A 3D unstructured adaptive multigrid scheme for the Euler equations

Connell, Stuart; Holmes, D. Graham

doi:10.2514/6.1993-3339

Cited by 23 publications

(14 citation statements)

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“…The first approach begins with a coarse mesh definition and generates finer grids by refinement [36,37]. The main advantage of this approach is that the inter-grid operators become simple because of grid nesting.…”

Section: Element Agglomerationmentioning

confidence: 99%

Parallelization of an Additive Multigrid Solver

Darwish

Saad

Hamdan

2008

Numerical Heat Transfer, Part B: Fundamentals

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This article deals with the implementation and performance analysis of a parallel algebraic multigrid solver (pAMG) for a finite-volume, unstructured computational fluid dynamics (CFD) code. The parallelization of the solver is based on the domain decomposition approach using the single program, multiple data paradigm. The Message Passing Interface library (MPI) is used for communication of data. An ILU(0) iterative solver is used for smoothing the errors arising within each partition at the different grid levels, and a multilevel synchronization across the computational domain partitions is enforced in order to improve the performance of the parallelized multigrid solver. Two synchronization strategies are evaluated. In the first the synchronization is applied across the multigrid levels during the restriction step in addition to the base level, while in the second the synchronization is enforced during the restriction and prolongation steps. The effect of gathering the coefficients across partitions for the coarsest level is also investigated. Tests on grids up to 800,000 elements are conducted for a number of diffusion and advection problems on up to 20 processors.Results show that synchronization across partitions for multigrid levels plays an essential role in ensuring good scalability. Furthermore, for a large number of partitions, gathering coefficients across partitions is important to ensure a convergence history that is consistent with the sequential solver, thus yielding the same number of iterations for parallel and sequential runs, which is crucial for retaining high scalability. The shadow-to-core elements ratio is also shown to be a good indicator for scalability.

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Section: Element Agglomerationmentioning

confidence: 99%

Parallelization of an Additive Multigrid Solver

Darwish

Saad

Hamdan

2008

Numerical Heat Transfer, Part B: Fundamentals

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show abstract

“…The first approach begins with a coarse mesh definition and generates finer grids by refinement 33,34 . The main advantage of this approach is that the inter-grid operators become simple because of grid nesting.…”

Section: Element Agglomerationmentioning

confidence: 99%

A high scalability parallel algebraic multigrid solver

Saad¹,

Darwish²

2009

Computational Fluid Dynamics 2006

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Abstract. This paper deals with the implementation and performance analysis of a parallel Algebraic Multigrid Solver (pAMG) for a finite volume unstructured CFD code. The parallelization of the solver is based on the domain decomposition approach using the single program multiple data paradigm. The Message passing interface Library (MPI) is used for communication of data. An ILU(0) iterative solver is used for smoothing the errors arising within each partition at the different grid levels, and a multi-level synchronization across the computational domain partitions is enforced in order to improve the performance of the parallelized Multigrid solver. Two synchronization strategies are evaluated: in the first the synchronization is applied across the multigrid levels during the restriction step in addition to the base level, while in the second the synchronization is enforced during the restriction and prolongation steps. To increase robustness gathering of coefficients across partitions for the coarsest level is investigated. Tests on a number of grids from 100,00 to 800,000 elements for diffusion and advection problems have been conducted on up to 20 processors.

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“…When using unstructured grids, there are three different approaches that can be adopted for AMG. The first approach resembles the classical grid-sequencing technique, where a coarse level grid is first generated and the refined grid levels are obtained by repeated refinements [8,9]. The second approach employs non-nested unstructured grids either with a subset of fine grid points to construct the coarse grids or with completely independent coarse and fine grids.…”

Section: Introductionmentioning

confidence: 99%

A new fast hybrid adaptive grid generation technique for arbitrary two‐dimensional domains

Ebeida

Davis

Freund

2010

Numerical Meth Engineering

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SUMMARYThis paper describes a new fast hybrid adaptive grid generation technique for arbitrary twodimensional domains. This technique is based on a Cartesian background grid with square elements and quadtree decomposition. A new algorithm is introduced for the distribution of boundary points based on the curvature of the domain boundaries. The quadtree decomposition is governed either by the distribution of the boundary points or by a size function when a solution-based adaptive grid is desired. The resulting grid is quad-dominant and ready for the application of finite-element, multigrid, or line-relaxation methods. All of the internal angles in the final grid have a lower bound of 45• and an upper bound of 135• . Although our main interest is in grid generation for unsteady flow simulations, the technique presented in this paper can be employed in many other fields. Several application examples are provided to illustrate the main features of this new approach.

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A 3D unstructured adaptive multigrid scheme for the Euler equations

Cited by 23 publications

References 0 publications

Parallelization of an Additive Multigrid Solver

Parallelization of an Additive Multigrid Solver

A high scalability parallel algebraic multigrid solver

A new fast hybrid adaptive grid generation technique for arbitrary two‐dimensional domains

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