Numerical performance of incomplete factorizations for 3D transient convection–diffusion problems

Ferran, Antonio Rodríguez; Sandoval, María Luisa

doi:10.1016/j.advengsoft.2006.09.003

Cited by 14 publications

(19 citation statements)

References 18 publications

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“…The results also indicate that the computational cost needed to compute the Cholesky decomposition, associated with the subproblems, is insignificant compared with the time to do the iterations. These conclusions agree with those in [5].…”

Section: Discussionsupporting

confidence: 82%

“…We now compare the best result that was obtained in the previous section (DD-IC(10 −2 )) with the best result reported in [5] when ICCG ( = 5×10 −3 ) is used to solve the global problem (i.e. without domain decomposition).…”

Section: Efficiency Of Msm With Active Subdomains Versus Solution Of mentioning

confidence: 91%

“…Since the matrices associated to the subsystems are principal submatrices of the global matrix A, they are symmetric and positive definite [16]. Hence, the linear subsystems are solved by either: (1) the Cholesky factorization [17] or (2) the preconditioned conjugate gradient method [11] with the drop-tolerance incomplete Cholesky factorizations [18], which are efficient for transient convection-diffusion problems according to the numerical results obtained in [5].…”

Section: Subsystems Solution: Direct and Iterative Methodsmentioning

confidence: 99%

“…We compare both memory requirements and central processing unit (CPU) time with three different approaches: the Cholesky factorization (without iterations), the Cholesky factorization with iterative refinement [19] and the incomplete Cholesky conjugate gradient method (ICCG) with threshold = 5×10 −3 , see [5]. Before we do the comparison, we verify the criteria to activate and inactivate subdomains and some properties that are preserved from the MSM.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Since it is important to order the subdomains (and nodes) in the flow direction [6, 10], the nodes of the mesh are reordered following the typical block-interface structure of many activated-carbon filters, see [5]. Therefore, a block-tridiagonal global matrix is obtained.…”

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confidence: 99%

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A multiplicative Schwarz method with active subdomains for transient convection–diffusion problems

Sandoval

Ferran

2009

Numer Methods Biomed Eng

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upwind Petrov-Galerkin, Galerkin/Least-Squares (GLS) and sub-grid scale (SGS). Least-squares stabilization, on the contrary, leads to a symmetric matrix. Hence, we should solve thousands of linear algebraic systemswhere the matrix A is large, sparse, symmetric, positive definite and constant at each time-step n. A finite element discretization described in [5] is applied. Owing to the formation of an abrupt front, the global solution varies only in a small part of the complete domain at each time-step. Our proposal is to exploit this fact by combining a domain decomposition method with the activation and inactivation of subdomains depending on how the hydrocarbon concentration front moves.We decided to use the multiplicative Schwarz method (MSM) because it converges faster than the additive Schwarz method [6], and its convergence rate depends on both the overlap size and the number of subdomains [7,8]. We want to emphasize that the MSM is used directly as a block Gauss-Seidel solver [9] rather than as a preconditioner.Since it is important to order the subdomains (and nodes) in the flow direction [6, 10], the nodes of the mesh are reordered following the typical block-interface structure of many activated-carbon filters, see [5]. Therefore, a block-tridiagonal global matrix is obtained. In addition, for each block, the reverse Cuthill-McKee algorithm [11] is used to reduce the bandwidth of the matrix.This article is organized as follows. In Section 2, we define the subdomains that are used in the MSM. In Section 3, we introduce the appropriate criteria to activate or inactivate subdomains. In Section 4, we present our proposal: the MSM with active subdomains. In Section 5, we show some numerical experiments illustrating the performance of the new algorithm, as well as some comparisons with the classical direct and iterative solvers. We close the paper with some concluding remarks. DEFINITION OF SUBDOMAINS FOR THE MSM

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Section: Discussionsupporting

confidence: 82%

Section: Efficiency Of Msm With Active Subdomains Versus Solution Of mentioning

confidence: 91%

Section: Subsystems Solution: Direct and Iterative Methodsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

mentioning

confidence: 99%

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A multiplicative Schwarz method with active subdomains for transient convection–diffusion problems

Sandoval

Ferran

2009

Numer Methods Biomed Eng

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A multimesh adaptive scheme for air quality modeling with the finite element method

Monforte

Foguet

2013

Numerical Methods in Fluids

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Abstract. A multi-mesh adaptive scheme for convection-diffusion-reaction problems is presented. The proposal is applied to air quality modeling, especifically to the simulation of a pollutant punctual emissions. The performance of the proposal is analyzed with different nonlinear reaction models, including the photochemical model CB05 implmented within the Comunity Multiscale Air Quality model, which involves sixty-two species and very different characteristic reaction times. The problem is solved with splitting of transport and reaction processes. This allows to discretize the species in distinct computational meshes, adapted to the distribution of the error indicator of each case. A common reference mesh is used for all species and during all problem evolution. A remeshing technique based on imposing the volume of new elements is used to define and update the computational meshes. An error indicator well suited for problems involving large variation of the unknowns is used. A single-mesh strategy, with remeshing adapted to the most demanding specie in each part of the domain, is used for comparison. The results of the examples presented show that the accuracy of single and multi-mesh strategies are similar. Instead, computational cost of multi-mesh is lower than single-mesh in most cases. Reduction increases with the number of species and the number of plumes. An example of a punctual emissor in a three-dimensional domain, with realistic values of CB05 components, is presented.

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Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

Ruiz‐Gironés

Oliver

Socorro-Marrero

et al. 2017

Numerical Meth Engineering

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This is the peer reviewed version of the following article: Ruiz Gironès , E., Oliver , A., Socorro, G., Cascón, J., Escobar, J.M., Montenegro, R., Sarrate, J. Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures. "International journal for numerical methods in engineering", 2018, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5706/pdf. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this paper, we present a new method for inserting several triangulated surfaces into an existing tetrahedral mesh generated by the meccano method. The result is a conformal mesh where each inserted surface is approximated by a set of faces of the final tetrahedral mesh. First, the tetrahedral mesh is refined around the inserted surfaces to capture their geometric features. Second, each immersed surface is approximated by a set of faces from the tetrahedral mesh. Third, following a novel approach, the nodes of the approximated surfaces are mapped to the corresponding immersed surface. Fourth, we untangle and smooth the mesh by optimizing a regularized shape distortion measure for tetrahedral elements in which we move all the nodes of the mesh, restricting the movement of the edge and surface nodes along the corresponding entity they belong to. The refining process allows approximating the immersed surface for any initial meccano tetrahedral mesh. Moreover, the proposed projection method avoids computational expensive geometric projections. Finally, the applied simultaneous untangling and smoothing process delivers a high-quality mesh and ensures that the immersed surfaces are interpolated. Several examples are presented to assess the properties of the proposed method.Peer ReviewedPostprint (author's final draft

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Numerical performance of incomplete factorizations for 3D transient convection–diffusion problems

Cited by 14 publications

References 18 publications

A multiplicative Schwarz method with active subdomains for transient convection–diffusion problems

A multiplicative Schwarz method with active subdomains for transient convection–diffusion problems

A multimesh adaptive scheme for air quality modeling with the finite element method

Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

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