Panayot S. Vassilevski

 

 

 

Appointment:


Professor of Mathematics
[Department]   [University]  

 

Contact:

 

Office:

Fariborz Maseeh Hall, 460Q

  [Campus map]

Mailing:

 1855 SW Broadway

  Portland, OR 97201

Phone:

  +1 503 725 3292

Email:

panayot @ pdx . edu

 

Teaching (2024-2025):

On Sabbatical Leave

 

Founding co-director:

Portland Institute for Computational Science (PICS)

 

Research areas: Computational Mathematics: Scalable Algorithms (Numerical PDEs and Discrete Mathematics)

 

Editor in Chief:

Numerical Linear Algebra with Applications

SIAM Fellow:

SIAM Fellows: Class of 2018

Book:

Multilevel Block Factorization Preconditioners, Matrix-based Analysis and Algorithms for Solving Finite Element Equations, Springer, New York, 2008. 514 p.

 

Personal:

An article about Virginia

 

Technical  reports

 

 

 

B. G. Quiring and P.S. Vassilevski, Properties of the Graph Modularity Matrix and Its Applications, Lawrence Livermore National Laboratory Technical Report LLNL-TR-779424, June 26, 2019,  Link.

 

 

Journal publications

 

C.S. Lee, F. Hamon, N. Castelletto, P.S. Vassilevski, and J. White,  Multilevel Well Modeling in Aggregation-based Nonlinear Multigrid for Multiphase Flow in Porous Media, Journal of Computational Physics 2024 (to appear), https://arxiv.org/pdf/2308.00125.

 

Will Pazner, Tzanio Kolev, and Panayot S. Vassilevski, Matrix-Free GPU-Accelerated Saddle-Point Solvers for High-order Problems in H(div), SIAM Journal on Scientific Computing 46(3)(2024), pp. B179-B204, https://doi.org/10.1137/23M1568806 (arXiv: https://arxiv.org/abs/2304.12387).

 

Colin Ponce, Ruipeng Li, Christina Mao, and Panayot Vassilevski,  Multilevel-in-Layer Training for Deep Neural Network Regression, Numerical Linear Algebra with Applications, 30(5)(2023), e2501. https://doi.org/10.1002/nla.2501 (arXiv:  https://arxiv.org/abs/2211.06515)

 

Pasqua D’Ambra, Panayot S. Vassilevski, and Luisa Cutillo, Extending Bootstrap AMG for Clustering of Attributed Graphs, Applied Mathematics and Computation, volume 447,  15 June 2023, 127904, https://doi.org/10.1016/j.amc.2023.127904.

 

D. Z. Kalchev, P.S. Vassilevski and U. Villa,  Parallel Element-Based Algebraic Multigrid for H(curl) and H(div) Problems Using the ParELAG Library, SIAM Journal on Scientific Computing 45(3)(2023), pp. S371-S400. https://doi.org/10.1137/21M1433253 (arXiv:2107.05613v2).

 

H. Fairbanks, U. Villa, and P. S. Vassilevski, Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo, SIAM Journal on Scientific Computing, 43(5)(2021), pp. S293–S316, https://doi.org/10.1137/20M1349606 .

 

C.S. Lee, F. Hamon, N. Castelletto, P.S. Vassilevski, and J. White, An Aggregation-Based Nonlinear Multigrid Solver for Two-Phase Flow and Transport in Porous Media, Computers and Mathematics with Applications, 113(2022), pp. 282-299, https://doi.org/10.1016/j.camwa.2022.03.026.

 

 

 

H. Fairbanks, S. Osborn, and P. S. Vassilevski, Estimating Posterior Quantity of Interest Expectations in a Multilevel Scalable Framework, Numerical Linear Algebra with Applications 2021;28:e2352. https://doi.org/10.1002/nla.2352 .

 

A. Schafelner and P. S. Vassilevski, Numerical Results for Adaptive (Negative Norm) Constrained First Order System Least Squares Formulations,  Computers and Mathematics with Applications 95(1)(2021), pp. 256-270, https://doi.org/10.1016/j.camwa.2020.08.025.

