Adaptive aggregation on graphs

Xu, Wenfang; Zikatanov, Ludmil T.

doi:10.1016/j.cam.2017.10.032

Title: Adaptive aggregation on graphs

Journal Article · 30 September 2018 · Journal of Computational and Applied Mathematics

DOI: https://doi.org/10.1016/j.cam.2017.10.032 · OSTI ID:1890524

Xu, Wenfang;

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Sponsoring Organization:: USDOE

OSTI ID:: 1890524

Journal Information:: Journal of Computational and Applied Mathematics, Journal Name: Journal of Computational and Applied Mathematics Journal Issue: C Vol. 340; ISSN 0377-0427

Publisher:: ElsevierCopyright Statement

Country of Publication:: Belgium

Language:: English

References (19)

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A multigrid method based on graph matching for convection-diffusion equations Kim, HwanHo; Xu, Jinchao; Zikatanov, Ludmil Numerical Linear Algebra with Applications, Vol. 10, Issue 1-2 https://doi.org/10.1002/nla.317	journal	January 2002
Coarsening by compatible relaxation Livne, O. E. Numerical Linear Algebra with Applications, Vol. 11, Issue 23 https://doi.org/10.1002/nla.378	journal	March 2004
Algebraic multilevel iteration method for lowest order Raviart-Thomas space and applications Kraus, J. K.; Tomar, S. K. International Journal for Numerical Methods in Engineering, Vol. 86, Issue 10 https://doi.org/10.1002/nme.3103	journal	January 2011
Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems Lazarov, Raytcho; Repin, Sergey; Tomar, Satyendra K. Numerical Methods for Partial Differential Equations, Vol. 25, Issue 4 https://doi.org/10.1002/num.20386	journal	July 2009
A posteriori estimators for obstacle problems by the hypercircle method Braess, Dietrich; Hoppe, Ronald H. W.; Schöberl, Joachim Computing and Visualization in Science, Vol. 11, Issue 4-6 https://doi.org/10.1007/s00791-008-0104-2	journal	March 2008
Adaptive AMG with coarsening based on compatible weighted matching D’Ambra, Pasqua; Vassilevski, Panayot S. Computing and Visualization in Science, Vol. 16, Issue 2 https://doi.org/10.1007/s00791-014-0224-9	journal	April 2013
Discrete p-robust $$\varvec{H}({{\mathrm{div}}})$$ H ( div ) -liftings and a posteriori estimates for elliptic problems with $$H^{-1}$$ H - 1 source terms Ern, Alexandre; Smears, Iain; Vohralík, Martin Calcolo, Vol. 54, Issue 3 https://doi.org/10.1007/s10092-017-0217-4	journal	January 2017
Convergence of algebraic multigrid based on smoothed aggregation Van\vek, Petr; Brezina, Marian; Mandel, Jan Numerische Mathematik, Vol. 88, Issue 3 https://doi.org/10.1007/s211-001-8015-y	journal	May 2001
Efficient computable error bounds for discontinuous Galerkin approximations of elliptic problems Tomar, S. K.; Repin, S. I. Journal of Computational and Applied Mathematics, Vol. 226, Issue 2 https://doi.org/10.1016/j.cam.2008.08.015	journal	April 2009
Explicit error bounds in a conforming finite element method Destuynder, Philippe; Métivet, Brigitte Mathematics of Computation, Vol. 68, Issue 228 https://doi.org/10.1090/S0025-5718-99-01093-5	journal	February 1999
Approximations in elasticity based on the concept of function space Prager, W.; Synge, J. L. Quarterly of Applied Mathematics, Vol. 5, Issue 3 https://doi.org/10.1090/qam/25902	journal	January 1947
Guaranteed and robust error bounds for nonconforming approximations of elliptic problems Repin, S. I.; Tomar, S. K. IMA Journal of Numerical Analysis, Vol. 31, Issue 2 https://doi.org/10.1093/imanum/drp037	journal	February 2010
A Convergent Adaptive Algorithm for Poisson’s Equation Dörfler, Willy SIAM Journal on Numerical Analysis, Vol. 33, Issue 3 https://doi.org/10.1137/0733054	journal	June 1996
Compatible Relaxation and Coarsening in Algebraic Multigrid Brannick, James J.; Falgout, Robert D. SIAM Journal on Scientific Computing, Vol. 32, Issue 3 https://doi.org/10.1137/090772216	journal	January 2010
An Algebraic Multigrid Method with Guaranteed Convergence Rate Napov, Artem; Notay, Yvan SIAM Journal on Scientific Computing, Vol. 34, Issue 2 https://doi.org/10.1137/100818509	journal	January 2012
Polynomial-Degree-Robust A Posteriori Estimates in a Unified Setting for Conforming, Nonconforming, Discontinuous Galerkin, and Mixed Discretizations Ern, Alexandre; Vohralík, Martin SIAM Journal on Numerical Analysis, Vol. 53, Issue 2 https://doi.org/10.1137/130950100	journal	January 2015
On Generalizing the Algebraic Multigrid Framework Falgout, Robert D.; Vassilevski, Panayot S. SIAM Journal on Numerical Analysis, Vol. 42, Issue 4 https://doi.org/10.1137/S0036142903429742	journal	January 2004
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs Karypis, George; Kumar, Vipin SIAM Journal on Scientific Computing, Vol. 20, Issue 1 https://doi.org/10.1137/S1064827595287997	journal	January 1998

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