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Showing 1 to 19 of 19 for “"Algebraic 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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Algebraic Multigrid for Discrete Differential Forms
… Our 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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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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Performance of Algebraic Multigrid for Parallelized Finite Element DNS/LES Solvers
The implementation of a hybrid spectral/finite-element discretization on the unsteady, incompressible, Navier-Stokes equations with a semi-implicit time-stepping method, an explicit treatment of the advective terms, and an implicit treatment of the pressure and viscous terms leads to an algorithm …
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Algebraic multigrid for stabilized finite element discretizations of the Navier Stokes equation
… 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 …
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A Parallel Aggregation Algorithm for Inter-Grid Transfer Operators in Algebraic Multigrid
… parallel approaches to solve such problems. Multigrid methods can be used to solve large-scale problems, or even better they can be used to precondition the conjugate gradient method, yielding better results in general. Capabilities of multigrid algorithms rely on the effectiveness of the …
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Application of distributed algebraic multigrid to nonlinear finite element analysis of geomechanics problems
Includes bibliographical references (pages 108-112).
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Improving the performance and scalability of algebraic multigrid solvers through applied performance modeling
… new landscape. In this dissertation, we focus on algebraic multigrid (AMG), a popular linear solver with many scientific and engineering applications. AMG has the attractive property of requiring work that is linear in the number of unknowns. However, it also has substantial communication …
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Developments in the Extended Finite Element Method and Algebraic Multigrid for Solid Mechanics Problems Involving Discontinuities
… and the primary solution method discussed is the algebraic multigrid. The extended finite element method has been shown to be effective for both weak and strong discontinuities. With respect to weak discontinuities, a new approach that couples the extended finite element method with Monte Carlo …
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Reducing communication in sparse solvers
… relatively small non-zeros throughout an algebraic multigrid hierarchy, yielding significant reductions to the cost of sparse matrix-vector multiplication that outweigh affects of reduced accuracy of the multiplication. Therefore, the reduction in per-iteration communication costs outweigh …
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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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Hodge Laplacians on simplicial meshes and graphs
… also providing some computational evidence that algebraic multigrid linear solvers for the resulting linear systems on Erdős-Rényi random graphs and on Barabási-Albert graphs do not perform very well in comparison with iterative Krylov solvers.
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Numerical simulations of die casting with uncertainty quantification and optimization using neural networks
… by unstructured hexahedral elements. The algebraic multigrid method, blended with a Krylov subspace solver is used to accelerate convergence. Multiple case studies are presented by coupling surrogate models such as polynomial chaos expansion (PCE) and neural network with OpenCast for …
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Impact of stability and surface area on fracture toughness of biological structures
… divided into two major themes of work: Theme 1: Multigrid methods for large-scale topology optimization with application to trabecular bone-inspired structures: We evaluate the computational cost involved in large-scale topology optimization problems encompassing multiple objectives. Some of …
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High performance computational simulations of gastrointestinal electrical activity
… Jacobi 1.6 s; and boomerAMG 5.8 s), whereas an algebraic multigrid-based boomerAMG preconditioned conjugate-gradient solver was found to be most efficient in terms of solver iteration count (anisotropic problem with extracellular stimulus mean solver iteration count: block-Jacobi 74; Jacobi 581; …
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Advancing domain decomposition methods and entity resolution with graph neural networks
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms