doc. RNDr. Tomas Vejchodsky, Ph.D.

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Contact information:
Mail: Institute of Mathematics, Czech Academy of Sciences
Zitna 25 
115 67 Praha 1 
Czech Republic 
Phone:  +420 222 090 713    (office) 
+420 222 090 711    (operator)
Fax: +420 222 211 638
E-mail:  see http://www.math.cas.cz/people.html

Professional interests:

Proposals of theses topics:

Education:

1995-2000
Master study at the Faculty of Mathematics and Physics of the Charles University in Prague.
2000-2003
Doctoral study at the Mathematical Institute of the Academy of Sciences of the Czech Republic
2004-
Scientific worker at the same insitute.

List of publications:

  1. T. Vejchodsky, A posteriori error estimates with the method of lines for parabolic equations, master thesis, Faculty of Mathematics and Physics, Charles University in Prague, 2000.
  2. T. Vejchodsky, Fully discrete error estimation with the method of lines of a nonlinear parabolic problem, Appl. Math. (Prague) 48 (2003), no. 2, 129-151. [MR 2003m:65162] Download.
  3. T. Vejchodsky, A posteriori error estimates for a nonlinear parabolic problem, WDS'01, Proceedings of contributed papers, Part I, Mathematics, Computer and Educational Sciences, pp. 16-20, 2001.
  4. M. Krizek, J. Nemec, T. Vejchodsky, A posteriori error estimates for axisymmetric and nonlinear problems, Adv. Comput. Math. 15 (2001), no. 1-4, 219-236. [MR 2002m:65123]
  5. T. Vejchodsky, Comparison principle for a nonlinear parabolic problem of a nonmonotone type, Appl. Math. (Warsaw) 29 (2002), no. 1, 65-73. [MR 2003g:35114]
  6. T. Vejchodsky, On the nonmonotony of nonlinear elliptic operators in divergence form, Adv. Math. Sci. Appl. 14 (2004), no. 1, 25-33. [MR 2005e:35083]
  7. T. Vejchodsky, On a posteriori error estimation strategies for elliptic problems, in: J. Privratska, J. Prihonska, D. Andrejsova (Eds.), Proceedings of international conference ICPM'05, Liberec, Czech Republic, 2005, pp. 373-386. Download preprint.
  8. T. Vejchodsky, Survey of a posteriori error estimates for elliptic and parabolic problems, in preparation.
  9. T. Vejchodsky, On the nonnegativity conservation in semidiscrete parabolic problems. In: M. Krizek, P. Neittaanmaki, R. Glowinski, S. Korotov (Eds.), Conjugate Gradients Algorithms and Finite Element Methods, pp. 197-210, Springer-Verlag, Berlin, 2004. [MR 2005i:65135]
  10. T. Vejchodsky, Finite element approximation of a nonlinear parabolic heat conduction problem and a posteriori error estimators, doctoral thesis, Faculty of Mathematics and Physics, Charles University in Prague, Mathematical Institute of the Academy of Sciences, 2003.
  11. T. Vejchodsky, Local a posteriori error estimator based on the hypercircle method, in: P. Neittaanmaki, T. Rossi, S. Korotov, E. Onate, J. Periaux, and D. Knorzer (eds.), European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2004, Jyvaskyla, 24-28 July 2004, 16pp. (electronic, http://www.mit.jyu.fi/eccomas2004/)
  12. T. Vejchodsky, Method of lines and conservation of nonnegativity, in: P. Neittaanmaki, T. Rossi, S. Korotov, E. Onate, J. Periaux, and D. Knorzer (eds.), European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2004, Jyvaskyla, 24-28 July 2004, 18pp. (electronic, http://www.mit.jyu.fi/eccomas2004/)
  13. T. Vejchodsky, Fast and guaranteed a posteriori error estimator, in: J. Chleboun, P. Prikryl, K. Segeth (Eds.), Programs and Algorithms of Numerical Mathematics 12, pp. 257-272, Prague, 2004.
  14. T. Vejchodsky, Guaranteed and locally computable a posteriori error estimate. IMA J. Numer. Anal. 26 (2006), no. 3, 525-540. [MR2241313, Zbl 1096.65112] Download offprint.
  15. P. Solin, T. Vejchodsky, A weak discrete maximum principle for hp-FEM, accepted by J. Comput. Appl. Math., 2006. Download preprint.
  16. T. Vejchodsky, P. Solin, M. Zitka, Modular hp-FEM System HERMES and Its Application to Maxwell's Equations, Math. Comput. Simulation 76 (2007) 223-228, doi:10.1016/j.matcom.2007.02.001.
  17. M. Zitka, P. Solin, T. Vejchodsky, F. Avila, Imposing Orthogonality to Hierarchic Higher-Order Finite Elements, Math. Comput. Simulation 76 (2007) 211-217, doi:10.1016/j.matcom.2007.01.025.
  18. P. Solin, T. Vejchodsky, R. Araiza, Discrete Conservation of Nonnegativity for Elliptic Problems Solved by the hp-FEM, Math. Comput. Simulation 76 (2007) 205-210, doi:10.1016/j.matcom.2007.01.015.
  19. P. Solin, T. Vejchodsky, M. Zitka, Orthogonal hp-FEM for Elliptic Problems Based on a Non-Affine Concept, in: A. Bermudes, D. Gomez, P. Quintela, P. Salgado (Eds.), Numerical Mathematics and Avanced Applications, ENUMATH 2005, Springer, Berlin, 2006, pp. 683-690.
