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 (2025-2026):

Fall term: MTH 231: “Data Science Seminar”

 

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

 

P. S. Vassilevski, Fractional Order Hierarchical Decompositions Using Multigrid Components, Numerical Linear Algebra with Applications, 32(6)(2025), e70048. https://doi.org/10.1002/nla.70048.

 

Hillary R. Fairbanks, Delyan Z. Kalchev, Chak Shing Lee, and P. S. Vassilevski, Scalable Multilevel Monte Carlo Methods Exploiting Parallel Redistribution on Coarse Levels, International Journal of High Performance Computing Applications, 2025 (accepted). https://arxiv.org/abs/2408.02241

 

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 513(2024), 113163, https://doi.org/10.1016/j.jcp.2024.113163.

(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.