Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Numerical experiments with MG continuation algorithms
Applied Numerical Mathematics
Compatible coarsening in the multigraph algorithm
Advances in Engineering Software
High-fidelity geometric modeling for biomedical applications
Finite Elements in Analysis and Design
Numerical experiments with MG continuation algorithms
Applied Numerical Mathematics
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We describe an algebraic multilevel multigraph algorithm. Many of the multilevel components are generalizations of algorithms originally applied to general sparse Gaussian elimination. Indeed, general sparse Gaussian elimination with minimum degree ordering is a limiting case of our algorithm. Our goal is to develop a procedure which has the robustness and simplicity of use of sparse direct methods, yet offers the opportunity to obtain the optimal or near-optimal complexity typical of classical multigrid methods.