Panayot S. Vassilevski is a computational mathematician at CASC. His research interests include numerical linear algebra and finite element methods at large, and in particular preconditioned iterative methods, multigrid methods, as well as the derivation and analysis of discretization schemes for partial differential equations.

Dr. Vassilevski joined LLNL in March 1998. He received his Ph.D. in Mathematics from the St. Kliment Ohridski University of Sofia in 1984. Prior to joining LLNL, he held a number of visiting faculty positions at UCLA (1991-1993), Texas A&M University (spring 1996), Bowling Green State University (spring 1997) and UCSD (spring 1998).

Here at CASC, Dr. Vassilevski research was related to the Scalable Linear Solvers project. Currently, he leads a project on Finite Element Upscaling and Algebraic Multigrid as well as a project on Bayesian UQ in Prediction of Flow in Highly Heterogeneous Porous Media.

He is the editor-in-chief for the journal Numerical Linear Algebra with Applications.

### Selected Publications

Monograph

### Recent Journal Publications

P.S. Vassilevski,

"Coarse Spaces by Algebraic Multigrid: Multigrid Convergence and Upscaling Error Estimates,"

(2010) (to appear).

Available as Lawrence Livermore National Laboratory Technical Report LLNL-PROC-432896, May 21, 2010.

Ming Gu, Xiaoye S. Li, and Panayot S. Vassilevski

"Direction-Preserving and Schur-Monotonic Semiseparable Approximations of Symmetric Positive Definite Matrices,"

SIAM Journal on Matrix Analysis and Applications 31(2010), pp. 2650-2664.

P.S. Vassilevski,

"General constrained energy minimization interpolation mappings for AMG,"

SIAM Journal on Scientific Computing 32(2010), pp. 1-13.

Also available as Lawrence Livermore National Laboratory Technical Report LLNL-JRNL-404462, June 5, 2008.

T.V. Kolev and P.S. Vassilevski,

"Parallel auxiliary space AMG for {H(curl)} problems, Journal of Computational Mathematics 27(2009), pp. 604--623.

Available as Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-237306, December 2007.

T.V. Kolev, J.E. Pasciak, and P.S. Vassilevski,

"H(curl) Auxiliary Mesh Preconditioning,"

Numerical Linear Algebra with Applications 15(2008), pp. 455--471.

Also available as LLNL Technical Report UCRL-JRNL-224227.

Y. Notay and P.S. Vassilevski,

"Recursive Krylov-based multigrid cycles,"

Numerical Linear Algebra with Applications 15(2008), pp. 473--487.

Also available as LLNL Technical Report UCRL-JRNL-226013.

I. Lashuk and P.S. Vassilevski,

"On Some Versions of the Element Agglomeration AMGe Method,"

Numerical Linear Algebra with Applications 15(2008), pp. 595--620.

Also available as Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-233772.

J.~E. Pasciak and P.S. Vassilevski,

"Exact de Rham Sequences of Spaces Defined on Macro-elements in Two and Three Spatial Dimensions,"

SIAM Journal on Scientific Computing 30(2008), pp. 2427-2446.

Also available as Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-233047, July 2007.

M. Brezina, T. Manteuffel, S. McCormick, J. Ruge, G. Sanders, and P.S. Vassilevski,

"Generalized Eigensolver based on Smoothed Aggregation (GES-SA) for Initializing Smoothed Aggregation Multigrid (SA),"

Numerical Linear Algebra with Applications 15(2008), pp. 249--269.

Also available as Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-231442.

R.E. Bank and P.S. Vassilevski, "Convergence Analysis of a Domain Decomposition Paradigm,''

Computing and Visualization in Science 11(2008), pp. 333--350.

Also available as Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-222227.

Dr. Vassilevski joined LLNL in March 1998. He received his Ph.D. in Mathematics from the St. Kliment Ohridski University of Sofia in 1984. Prior to joining LLNL, he held a number of visiting faculty positions at UCLA (1991-1993), Texas A&M University (spring 1996), Bowling Green State University (spring 1997) and UCSD (spring 1998).

Here at CASC, Dr. Vassilevski research was related to the Scalable Linear Solvers project. Currently, he leads a project on Finite Element Upscaling and Algebraic Multigrid as well as a project on Bayesian UQ in Prediction of Flow in Highly Heterogeneous Porous Media.

He is the editor-in-chief for the journal Numerical Linear Algebra with Applications.

Panayot S. Vassilevski,

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

Panayot S. Vassilevski,

Lecture Notes on Multigrid Methods, Available as Lawrence Livermore National Laboratory Technical Report LLNL-TR-439511 [pdf]

"Coarse Spaces by Algebraic Multigrid: Multigrid Convergence and Upscaling Error Estimates,"

(2010) (to appear).

Available as Lawrence Livermore National Laboratory Technical Report LLNL-PROC-432896, May 21, 2010.

Ming Gu, Xiaoye S. Li, and Panayot S. Vassilevski

"Direction-Preserving and Schur-Monotonic Semiseparable Approximations of Symmetric Positive Definite Matrices,"

SIAM Journal on Matrix Analysis and Applications 31(2010), pp. 2650-2664.

P.S. Vassilevski,

"General constrained energy minimization interpolation mappings for AMG,"

SIAM Journal on Scientific Computing 32(2010), pp. 1-13.

Also available as Lawrence Livermore National Laboratory Technical Report LLNL-JRNL-404462, June 5, 2008.

T.V. Kolev and P.S. Vassilevski,

"Parallel auxiliary space AMG for {H(curl)} problems, Journal of Computational Mathematics 27(2009), pp. 604--623.

Available as Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-237306, December 2007.

T.V. Kolev, J.E. Pasciak, and P.S. Vassilevski,

"H(curl) Auxiliary Mesh Preconditioning,"

Numerical Linear Algebra with Applications 15(2008), pp. 455--471.

Also available as LLNL Technical Report UCRL-JRNL-224227.

Y. Notay and P.S. Vassilevski,

"Recursive Krylov-based multigrid cycles,"

Numerical Linear Algebra with Applications 15(2008), pp. 473--487.

Also available as LLNL Technical Report UCRL-JRNL-226013.

I. Lashuk and P.S. Vassilevski,

"On Some Versions of the Element Agglomeration AMGe Method,"

Numerical Linear Algebra with Applications 15(2008), pp. 595--620.

Also available as Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-233772.

J.~E. Pasciak and P.S. Vassilevski,

"Exact de Rham Sequences of Spaces Defined on Macro-elements in Two and Three Spatial Dimensions,"

SIAM Journal on Scientific Computing 30(2008), pp. 2427-2446.

Also available as Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-233047, July 2007.

M. Brezina, T. Manteuffel, S. McCormick, J. Ruge, G. Sanders, and P.S. Vassilevski,

"Generalized Eigensolver based on Smoothed Aggregation (GES-SA) for Initializing Smoothed Aggregation Multigrid (SA),"

Numerical Linear Algebra with Applications 15(2008), pp. 249--269.

Also available as Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-231442.

R.E. Bank and P.S. Vassilevski, "Convergence Analysis of a Domain Decomposition Paradigm,''

Computing and Visualization in Science 11(2008), pp. 333--350.

Also available as Lawrence Livermore National Laboratory Technical Report UCRL-JRNL-222227.