7 citations · 31 across the 20 of their papers we have counts for
24 papers
Characterization of the near-null error components utilized in composite adaptive AMG solvers
Austen J. Nelson, Panayot S. Vassilevski
We provide a theoretical justification for the construction of adaptive composite solvers based on a sequence of AMG (algebraic multigrid) -cycle methods that exploit error comp…
Scalable Multilevel Monte Carlo Methods Exploiting Parallel Redistribution on Coarse Levels
Hillary R. Fairbanks, Delyan Z. Kalchev, Chak Shing Lee +1
We study an element agglomeration coarsening strategy that requires data redistribution at coarse levels when the number of coarse elements becomes smaller than the used computatio…
Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media
Chak Shing Lee, François P. Hamon, Nicola Castelletto +2
A full approximation scheme (FAS) nonlinear multigrid solver for two-phase flow and transport problems driven by wells with multiple perforations is developed. It is an extension t…
Matrix-free GPU-accelerated saddle-point solvers for high-order problems in
Will Pazner, Tzanio Kolev, Panayot Vassilevski
This work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in . The solvers are applicable to grad-div and D…
Multilevel-in-Layer Training for Deep Neural Network Regression
Colin Ponce, Ruipeng Li, Christina Mao +1
A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of st…
An Aggregation-based Nonlinear Multigrid Solver for Two-phase Flow and Transport in Porous Media
Chak Shing Lee, François P. Hamon, Nicola Castelletto +2
A nonlinear multigrid solver for two-phase flow and transport in a mixed fractional-flow velocity-pressure-saturation formulation is proposed. The solver, which is under the framew…
Extending Bootstrap AMG for Clustering of Attributed Graphs
Pasqua D'Ambra, Panayot S. Vassilevski, Luisa Cutillo
In this paper we propose a new approach to detect clusters in undirected graphs with attributed vertices. We incorporate structural and attribute similarities between the vertices…
Parallel Element-based Algebraic Multigrid for H(curl) and H(div) Problems Using the ParELAG Library
Delyan Z. Kalchev, Panayot S. Vassilevski, Umberto Villa
This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and So…
Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo
Hillary R. Fairbanks, Umberto Villa, Panayot S. Vassilevski
In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well-suited to incorpora…
Nonlinear multigrid based on local spectral coarsening for heterogeneous diffusion problems
Chak Shing Lee, François Hamon, Nicola Castelletto +2
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is…
Multilevel spectral coarsening for graph Laplacian problems with application to reservoir simulation
Andrew T. Barker, Stephan V. Gelever, Chak S. Lee +2
We extend previously developed two-level coarsening procedures for graph Laplacian problems written in a mixed saddle point form to the fully recursive multilevel case. The resulti…
A Condensed Constrained Nonconforming Mortar-based Approach for Preconditioning Finite Element Discretization Problems
Delyan Z. Kalchev, Panayot S. Vassilevski
This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation, that is ba…
DNN Approximation of Nonlinear Finite Element Equations
Tuyen Tran, Aidan Hamilton, Maricela Best McKay +2
We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial…
Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation
Delyan Z. Kalchev, Panayot S. Vassilevski
We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additi…
Improving Solve Time of aggregation-based adaptive AMG
Pasqua D'Ambra, Panayot S. Vassilevski
This paper proposes improving the solve time of a bootstrap AMG designed previously by the authors. This is achieved by incorporating the information, set of algebraically smooth v…
Modifying AMG coarse spaces with weak approximation property to exhibit approximation in energy norm
Xiaozhe Hu, Panayot S. Vassilevski
Algebraic multigrid (AMG) coarse spaces are commonly constructed so that they exhibit the so-called weak approximation (WAP) property which is necessary and sufficient condition fo…
Algebraic Hybridization and Static Condensation with Application to Scalable H(div) Preconditioning
Veselin A. Dobrev, Tzanio V. Kolev, Chak S. Lee +2
We propose an unified algebraic approach for static condensation and hybridization, two popular techniques in finite element discretizations. The algebraic approach is supported by…
Scalable hierarchical PDE sampler for generating spatially correlated random fields using non-matching meshes
Sarah Osborn, Patrick Zulian, Thomas Benson +3
This work describes a domain embedding technique between two non-matching meshes used for generating realizations of spatially correlated random fields with applications to large-s…
The auxiliary space preconditioner for the de Rham complex
Jay Gopalakrishnan, Martin Neumüller, Panayot Vassilevski
We generalize the construction and analysis of auxiliary space preconditioners to the n-dimensional finite element subcomplex of the de Rham complex. These preconditioners are base…
A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields
Sarah Osborn, Panayot Vassilevski, Umberto Villa
We propose an alternative method to generate samples of a spatially correlated random field with applications to large-scale problems for forward propagation of uncertainty. A clas…
Arbitrary Dimension Convection-Diffusion Schemes for Space-Time Discretizations
Randolph E. Bank, Panayot S. Vassilevski, Ludmil T. Zikatanov
This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the c…
A Combined Preconditioning Strategy for Nonsymmetric Systems
Blanca Ayuso de Dios, Andrew T. Barker, Panayot S. Vassilevski
We present and analyze a class of nonsymmetric preconditioners within a normal (weighted least-squares) matrix form for use in GMRES to solve nonsymmetric matrix problems that typi…
Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid
Xiaozhe Hu, Panayot S. Vassilevski, Jinchao Xu
The main purpose of this paper is to provide a comprehensive convergence analysis of nonlinear AMLI-cycle multigrid method for symmetric positive definite problems. Based on classi…
Polynomial of best uniform approximation to and smoothing in two-level methods
Johannes K. Kraus, Panayot S. Vassilevski, Ludmil T. Zikatanov
We derive a three-term recurrence relation for computing the polynomial of best approximation in the uniform norm to on a finite interval with positive endpoints. As appli…