 

B. G. Quiring and P. S. Vassilevski, Multilevel Graph Embedding, Numerical Linear Algebra with Applications, 2021;28:e2326. https://doi.org/10.1002/nla.2326.

 

C.S. Lee, F. Hamon, N, Castelletto, P.S. Vassilevski, and J. White, Nonlinear Multigrid Based on Local Spectral Coarsening for Heterogeneous Diffusion Problems, Computer Methods in Applied Mechanics and Engineering, 113432. https://doi.org/10.1016/j.cma.2020.113432.

 

A.T. Barker, S.V. Gelever, C.S. Lee, S.V. Osborn, and P.S. Vassilevski,  Multilevel Spectral Coarsening for Graph Laplacian Problems with Application to Reservoir Simulation, SIAM Journal on Scientific Computing  43(4)(2021), pp. A2737-A2765, https://doi.org/10.1137/19M1296343.

 

D. Kalchev and P. S. Vassilevski,

A Condensed Constrained Nonconforming Mortar-based Approach for Preconditioning Finite Element Discretization Problems, SIAM Journal on Scientific Computing  42(5)(2020), pp. A3136–A3156, https://doi.org/10.1137/19M1305690.

 

D. Kalchev and P. S. Vassilevski,

Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation, SIAM Journal on Scientific Computing  42(3)(2020), pp. A1741–A1764, https://doi.org/10.1137/19M1286815.

 

P. D'Ambra and P. S. Vassilevski,

Improving Solve Time of Aggregation-based Adaptive AMG, Numerical Linear Algebra with Applications, 2019; 26:e2269. https://doi.org/10.1002/nla.2269.

 

X. Hu and  P. S. Vassilevski,

Modifying AMG Coarse Spaces with Weak Approximation Property to Exhibit Approximation in Energy Norm, SIAM Journal on Matrix Analysis and Applications  40(3) (2019), pp. 1131-1152, https://doi.org/10.1137/18M1165190.

 

P. D'Ambra, L. Cutillo, and P. S. Vassilevski,

Bootstrap AMG for Spectral Clustering, Computational and Mathematical Methods 2019; e1020. https://doi.org/10.1002/cmm4.1020.

 

D. Cai and P. S. Vassilevski,

Eigenvalue Problems for Exponential Type Kernels,  Computational Methods in Applied Mathematics, (published online: 2019-04-06) 10.1515/cmam-2018-0186.

 

V.A. Dobrev, T. Kolev, C.S. Lee, V.Z. Tomov, and P. S. Vassilevski,

Algebraic Hybridization and Static Condensation with Application to H(div) Preconditioning, SIAM Journal on Scientific Computing  41(3) (2019), pp. B425-B447, https://doi.org/10.1137/17M1132562.

 

J. Gopalakrishnan, M. Neumueller, and P. S. Vassilevski,

The Auxiliary Space Preconditioner for the de Rham Complex, SIAM Journal on Numerical Analysis 56 (6) (2018), pp. 3196-3218, https://doi.org/10.1137/17M1153376.

 

K. Voronin, C.S. Lee, M. Neumueller, P. Sepulveda, and P. S. Vassilevski,

Space-Time Discretizations Using Constrained First-Order System Least-Squares (CFOSLS), Journal of Computational Physics 373(2018), pp. 863-876, https://doi.org/10.1016/j.jcp.2018.07.024.

 

C. Ponce, D.S. Bindel, and P. S. Vassilevski,

A Nonlinear Algebraic Multigrid Framework for the Power Flow Equations, SIAM Journal on Scientific Computing 40(3) (2018), pp. B811-B833, https://doi.org/10.1137/16M1109965.

 

P. D'Ambra, S. Filippone, and P. S. Vassilevski,

BootCMatch: A Software Package for Bootstrap AMG Based on Graph Weighted Matching, ACM Transactions on Mathematical Software (TOMS) 44(4) (2018) Article No. 39, https://dl.acm.org/citation.cfm?doid=3233179.3190647.

