Algebraic multigrid theory: The symmetric case
Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
Adaptive Smoothed Aggregation ($\alpha$SA)
SIAM Journal on Scientific Computing
On Generalizing the Algebraic Multigrid Framework
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
One-Dimensional Algorithm for Finding Eigenbasis of the Schrödinger Operator
SIAM Journal on Scientific Computing
Algebraic Multigrid Solvers for Complex-Valued Matrices
SIAM Journal on Scientific Computing
Compatible Relaxation and Coarsening in Algebraic Multigrid
SIAM Journal on Scientific Computing
Modification and Compensation Strategies for Threshold-based Incomplete Factorizations
SIAM Journal on Scientific Computing
A Bootstrap Algebraic Multilevel Method for Markov Chains
SIAM Journal on Scientific Computing
Efficient preconditioning of laplacian matrices for computer graphics
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Parallel design and performance of nested filtering factorization preconditioner
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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We develop an algebraic multigrid (AMG) setup scheme based on the bootstrap framework for multiscale scientific computation. Our approach uses a weighted least squares definition of interpolation, based on a set of test vectors that are computed by a bootstrap setup cycle and then improved by a multigrid eigensolver and a local residual-based adaptive relaxation process. To emphasize the robustness, efficiency, and flexibility of the individual components of the proposed approach, we include extensive numerical results of the method applied to scalar elliptic partial differential equations discretized on structured meshes. As a first test problem, we consider the Laplace equation discretized on a uniform quadrilateral mesh, a problem for which multigrid is well understood. Then, we consider various more challenging variable coefficient systems coming from covariant finite-difference approximations of the two-dimensional gauge Laplacian system, a commonly used model problem in AMG algorithm development for linear systems arising in lattice field theory computations.