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Showing 1 to 20 of 110 for “"Multigrid"”.
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Data parallel algebraic multigrid
Algebraic multigrid methods for large, sparse linear systems are central to many computational simulations. Parallel algorithms for such solvers are generally decomposed into coarse-grain tasks suitable for distributed computers with traditional processing cores. Accelerating multigrid methods on …
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Multigrid Algorithms for Massively Parallel Machines
… of solving <em>pde's</em> is the use of the multigrid algorithm. However, the implementation of the multigrid algorithm on massively parallel machines is not very efficient because of (i) low processor utilization and (ii) high communication overheads. These problems need to be addressed to …
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Algebraic Multigrid for Discrete Differential Forms
… approach is based on the principles of algebraic multigrid (AMG) which is designed to solve large-scale linear systems with optimal, or near-optimal efficiency. Since the k-form problems to be solved are arbitrarily large, the need for scalable numerical solvers is clear.
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Generalizing smoothed aggregation-based algebraic multigrid
Smoothed aggregation-based (SA) algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. While SA has been effective over a broad class of problems, it has several limitations and weaknesses that this …
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Monolithic multigrid for saddle point systems
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2024-09-16 without embargo terms
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Robust structured multigrid at extreme scales
… structure in a problem, robust structured multigrid methods gain important performance benefits because they preserve structure throughout the multigrid hierarchy. In parallel these methods benefit from nearest neighbor stencil-based communication patterns; however, the increased …
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Multigrid solutions of elliptic fluid flow problems
… an extremely good indication of the power of a multigrid approach. Next, the solution methodology is applied to flow in a three-dimensional lid-driven cavity at different Reynolds numbers, with cross-reference being made to predictions obtained in the corresponding two-dimensional simulations, …
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Efficient Setup Algorithms for Parallel Algebraic Multigrid
The experimental results motivate the design of new coarsening algorithms to improve the performance of coarse-grid selection itself. A new algorithm labeled Bucket Sorted Independent Sets (BSIS) is developed and contributes two major advances. First, the cost of selecting independent sets while …
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Learning aggregates and interpolation for algebraic multigrid
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-11 without embargo terms
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Optimization-based algebraic multigrid coarsening using reinforcement learning
DSpace SAF Submission Ingestion Package generated from Vireo submission #16982 on 2022-01-12 at 12:46:07
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Parallel multigrid for large-scale least squares sensitivity
… Least Squares Sensitivity (LSS) method. A multigrid algorithm is developed that can, in parallel, solve the discrete LSS system. This generic algorithm can be applied to ordinary differential equations such as the Lorenz System. Additionally, this parallel method enables the estimation of …
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Quasi-Newton and Multigrid Methods for Semiconductor Device Simulation
A finite difference approximation to the semiconductor device equations using the Bernoulli function approximation to the exponential function is described, and the robustness of this approximation is demonstrated. Sheikh's convergence analysis of Gummel's method and quasi-Newton methods is …
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Multigrid methods for complex engineering geometries and unstructured meshes
The convergence of standard multigrid methods decays significantly if locally poor quality cells are present, and it is found that the poor convergence is due to the local failure of the smoothing property. The high frequency error localised in regions of low quality cells is not eliminated by …
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A multigrid relevance filtering technique for distributed interactive simulation
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.
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The Parallel Performance and Implementation of an Adaptive Multigrid Algorithm
An adaptive multigrid algorithm has been implemented on shared memory parallel computers to solve large-scale structural mechanics problems. The solution algorithm begins by solving the problem on the initial mesh, refining this mesh as required by the chosen adaptive scheme, and then solving the …
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A high-order discontinuous Galerkin multigrid solver for aerodynamic applications
… Galerkin finite element solver using p-multigrid with line Jacobi smoothing. The line smoothing algorithm is presented for unstructured meshes, and p-multigrid is outlined for the nonlinear Euler equations of gas dynamics. Analysis of 2-D advection shows the improved performance of line …
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