  20. T. Vejchodsky, P. Solin, M. Zitka, On some aspects of the hp-FEM for time-harmonic Maxwell's equations, in: A. Bermudes, D. Gomez, P. Quintela, P. Salgado (Eds.), Numerical Mathematics and Avanced Applications, ENUMATH 2005, Springer, Berlin, 2006, pp. 691-699.
  21. T. Vejchodsky, P. Solin, Discrete Maximum Principle for Poisson Equation with Mixed Boundary Conditions Solved by hp-FEM, submitted 2006. Download preprint.
  22. T. Vejchodsky, P. Solin, Discrete Maximum Principle for Higher-Order Finite Elements in 1D, Math. Comp. 76 (2007), 1833-1846. Download preprint.
  23. T. Vejchodsky, P. Solin, Discrete Maximum Principle for a 1D Problem with Piecewise-Constant Coefficients Solved by hp-FEM, accepted by J. Numer. Math., 2007. Download preprint.
  24. P. Solin, T. Vejchodsky, Higher-Order Finite Elements Based on Generalized Eigenfunctions of the Laplacian, Internat. J. Numer. Meth. Engrg. 2008, in press, doi: 10.1002/nme.2129. Download preprint.
  25. T. Vejchodsky, The problem of adaptivity for hp-FEM, in: J. Privratska, J. Prihonska, Z. Andres (eds.) ICPM'06, Technicka univerzita v Liberci, Liberec, 2006, pp. 247-254. Download preprint.
  26. T. Vejchodsky, P. Solin, Discrete Green's function and Maximum Principles, in: J. Chleboun, K. Segeth, T. Vejchodsky (Eds.), Programs and Algorithms of Numerical Mathematics 13, Mathematical Institute ASCR, Prague, 2006, pp. 247-252. Download the proceedings.
  27. T. Vejchodsky, P. Solin, Improving Conditioning of hp-FEM, in: SNA'07 Modelling and Simulation of Challenging Engineering Prolems, Institute of Geonics AS CR, Ostrava, 2007, pp. 126-129. Download preprint.
  28. T. Vejchodsky, P. Solin, Static condensation, partial orthogonalization of basis functions, and ILU preconditioning in hp-FEM, accepted by J. Comput. Appl. Math., 2007, doi: 10.1016/j.cam.2007.04.04. Download preprint.
  29. J. Chleboun, K. Segeth, T. Vejchodsky (Eds.), Programs and Algorithms of Numerical Mathematics 13, Mathematical Institute ASCR, Prague, 2006, 257 p., ISBN 80-85823-54-3. Download PDF.
  30. T. Vejchodsky, Higher-order discrete maximum principle for 1D diffusion-reaction problems, submitted to Appl. Numer. Math., 2008. Download preprint. Special web of this paper.
  31. A. Hannukainen, S. Korotov, T. Vejchodsky, Discrete maximum principle for 3D-FE solutions of the diffusion-reaction problem on prismatic meshes, accepted by J. Comput. Appl. Math., 2008. Download preprint.
  32. T. Vejchodsky, On Efficient Solution of Linear Systems Arising in hp-FEM, in: K. Kunish, G. Of, O. Steinbach (eds.) Numerical Mathematics and Advanced Applications, ENUMATH 2007, Springer, Berlin, 2008, pp. 199–206. Download preprint.
  33. T. Vejchodsky, Computational comparison of the discretization and iteration errors, in: SNA'08 Modelling and Simulation of Challenging Engineering Problems, Technical University of Liberec, Liberec, 2007, pp. 131-134. Download preprint.
  34. R. Erban, S.J. Chapman, I.G. Kevrekidis, T. Vejchodsky, Analysis of a stochastic chemical system close to a SNIPER bifurcation of its mean-field model, SIAM J. Appl. Math. 70 (2009) 984-1016. Download paper.
  35. A. Hannukainen, S. Korotov, T. Vejchodsky, Discrete maximum principle for parabolic problems solved by prismatic finite elements, Math. Comput. Simulation, to appear. Download preprint.
  36. T. Vejchodsky, Complementarity based a posteriori error estimates and their properties, submitted to Math. Comput. Simulation, 2009. Download preprint.
  37. S. Korotov, T. Vejchodsky, A comparison of simplicial and block finite elements, submitted to proceedings of ENUMATH'09.
  38. T. Vejchodsky, Angle Conditions for Discrete Maximum Principles in Higher-Order FEM, submitted to proceedings of ENUMATH'09.

Theses:

  1. Master thesis: A posteriori error estimates with the method of lines for parabolic equations, Faculty of Mathematics and Physics, Charles University in Prague, 2000. Download: "MasterTh.zip" (zipped PostScript - 0.5 MB).
  2. Doctoral thesis: Finite element approximation of a nonlinear parabolic heat conduction problem and a posteriori error estimators, Mathematical Institute of the Academy of Sciences and Faculty of Mathematics and Physics, Charles University in Prague, 2003. Download: "DoctorTh.zip" (zipped PostScript - 3.3 MB).
  3. Habilitation thesis: Discrete maximum principles, Institute of Mathematics of the Academy of Sciences and Faculty of Mathematics and Physics, Charles University in Prague, 2011. Download: "habil_vejch_lowq.pdf" (PDF - 7.1 MB, 150 DPI).

Presentations to download:

Software:

hplab2D
An hp-FEM solver for Matlab.
GillespieSSA
Gillespie Stochastic Simulation Algorithm for Matlab.

Last actualization 29. 9. 2011.
e-mail: see http://www.math.cas.cz/people.html
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