 

S. Osborn, P. Zulian, T. Benson, U. Villa, R. Krause, and P. S. Vassilevski,

Scalable Hierarchical PDE Sampler for Generating Spatially Correlated Random Fields Using Non-Matching Meshes, Numerical Linear Algebra with Applications 2018; e2146, https://doi.org/10.1002/nla.2146.

 

Max la Cour Christensen, Panayot S. Vassilevski, and Umberto Villa,

Nonlinear Multigrid Solvers Exploiting AMGe Coarse Spaces with Approximation Properties, Journal of Computational and Applied Mathematics 340 (2018), pp. 691-708, https://doi.org/10.1016/j.cam.2017.10.029.

S. Osborn, P. S. Vassilevski, and U. Villa,

A Multilevel, Hierarchical Sampling Technique for Spatially Correlated Random Fields, SIAM Journal on Scientific Computing 39(5) (2017), pp. S543-S562, https://doi.org/10.1137/16M1082688.

 

C. Ponce and P. S. Vassilevski,

Solving Graph Laplacian Systems through Recursive Bisection and Two-grid Preconditioning, SIAM Journal on Matrix Analysis and Applications 38(2) (2017), pp. 621-648, https://doi.org/10.1137/15M1050872.

 

A.T. Barker, C.S. Lee, and P. S. Vassilevski,

Spectral Upscaling for Graph Laplacian Problems with Application to Reservoir Simulation, SIAM Journal on Scientific Computing 39(5) (2017), pp. S323-S346, https://doi.org/10.1137/16M1077581.

 

Max la Cour Christensen, Umberto Villa, Allan P. Engsig-Karup, and Panayot S. Vassilevski, Numerical Upscaling for Incompressible Flow in Reservoir Simulation: An Element-based Algebraic Multigrid (AMGe) Approach, SIAM Journal on Scientific Computing 39(1) (2017), pp. B102-B137, https://doi.org/10.1137/140988991.

 

D. Kalchev, C. S. Lee, U. Villa, Y. Efendiev, and P. S. Vassilevski,

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method, SIAM Journal on Scientific Computing 38(5) (2016), pp. A2912-A2933, https://doi.org/10.1137/15M1036683.

 

R. E. Bank, P. S. Vassilevski, and L. T. Zikatanov,

Arbitrary Dimension Convection-Diffusion Schemes for Space-Time Discretizations, Journal of Computational and Applied Mathematics 310 (2017), pp. 19-31, https://doi.org/10.1016/j.cam.2016.04.029.

 

X. Hu, P. S. Vassilevski, and J. Xu,

A Two-Grid SA-AMG Convergence Bound that Improves when Increasing the Polynomial Degree, Numerical Linear Algebra with Applications 23 (4) (2016), pp. 746-771, https://doi.org/10.1002/nla.2053.

 

B. Ayuso de Dios, A.T. Barker, and P. S. Vassilevski,

A Combined Preconditioning Strategy for Nonsymmetric Systems, SIAM Journal on Scientific Computing 36 (6)(2014), pp. A2533-A2556, https://doi.org/10.1137/120888946.

 

P. D'Ambra and P. S. Vassilevski,

Adaptive AMG with Coarsening Based on Compatible Weighted Matching, Computing and Visualization in Science 16 (2013), pp. 59-76, https://doi.org/10.1007/s00791-014-0224-9.

 

I.V. Lashuk and P.S. Vassilevski,

The Construction of Coarse de Rham Complexes with Improved Approximation Properties, Computational Methods in Applied Mathematics 14 (2) (2014), pp. 257-303, https://doi.org/10.1515/cmam-2014-0004.

 

J. H. Adler and P. S. Vassilevski,

Error Analysis for Constrained First-Order System Least-Squares Finite Element Methods, SIAM Journal on Scientific Computing 36 (3) (2014), pp. A1071-A1088, https://doi.org/10.1137/130943091

 

A. Aposporidis, P. S. Vassilevski, and A. Veneziani,

Multigrid Preconditioning of the Non-regularized Augmented Bingham Fluid Problem, Electronic Transaction on Numerical Analysis 41 (2014), pp. 42-61, Link.

