Tzanio Kolev is a computational mathematician at the Center for Applied Scientific Computing, where he works on finite element discretizations and solvers for problems arising in various application areas, such as compressible shock hydrodynamics, multi-material ALE simulations, radiation-hydrodynamics and computational electromagnetics. He is the project leader of the MFEM finite element library and the High-Order Curvilinear Finite Elements for Shock Hydrodynamics (BLAST) projects. He is also a member of the Scalable Linear Solvers (hypre) and the Parallel Time Integration with Multigrid (XBraid) projects.
Tzanio's research interests include the development and analysis of advanced finite element discretization methods, massively parallel preconditioners, discretization-enhanced algebraic multigrid algorithms, and the design and implementation of large-scale scientific software. He joined Lawrence Livermore National Laboratory in 2004 after earning a Ph.D. in Mathematics from Texas A&M University. His dissertation was on least-squares methods for electromagnetic problems.
Scalable Finite Elements
High-order Shock Hydrodynamics
Finite Element Visualization
Scalable Linear Solvers
Parallel Time Integration
High-order Mesh Optimization
- MFEM version 3.2 and GLVis version 3.2 released. (Jun 30, 2016)
- New LLNL open-source software Blog and Twitter. (Mar 4, 2016)
- MFEM version 3.1 released. See the interactive documentation. (Feb 16, 2016)
- BLAST and MFEM simulation images in the "Art of Science" exhibition at the Livermore public library. (Feb 5, 2016)
- GLVis version 3.1 released. See the new features. (Feb 5, 2016)
- News highlight: "High-Order Finite Element Library Provides Scientists with Access to Cutting-Edge Algorithms". (Jan 6, 2016)
- MFEM and GLVis repositories moved to GitHub. New websites: mfem.org and glvis.org. (Aug 18, 2015)
- News highlight: "Interweaving Timelines to Save Time". (Apr 13, 2015)
- MFEM version 3.0 released. (Jan 26, 2015)
- GLVis version 3.0 released. (Jan 26, 2015)
- News highlight: "Remapping Algorithm Boosts BLAST Simulations". (Jan 13, 2015)
Publications hosted at LLNL (no longer updated)
R. Anderson V. Dobrev, Tz. Kolev and R. Rieben, Monotonicity in High-Order Curvilinear Finite Element ALE Remap, International Journal for Numerical Methods in Fluids, 2014, pp. 249-273.
R. Falgout, S. Friedhoff, Tz. Kolev, S. MacLachlan and J. Schroder, Parallel Time Integration with Multigrid, SIAM Journal on Scientific Computing, 2014, pp.C635–C661.
V. Dobrev, Tz. Kolev and R. Rieben, High-order curvilinear finite element methods for elastic-plastic Lagrangian dynamics, Journal of Computational Physics, 2014, pp.1062-1080.
V. Dobrev, T. Ellis, Tz. Kolev and R. Rieben, High-order curvilinear finite elements for axisymmetric Lagrangian hydrodynamics, Computers and Fluids, 2013, pp.58-69.
Tz. Kolev and P. Vassilevski, Parallel auxiliary space AMG solver for H(div) problems, SIAM Journal on Scientific Computing, (34) 2012, pp. A3079-A3098.
Tz. Kolev and P. Vassilevski, Regular decompositions for H(div) spaces, Computational Methods in Applied Mathematics, (12) 2012, pp.437-447.
V. Dobrev, Tz. Kolev and R. Rieben, High-order curvilinear finite element methods for Lagrangian hydrodynamics, SIAM Journal on Scientific Computing, (34) 2012, pp.B606–B641.
A.Baker, R. Falgout, Tz. Kolev and U. Yang, Scaling hypre's multigrid solvers to 100,000 cores, High Performance Scientific Computing: Algorithms and Applications - A Tribute to Prof. Ahmed Sameh, M. Berry et al., eds., Springer 2012, pp.261-279.
A. Baker, R. Falgout, T. Gamblin, Tz. Kolev, M. Schulz, and U. Yang, Scaling algebraic multigrid solvers: on the road to exascale, Proc. of Competence in High Performance Computing, CiHPC 2010, Schwetzingen Germany, Springer 2012, pp 215-226.
