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Performance Of Algebraic Multigrid For Parallelized Finite Element Dns Les Solvers
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Book Synopsis Performance of Algebraic Multigrid for Parallelized Finite Element DNS/LES Solvers by : Gregory James Larson
Download or read book Performance of Algebraic Multigrid for Parallelized Finite Element DNS/LES Solvers written by Gregory James Larson and published by . This book was released on 2006 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results of these studies are particularly useful for implementation of this algorithm on challenging and complex flows, especially direct numerical and large-eddy simulations. Reducing computational cost allows the analysis and understanding of more flows of practical interest.
Book Synopsis Parallel Multigrid Algorithms for Unstructured 3D Large Deformation Elasticity and Plasticity Finite Element Problems by : Mark Adams
Download or read book Parallel Multigrid Algorithms for Unstructured 3D Large Deformation Elasticity and Plasticity Finite Element Problems written by Mark Adams and published by . This book was released on 1999 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients by :
Download or read book Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients written by and published by . This book was released on 2012 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-?AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the coarse basis used to define the new two-level method of our interest. We illustrate the performance of this adaptive two-level procedure with a large set of numerical experiments that demonstrate its efficiency over building the solvers from scratch.
Book Synopsis Multigrid Equation Solvers of Large Scale Nonlinear Finite Element Simulations by : Mark Francis Adams
Download or read book Multigrid Equation Solvers of Large Scale Nonlinear Finite Element Simulations written by Mark Francis Adams and published by . This book was released on 1998 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis of an Aggregation-based Algebraic Multigrid Method and Its Parallelization by : Meng-Huo Chen
Download or read book Analysis of an Aggregation-based Algebraic Multigrid Method and Its Parallelization written by Meng-Huo Chen and published by . This book was released on 2014 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interests of this thesis are twofold. First, a two-grid convergence analysis based on the paper [Algebraic analysis of aggregation-based multigrid by A. Napov and Y. Notay, Numer. Lin. Alg. Appl. 18 (2011), pp. 539-564 ] is derived for various aggregation schemes applied to a finite element discretization of a rotated anisotropic diffusion equation. As expected, it is shown that the best aggregation scheme is one in which aggregates are aligned with the anisotropy. In practice, however, this is not what automatic aggregation procedures do. We suggest an approach for determining appropriate aggregates based on eigenvectors associated with small eigenvalues of a block splitting matrix. In the second part of the thesis several issues regarding the parallel implementation of aggregation-based multigrid methods are discussed. The coarsest grid solving stage of multigrid cycles has been a bottleneck for parallel multigrid algorithms to attain a good speedup. A comparison between a parallel linear system direct solver (MUMPS) and a few steps of preconditioned conjugate gradient (PCG) methods for solving the coarsest grid system is carried out and tested on TACC Lonestar multi-processor machine. Regarding the preconditioner of conjugate gradient iterations, a parallel sparse approximate inverse (SAI) algorithm is used to construct an approximate inverse of the original matrix in order to replace the preconditioner solving step, which is inherently sequential, by matrix-vector multiplications. The linear systems tested arise from discretization of 2D or 3D partial differential equations, which are symmetric positive definite. The results exhibit that using PCG on the coarsest grid attains better speedup and overall better performance than MUMPS when the number of processors is greater than about 100. The effects of different decompositions of the physical domain (rows/slab versus blocks/pencils) on the scaling and efficiency of aggregation-based algebraic multigrid are also studied and one sees that the blocks/pencils decomposition of the physical domain reduces the amount of communication and hence has better performance.
Book Synopsis A Parallel Algebraic Multigrid Solver for Finite Element Method Based Source Localization in the Human Brain by :
Download or read book A Parallel Algebraic Multigrid Solver for Finite Element Method Based Source Localization in the Human Brain written by and published by . This book was released on 2001 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Multigrid Tutorial by : William L. Briggs
Download or read book A Multigrid Tutorial written by William L. Briggs and published by SIAM. This book was released on 2000-01-01 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition preserves the introductory spirit of the first edition while roughly doubling the amount of material covered. The topics of the first edition have been enhanced with additional discussion, new numerical experiments, and improved figures. New topics in the second edition include nonlinear equations, Neumann boundary conditions, variable mesh and variable coefficient problems, anisotropic problems, algebraic multigrid (AMG), adaptive methods, and finite elements. This introductory book is ideally suited as a companion textbook for graduate numerical analysis courses. It is written for computational mathematicians, engineers, and other scientists interested in learning about multigrid.
Book Synopsis Performance of Algebraic Multigrid Preconditioners for Large-Scale Finite Element Simulations by :
Download or read book Performance of Algebraic Multigrid Preconditioners for Large-Scale Finite Element Simulations written by and published by . This book was released on 2015 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multigrid Methods V by : Wolfgang Hackbusch
Download or read book Multigrid Methods V written by Wolfgang Hackbusch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection from the papers presented at the Fifth European Multigrid Conference, held in Stuttgart, October 1996. All contributions were carefully refereed. The conference was organized by the Institute for Computer Applications (ICA) of the University of Stuttgart, in cooperation with the GAMM Committee for Scientific Computing, SFB 359 and 404 and the research network WiR Ba-Wü. The list of topics contained lectures on Multigrid Methods: robustness, adaptivity, wavelets, parallelization, application in computational fluid dynamics, porous media flow, optimisation and computational mechanics. A considerable part of the talks focused on algebraic multigrid methods.