 

P. S. Vassilevski and U. M. Yang,

Reducing Communication in Algebraic Multigrid Using Additive Variants, Numerical Linear Algebra with Applications 21 (2) (2014), pp. 275-296, https://doi.org/10.1002/nla.1928.

 

P. S. Vassilevski and U. Villa,

A Mixed Formulation for the Brinkman Problem, SIAM Journal on Numerical Analysis 52 (1) (2014), pp. 258-281, https://doi.org/10.1137/120884109.

 

V. Kuhlemann and P. S. Vassilevski,

Improving the Communication Pattern in Mat-Vec Operations for Large Scale-free Graphs by Disaggregation, SIAM Journal on Scientific Computing 35 (5) (2013), pp. S465-S486, https://doi.org/10.1137/12088313X.

 

D. Kalchev, C. Ketelsen, and P. S. Vassilevski,

Two-Level Adaptive Algebraic Multigrid for a Sequence of Problems with Slowly Varying Random Coefficients, SIAM Journal on Scientific Computing 35 (6) (2013), pp. B1215-B1234, https://doi.org/10.1137/120895366.

 

P. S. Vassilevski and L.T. Zikatanov, Commuting Projections on Graphs, Numerical Linear Algebra with Applications 21 (3) (2014), pp. 297-315, https://doi.org/10.1002/nla.1872.

 

X. Hu, P. S. Vassilevski, and J. Xu, Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid, SIAM Journal on Numerical Analysis 51 (2) (2013), pp. 1349-1369, https://doi.org/10.1137/110850049.

 

P. S. Vassilevski and U. Villa, A Block-Diagonal Algebraic Multigrid Preconditioner for the Brinkman Problem, SIAM Journal on Scientific Computing 35 (5) (2013), pp. S3-S17, https://doi.org/10.1137/120882846.

 

T. V. Kolev and P. S. Vassilevski, Parallel Auxiliary Space AMG for H(div) Problems, SIAM Journal on Scientific Computing 34 (2012), pp. A3079-A3098, https://doi.org/10.1137/110859361.

 

J. Kraus, P.S. Vassilevski, and L.T. Zikatanov, Polynomial of Best Uniform Approximation to 1/x and Smoothing in Two-Level Methods, Computational Methods in Applied Mathematics 12 (4) (2012), pp. 448-468, https://doi.org/10.2478/cmam-2012-0026.

 

T. V. Kolev and P. S. Vassilevski, Regular Decompositions for H(div) Spaces, Computational Methods in Applied Mathematics 12 (4) (2012), pp. 437-447, https://doi.org/10.2478/cmam-2012-0024.

 

R. Scheichl, P. S. Vassilevski, and L.T. Zikatanov, Multilevel Methods for Elliptic Problems with Highly Varying Coefficients on Non-aligned Coarse Grids, SIAM Journal on Numerical Analysis 50 (2012), pp. 1675-1694, https://doi.org/10.1137/100805248.

 

I. Lashuk and P. S. Vassilevski, Element Agglomeration Coarse Raviart-Thomas Spaces with Improved Approximation Properties, Numerical Linear Algebra with Applications 19 (2) (2012), pp. 414-426, https://doi.org/10.1002/nla.1819.

 

R. Scheichl, P. S. Vassilevski, and L.T. Zikatanov, Weak Approximation Properties of Elliptic Projections with Functional Constraints, Multiscale Modeling & Simulation 9 (2011), pp. 1677-1699, https://doi.org/10.1137/110821639.

 

M. Brezina, P. Vanek, and P. S. Vassilevski, An Improved Convergence Analysis of Smoothed Aggregation Algebraic Multigrid, Numerical Linear Algebra with Applications 19 (3) (2012), pp. 441-469, https://doi.org/10.1002/nla.775.

 

P. S. Vassilevski, Coarse Spaces by Algebraic Multigrid: Multigrid Convergence and Upscaling Error Estimates, Advances in Adaptive Data Analysis 3 (1 & 2) (2011), pp. 229-249, https://doi.org/10.1142/S1793536911000830.