T. Brunner and Tz. Kolev, Algebraic multigrid for linear systems obtained by explicit element reduction, SIAM Journal on Scientific Computing, (33) 2011, pp.2706-2731.
V. Dobrev, T. Ellis, Tz. Kolev and R. Rieben, Curvilinear finite elements for Lagrangian hydrodynamics, International Journal for Numerical Methods in Fluids, (65) 2011, pp. 1295–1310.
A. Baker, Tz. Kolev and U. Yang, Improving algebraic multigrid interpolation operators for elasticity problems, Numer. Linear Algebra Appl., (17) 2010, pp. 495-517.
Tz. Kolev and P. Vassilevski, Parallel auxiliary space AMG for H(curl) problems, special issue on “Adaptive and Multilevel Methods in Electromagnetics”, Journal of Computational Mathematics, (27) 2009, pp. 604-623.
A. Baker, E. Jessup, and Tz. Kolev, A simple strategy for varying the restart parameter in GMRES(m), Journal of Computational and Applied Mathematics, (230) 2009, pp. 751-761.
Tz. Kolev and P. Vassilevski, Auxiliary space AMG for H(curl) problems, Proceedings of the 17th International Conference on Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering, Springer, 2008, pp.147-154.
Tz. Kolev, J. Pasciak, and P. Vassilevski, H(curl) auxiliary mesh preconditioning, Numer. Linear Algebra Appl., (15) 2008, pp. 455-471.
Tz. Kolev and P. Vassilevski, AMG by element agglomeration and constrained energy minimization interpolation, Numer. Linear Algebra Appl., (13) 2006, pp. 771-788.
J. Bramble, Tz. Kolev and J. Pasciak, A least-squares method for the time-harmonic Maxwell equations, Journal of Numerical Mathematics, (13) 2005, pp. 237-263.
J. Bramble, Tz. Kolev and J. Pasciak, The approximation of the Maxwell eigenvalue problem using a least-squares method, Math. Comp., (74) 2005, pp. 1575-1598.
Tz. Kolev and S. Margenov, AMLI preconditioning of pure displacement non-conforming elasticity FEM systems, Proceedings of the Second Conference on Numerical Analysis and Applications, Lecture Notes in Computer Science, Springer, 2001, pp. 482-489.
Tz. Kolev and S. Margenov, Two-level preconditioning of pure displacement non-conforming FEM systems, Numer. Linear Algebra Appl., (6) 1999, pp. 535-555.
Other documents (no longer updated)NNSA Office of Advanced Scientific Computing eNews, March 2013.
NNSA LDRD Symposium, 2011.
A. Baker, R. Falgout, Tz. Kolev and U. Yang, Multigrid smoothers for ultra-parallel computing: Additional theory and discussion, LLNL Technical Report, 2011. LLNL-JRNL-489114
T. Ellis, High Order Finite Elements for Lagrangian Computational Fluid Dynamics, Master's Thesis, California Polytechnic State University - San Luis Obispo, 2010.
Novel solver enables scalable electromagnetic simulations, plenary talk at the SciDAC 2009 conference.
Top Breakthroughs in Computational Science, SciDAC Review, (11) 2009.
Linear solutions at hypre speed, 2007.
Mathematisches Forschungsinstitut Oberwolfach, Report No. 5/2007 on Computational Electromagnetism and Acoustics.
Tz. Kolev and P. Vassilevski, Parallel eigensolver for H(curl) problems using H1-auxiliary space AMG preconditioning, LLNL Technical Report 226197, 2006.
Tz. Kolev and P. Vassilevski, Parallel H1-based auxiliary space AMG solver for H(curl) problems, LLNL Technical Report 222763, 2006.Tz. Kolev and P. Vassilevski, Some experience with a H1-based auxiliary space AMG for H(curl) problems, LLNL Technical Report 221841, 2006.
Tz. Kolev, Least-Squares Methods for Computational Electromagnetics, Dissertation, Texas A&M University, 2004.
Tz. Kolev, J. Pasciak, and P. Vassilevski, Algebraic construction of mortar finite element spaces with application to parallel AMGe, LLNL Technical Report UCRL-JC-153326, 2003.