Download or read book Выставки, ярмарки written by and published by . This book was released on 1993 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Multigrid Methods for Large Scale Finite Element Equations by : Stefan Reitzinger
Download or read book Algebraic Multigrid Methods for Large Scale Finite Element Equations written by Stefan Reitzinger and published by . This book was released on 2001 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parallelization of an Adaptive Multigrid Algorithm for Fast Solution of Finite Element Structural Problems by :
Download or read book Parallelization of an Adaptive Multigrid Algorithm for Fast Solution of Finite Element Structural Problems written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive mesh refinement selectively subdivides the elements of a coarse user supplied mesh to produce a fine mesh with reduced discretization error. Effective use of adaptive mesh refinement coupled with an a posteriori error estimator can produce a mesh that solves a problem to a given discretization error using far fewer elements than uniform refinement. A geometric multigrid solver uses increasingly finer discretizations of the same geometry to produce a very fast and numerically scalable solution to a set of linear equations. Adaptive mesh refinement is a natural method for creating the different meshes required by the multigrid solver. This paper describes the implementation of a scalable adaptive multigrid method on a distributed memory parallel computer. Results are presented that demonstrate the parallel performance of the methodology by solving a linear elastic rocket fuel deformation problem on an SGI Origin 3000. Two challenges must be met when implementing adaptive multigrid algorithms on massively parallel computing platforms. First, although the fine mesh for which the solution is desired may be large and scaled to the number of processors, the multigrid algorithm must also operate on much smaller fixed-size data sets on the coarse levels. Second, the mesh must be repartitioned as it is adapted to maintain good load balancing. In an adaptive multigrid algorithm, separate mesh levels may require separate partitioning, further complicating the load balance problem. This paper shows that, when the proper optimizations are made, parallel adaptive multigrid algorithms perform well on machines with several hundreds of processors.
Book Synopsis Efficient Solution of finite difference and finite element equations by algebraic multigrid AMG by : John Ruge
Download or read book Efficient Solution of finite difference and finite element equations by algebraic multigrid AMG written by John Ruge and published by . This book was released on 1984 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hampstead Advertiser written by and published by . This book was released on 1874 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Multigrid for Stabilized Finite Element Discretizations of the Navier Stokes Equation by : Tolulope Olawale Okusanya
Download or read book Algebraic Multigrid for Stabilized Finite Element Discretizations of the Navier Stokes Equation written by Tolulope Olawale Okusanya and published by . This book was released on 2002 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: A multilevel method for the solution of systems of equations generated by stabilized Finite Element discretizations of the Euler and Navier Stokes equations on generalized unstructured grids is described. The method is based on an elemental agglomeration multigrid which produces a hierarchical sequence of coarse subspaces. Linear combinations of the basis functions from a given space form the next subspace and the use of the Galerkin Coarse Grid Approximation (GCA) within an Algebraic Multigrid (AMG) context properly defines the hierarchical sequence. The multigrid coarse spaces constructed by the elemental agglomeration algorithm are based on a semi-coarsening scheme designed to reduce grid anisotropy. The multigrid transfer operators are induced by the graph of the coarse space mesh and proper consideration is given to the boundary conditions for an accurate representation of the coarse space operators. A generalized line implicit relaxation scheme is also described where the lines are constructed to follow the direction of strongest coupling. The solution algorithm is motivated by the decomposition of the system characteristics into acoustic and convective modes. Analysis of the application of elemental agglomeration AMG (AMGe) to stabilized numerical schemes shows that a characteristic length based rescaling of the numerical stabilization is necessary for a consistent multigrid representation.
Book Synopsis Large-Scale Parallel Performance of Algebraic Multigrid Preconditioners for Multiphysics Systems by :
Download or read book Large-Scale Parallel Performance of Algebraic Multigrid Preconditioners for Multiphysics Systems written by and published by . This book was released on 2011 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multigrid and Krylov Solvers for Large Scale Finite Element Groundwater Flow Simulations on Distributed Memory Parallel Platforms by :
Download or read book Multigrid and Krylov Solvers for Large Scale Finite Element Groundwater Flow Simulations on Distributed Memory Parallel Platforms written by and published by . This book was released on 1997 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report we present parallel solvers for large linear systems arising from the finite-element discretization of the three-dimensional steady-state groundwater flow problem. Our solvers are based on multigrid and Krylov subspace methods. The parallel implementation is based on a domain decomposition strategy with explicit message passing using NX and MPI libraries. We have tested our parallel implementations on the Intel Paragon XP/S 150 supercomputer using up to 1024 parallel processors and on other parallel platforms such as SGI/Power Challenge Array, Cray/SGI Origin 2000, Convex Exemplar SPP-1200, and IBM SP using up to 64 processors. We show that multigrid can be a scalable algorithm on distributed memory machines. We demonstrate the effectiveness of parallel multigrid based solvers by solving problems requiring more than 70 million nodes in less than a minute. This is more than 25 times faster than the diagonal preconditioned conjugate gradient method which is one of the more popular methods for large sparse linear systems. Our results also show that multigrid as a stand alone solver works best for problems with smooth coefficients, but for rough coefficients it is best used as a preconditioner for a Krylov subspace method such as the conjugate gradient method. We show that even for extremely heterogeneous systems the multigrid pre-conditioned conjugate gradient method is at least 10 times faster than the diagonally preconditioned conjugate gradient method.
