catherine E. Powell
2012 Discrete and Continuous Dynamical Systems. Series S  
This survey paper reviews some recent developments in the design of robust solution methods for the Navier-Stokes equations modelling incompressible fluid flow.  ...  in the sense that they have uncertain input data.  ...  Some of the ideas in this paper were described in a series of four lectures given at the 12th School on Mathematical Theory in Fluid Mechanics held in Kacov, Czech Republic, May 27-June 3, 2011.  ... 
doi:10.3934/dcdss.2012.5.1195 fatcat:uvmvjlcogzarzixp3nt4i2rmgq

Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms

Layne T. Watson, Maria Sosonkina, Robert C. Melville, Alexander P. Morgan, Homer F. Walker
1997 ACM Transactions on Mathematical Software  
Three qualitatively different algorithmsordinary differential equation based, normal flow, quasi-Newton augmented Jacobian matrix-are provided for tracking homotopy zero curves, as well as separate routines  ...  ACKNOWLEDGMENT The authors gratefully acknowledge suggestions from Nick Gould, Tim Hopkins, John Reid, and a referee for significantly improving this article and the Fortran 90 code in HOMPACK90.  ...  The normal flow algorithm needs both kernels and Newton corrections, but again this last row ͑c t d͒ in (18) can be (almost) anything.  ... 
doi:10.1145/279232.279235 fatcat:7osen7wstfhthphbr274x5kp7y

Effect of Small-Scale Output Unsteadiness on Adjoint-Based Sensitivity

Joshua A. Krakos, David L. Darmofal
2010 AIAA Journal  
can vary significantly, due to linearizing about different solution iterates of the steady flow solver.  ...  in the outputs is small.  ...  Regardless, the mean flow near the airfoil appears almost identical to the stationary point, as in a comparison of Figs. 2a and 5c.  ... 
doi:10.2514/1.j050412 fatcat:3pg7j2bbvzezdbwnyknc6cpxxq

Efficient monolithic simulation techniques for the stationary Lattice Boltzmann equation on general meshes

T. Hübner, S. Turek
2009 Computing and Visualization in Science  
With special exact preconditioning by the transport part due to the short-characteristic upwinding, we obtain an efficient linear solver for transport dominated configurations (macroscopic Stokes regime  ...  In [11] the concept of the generalized mean intensity had been proposed for radiative transfer equations which we adapt here to the LBE, treating it as an analogous (semi-discretized) integro-differential  ...  Therein, we will also focus on unsteady flow problems, especially the Flow around Cylinder benchmark at Re = 100, and higher order time stepping schemes with large, resp., adaptive choice of ∆t.  ... 
doi:10.1007/s00791-009-0132-6 fatcat:7bmini6s7rc5ddryrkcrmlzd6i

Parallel Adaptive Solvers in Compressible PETSc-FUN3D Simulations* [chapter]

S. Bhowmick, D. Kaushik, L. McInnes, B. Norris, P. Raghavan
2006 Parallel Computational Fluid Dynamics 2005  
We demonstrate that this adaptive, polyalgorithmic approach leads to improvements in overall simulation time, is easily parallelized, and is scalable in the context of this large-scale computational fluid  ...  Solving a large, sparse linear system at each nonlinear iteration dominates the overall simulation time for this fully implicit strategy.  ...  This situation has motivated us to develop an adaptive, polyalgorithmic approach for linear solvers, which this paper discusses in the context of parallel, three-dimensional transonic Euler flow using  ... 
doi:10.1016/b978-044452206-1/50033-1 fatcat:rwl2maen5vh3rbkioynkev3jny

Algorithms for Solving Darcian Flow in Structured Porous Media

Michal Kuráž, Petr Mayer
2013 Acta Polytechnica  
DRUtES is a finite element solver for coupled nonlinear parabolic problems, namely the Richards equation with the dual porosity approach (modeling the flow of liquids in a porous medium).  ...  An algorithm for automatic time step selection is presented, as the proper time step length is crucial for achieving accuracy of the Euler time integration method.  ...  Due to the non-linearities involved in the constitutive mass function, see Figure 1 , an efficient and accurate time integration algorithm based on the Euler method should handle the selection of an adaptive  ... 
doaj:543a740cfe1f4636adc2d777a4573a1c fatcat:nmzf2bov4zaizld52rft6zbgtu

