Finite element analysis of convection dominated reaction–diffusion problems

Galeão, Augusto C. N. R.; Almeida, Regina C.; Malta, Sandra M. C.; Loula, Abimael F. D.

doi:10.1016/j.apnum.2003.10.002

Cited by 45 publications

(19 citation statements)

References 32 publications

(53 reference statements)

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“…The most successful approaches are the streamline upwind Petrov Galerkin method, also known as streamline diffusion finite element method , the Galerkin least squares approximation , and the Douglas-Wang method. We are not concerned in this work by the stabilization techniques, we refer the reader to a extensive literature work of [12,20,24,27,29].…”

Section: Effect Of the Péclet Numbermentioning

confidence: 99%

Parallel algebraic hybrid solvers for large 3D convection-diffusion problems

Giraud

Haidar

2008

Numer Algor

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In this paper we study the parallel scalability of variants of an algebraic additive Schwarz preconditioner for the solution of large three dimensional convection diffusion problems in a non-overlapping domain decomposition framework. To alleviate the computational cost, both in terms of memory and floating-point complexity, we investigate variants based on a sparse approximation or on mixed 32-and 64-bit calculation. The robustness and the scalability of the preconditioners are investigated through extensive parallel experiments on up to 2,000 processors. Their efficiency from a numerical and parallel performance view point are reported.Keywords Parallel iterative solution of large sparse linear system · Preconditioned Krylov subspace methods · Algebraic additive Schwarz preconditioner · Non-overlapping domain decomposition · Mixed arithmetic algorithms · Massively parallel processing

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Section: Effect Of the Péclet Numbermentioning

confidence: 99%

Parallel algebraic hybrid solvers for large 3D convection-diffusion problems

Giraud

Haidar

2008

Numer Algor

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“…See Hughes, Mallet and Mizukami [86] and Hughes and Mallet [85] for the initial conceptions. Numerous improved variants have been developed subsequently by other researchers (see, e.g., [28,[52][53][54][55]59,64,141]). Within the framework of the multiscale discontinuous Galerkin method, the local problem provides a vehicle for incorporating desired features.…”

Section: Discussionmentioning

confidence: 99%

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

Shadid¹,

Lehoucq²,

Christon³

et al. 2004

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This report is a collection of documents written as part of the Laboratory Directed Research and Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering: The Variational Multiscale Method and Interscale Transfer Operators. We present developments in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC) multiscale, includes problems that allow application of the same continuum model at all scales with the primary barrier to simulation being computing resources. The second, atomistic-to-continuum (AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level must be simulated to resolve the small scales, but the effect on and coupling to the continuum level is frequently unclear.

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“…As far as the first difficulty is concerned, numerical methods defined on uniform grids suffer from severe non-physical oscillations or excessive numerical diffusion. These unphysical behaviours can be eliminated considering several approaches (see, for instance [7][8][9][10]14,[16][17][18]22]. The numerical difficulties due to the lack of smoothness when Newton's method is used to solve the algebraic system resulting from the discretization are considered, for example, in [2,4,11,12].…”

Section: Introductionmentioning

confidence: 99%

Lifting solutions of quasilinear convection-dominated problems

Ferreira

Mouro

Oliveira

2010

International Journal of Computer Mathematics

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In certain cases, quasilinear convection-diffusion-reaction equations range from parabolic to almost hyperbolic, depending on the ratio between convection and diffusion coefficients. From a numerical point of view, two main difficulties can arise related to the existence of layers and/or the non-smoothness of the coefficients of such equations. In this paper we study the steady-state solution of a convection-dominated problem. We present a new numerical method based on the idea of solving an associated modified problem, whose solution corresponds to a lifting of the solution of the initial problem. The method introduced here avoids an a priori knowledge of the layer(s) location and allows an efficient handling of the lack of smoothness of the coefficients. Numerical simulations that show the effectiveness of our approach are included.

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Finite element analysis of convection dominated reaction–diffusion problems

Cited by 45 publications

References 32 publications

Parallel algebraic hybrid solvers for large 3D convection-diffusion problems

Parallel algebraic hybrid solvers for large 3D convection-diffusion problems

A mathematical framework for multiscale science and engineering : the variational multiscale method and interscale transfer operators.

Lifting solutions of quasilinear convection-dominated problems

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