A parallel fictitious domain multigrid preconditioner for the solution of Poisson’s equation in complex geometries

Singh, Krishna M.; Williams, J.J.R.

doi:10.1016/j.cma.2005.01.003

Cited by 19 publications

(13 citation statements)

References 17 publications

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“…Although this latter approach leads to a problem‐dependent method, it is also likely to lead to an optimal set of methods for a given application. Advantages of this approach have already been observed in case of numerical simulations based on uniform Cartesian grids irrespective of the complexity of the problem domain which can be overcome using fictitious domain or immersed boundary approach . The present work is another attempt in this direction but with non‐uniform Cartesian grids which can better capture the development of shear driven flows.…”

Section: Introductionmentioning

confidence: 87%

“…On structured Cartesian grids where a sequence of nested grids can be easily generated, the GMG scheme provides an optimal performance, and can be easily parallelized . It has also been extended for use on complex problem domains in conjunction with fictitious domain or immersed boundary method . AMG method is very promising for unstructured grids on complex geometries .…”

Section: Introductionmentioning

confidence: 99%

“…It was augmented with a fictitious domain multigrid preconditioner along with PCG method as Poisson solver. This development significantly enhanced the parallel scalability and efficiency of this code . With incorporation of immersed boundary method, CgLES has been used to solve a wide variety of flow problems .…”

Section: Introductionmentioning

confidence: 99%

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On parallel pre‐conditioners for pressure Poisson equation in LES of complex geometry flows

Singh

Avital

Williams

et al. 2016

Numerical Methods in Fluids

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Summary This paper presents an assessment of fast parallel pre‐conditioners for numerical solution of the pressure Poisson equation arising in large eddy simulation of turbulent incompressible flows. Focus is primarily on the pre‐conditioners suitable for domain decomposition based parallel implementation of finite volume solver on non‐uniform structured Cartesian grids. Bi‐conjugate gradient stabilized method has been adopted as the Krylov solver for the linear algebraic system resulting from the discretization of the pressure Poisson equation. We explore the performance of multigrid pre‐conditioner for the non‐uniform grid and compare its performance with additive Schwarz pre‐conditioner, Jacobi and SOR(k) pre‐conditioners. Numerical experiments have been performed to assess the suitability of these pre‐conditioners for a wide range of non‐uniformity (stretching) of the grid in the context of large eddy simulation of a typical flow problem. It is seen that the multigrid preconditioner shows the best performance. Further, the SOR(k) preconditioner emerges as the next best alternative. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

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On parallel pre‐conditioners for pressure Poisson equation in LES of complex geometry flows

Singh

Avital

Williams

et al. 2016

Numerical Methods in Fluids

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“…There is a significant number of publications related to the numerical solution of different PDE on irregular domains with uniform embedded meshes. For example, we can mention the following fictitious domain numerical methods that use uniform embedded meshes: the embedded finite difference method, the cut finite element method, the finite cell method, the Cartesian grid method, the immersed interface method, the virtual boundary method, the embedded boundary method, etc; e.g., see [44,47,6,40,41,11,16,52,36,31,29,30,28,27,15,7,5,4,35,42,10,8,9,37,26,3,46,33,45,17] and many others. The main objective of these techniques is to simplify the mesh generation for irregular domains as well as to mitigate the effect of 'bad' elements.…”

Section: Introductionmentioning

confidence: 99%

A New Numerical Approach to the Solution of Partial Differential Equations With Optimal Accuracy on Irregular Domains and Cartesian Meshes

Idesman¹

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…The core idea is again to immerse the original domain into a geometrically bigger and simpler one [15]. Finite difference, finite volume and low order finite element methods have been used to discretize the fictitious domain, see for example [4,14,21,25]. To treat the boundary conditions, the literature provides a wide scope of ideas and techniques similar in nature but different in names, such as Lagrange multiplier method [9] or fat boundary method [10].…”

Section: Introductionmentioning

confidence: 99%

Finite cell method

2007

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A simple yet effective modification to the standard finite element method is presented in this paper. The basic idea is an extension of a partial differential equation beyond the physical domain of computation up to the boundaries of an embedding domain, which can easier be meshed. If this extension is smooth, the extended solution can be well approximated by high order polynomials. This way, the finite element mesh can be replaced by structured or unstructured cells embedding the domain where classical h-or p-Ansatz functions are defined. An adequate scheme for numerical integration has to be used to differentiate between inside and outside the physical domain, very similar to strategies used in the level set method. In contrast to earlier works, e.g., the extended or the generalized finite element method, no special interpolation function is introduced for enrichment purposes. Nevertheless, when using p-extension, the method shows exponential rate of convergence for smooth problems and good accuracy even in the presence of singularities.

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A parallel fictitious domain multigrid preconditioner for the solution of Poisson’s equation in complex geometries

Cited by 19 publications

References 17 publications

On parallel pre‐conditioners for pressure Poisson equation in LES of complex geometry flows

On parallel pre‐conditioners for pressure Poisson equation in LES of complex geometry flows

A New Numerical Approach to the Solution of Partial Differential Equations With Optimal Accuracy on Irregular Domains and Cartesian Meshes

Finite cell method

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