A new adaptive GMRES algorithm for achieving high accuracy

Maria Sosonkina, Layne T. Watson, Rakesh K. Kapania, Homer F. Walker
1998 Numerical Linear Algebra with Applications  
There are some applications, such as homotopy methods for high Reynolds number viscous flows, solid mechanics postbuckling analysis, and analog circuit simulation, where very high accuracy in the linear  ...  GMRES(k) is widely used for solving nonsymmetric linear systems.  ...  Specifically a FORTRAN 90 version of the normal flow subroutine FIXPNS was used, resulting in the (n + 1) × (n + 1) linear systems described in [12] -note that these are slightly different from the linear  ... 
doi:10.1002/(sici)1099-1506(199807/08)5:4<275::aid-nla131>;2-b fatcat:aa2l57utujbdtncrwrbhz6wqee

PCBDDC: A Class of Robust Dual-Primal Methods in PETSc

Stefano Zampini
2016 SIAM Journal on Scientific Computing  
The algorithm and the underlying nonoverlapping domain decomposition framework are described with a specific focus on their current implementation in the library.  ...  A class of preconditioners based on balancing domain decomposition by constraints methods is introduced in the Portable, Extensible Toolkit for Scientific Computation (PETSc).  ...  The author wishes to thank the KAUST Supercomputing Laboratory and Cray Inc. for early access to Shaheen and the Swiss National Supercomputing Centre (CSCS), in particular its director Thomas Schultess  ... 
doi:10.1137/15m1025785 fatcat:vpdnlsloqnf3nh46n475opr2lq

Efficient Preconditioners for Large Scale Binary Cahn-Hilliard Models

Petia Boyanova, Minh Do-Quang, Maya Neytcheva
2012 Computational Methods in Applied Mathematics  
We focus on diphasic flows and the construction and efficiency of a preconditioner for the algebraic systems arising from finite element discretizations in space and the -method in time.  ...  In this work we consider preconditioned iterative solution methods for numerical simulations of multiphase flow problems, modelled by the Cahn-Hilliard equation.  ...  for algebraic problems as arising in modelling of multiphase microstructures'.  ... 
doi:10.2478/cmam-2012-0001 fatcat:pfxdk36o7zdmvl77sam5hcvbze

Robust stabilised finite element solvers for generalised Newtonian fluid flows

Richard Schussnig, Douglas R.Q. Pacheco, Olaf Steinbach, Thomas-Peter Fries
2021 Journal of Computational Physics  
of velocity-pressure-viscosity system via extrapolation. • Adaptive timestepping via predictor-corrector approach or fractional step θ -scheme. • Fast physics-based preconditioned Krylov subspace solver  ...  Highlights • Stabilised finite element method for incompressible non-Newtonian fluid flow. • Preserve consistency for low-order pairs by using only first-order derivatives. • Linearization and decoupling  ...  Respecting these considerations, a novel solver for non-Newtonian fluid flows is presented combining lowerorder stabilised formulations with a modern physics-based preconditioned linear solver, adaptive  ... 
doi:10.1016/ fatcat:y4ri27foqjaelflxtij3q5hkzm

Alternative Solution Algorithms For Primal And Adjoint Incompressible Navier-Stokes

M. Oriani, G. Pierrot
2017 Zenodo  
preconditioning techniques.  ...  The second aspect in particular is extremely relevant in the context of adjoint-based optimisation, as evidence suggests that an adjoint system may be affected by convergence issues when the primal flow  ...  Of course the issue -which is schemedependent and may be less aggravating for traditional FV methods -could be circumvented via a more efficient preconditioning of the AL linear solves but, as we mentioned  ... 
doi:10.5281/zenodo.808279 fatcat:aw5glxau5zgbzospmzipoxpmtm
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