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Mathematical methods of preconditioning in nonlinear physical models
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I. Dimov, I. Faragó, A. Z. Zlatev: Parallel computations with large-scale air pollution models, Problems in Programming 3, 44-52., 2003 | L. Lóczi: A normal form for the fold bifurcation and its discretization, Preprint 03/006, DFG research group ''Spectral analysis, asymptotic distributions and stochastic dynamics'', Univ. of Bielefeld, www.mathematik.uni-b, 2003 | I. Faragó, Á. Havasi: Relationship between vanishing splitting errors and pairwise commutativity, Applied Math. Letters (közlésre elfogadva), 2007 | L. Lóczi: A thesaurus.maths.org többnyelvű internetes matematikai fogalomtár, Matematika Tanári Kincsestár, 13. kieg. kötet, 2004. szept., I 4.2. 1-8., 2004 | L. Lóczi: Könyvismertető: Prem K. Kythe, Pratap Puri, Michael R. Schäferkotter: Partial Differential Equations and Mathematica, Alkalmazott Matematikai Lapok, 21 (2003) 177-179., 2003 | L. Lóczi: Two centuries of the equations of commutativity and associativity of exponentiation, Teaching Math. and Comp. Sci., 1/2 (2003) 219-233., 2003 | P. Csomós, Á. Havasi, I. Faragó: Weighted sequential splittings and their analysis, Comp. Math. Appl., 50, 1017-1031., 2005 | P. Csomós: Some aspects of interaction between operator splitting procedures and numerical methods, Adv. in Air Pollution Modeling for Environmental Sec., NATO Science Series, 54, Springer Verlag, 77-91., 2005 | I. Dimov, I. Faragó, Á. Havasi, Z. Zlatev: Operator splitting and commutativity analysis in the Danish Eulerian Model, Math. Comp. Sim. V. 67 (2004) 217-233., 2004 | M. Botchev, I. Faragó, A. Havasi: Testing weighted splitting schemes on a one-column transport-chemistry model, Int. J. Environmental Pollution 22, 3-16., 2004 | I. Faragó: Operator splittings and numerical methods, Lect. Notes Comp. Sci. 3743, Springer Verlag, Berlin, 347-354., 2006 | R. Horváth, I. Faragó, W.H.A. Schilders: Iterative Solution Methods of the Maxwell Equations Using Staggered Grid Spatial Discretization, : Fifty Years of Conjugate Gradient, Springer Verlag Berlin, 2004, 211-220., 2004 | F. Izsák, I. Lagzi: Precipitate pattern formation in fluctuating media, J. Chem. Phys., V.120 (2004) 1837-1840., 2004 | J. Karátson: Constructive Sobolev gradient preconditioning for semilinear elliptic systems, Electron. J. Diff. Eqns. (2004), N 75, 1-26., 2004 | M. Botchev, I. Faragó, R. Horváth: Application of the operator splitting to the Maxwell equations with the source term, Memorandum 1818, Department of Applied Mathematics, University of Twente, Enschede. ISSN 0169-2690. http://eprints.eemcs.utwente.nl/9206/, 2007 | O. Axelsson, J. Karátson,: , Conditioning analysis of separate displacement preconditioners for some nonlinear elasticity systems, Comput. Math. Simul., .64 (2004), 649-668., 2004 | O. Axelsson, I. Faragó, J. Karátson: On the application of preconditioning operators for nonlinear elliptic problems, Conjugate Gradient Algorithms and Finite Element Methods, Springer, 2004, 247-261., 2004 | I. Faragó, S. Korotov: Nonnegativity preservation in the numerical solution of linear partial differntial equations, Conjugate Gradient Algorithms and Finite Element Methods, Springer Verlag, Berlin, 2004, 185-196., 2004 | I. Faragó, R. Horváth, S. Korotov: Discrete maximum principle for Galerkin finite element solutions to parabolic problems on rectangular meshes, Feistauer, M. et all ed; Numerical Mathematics and Advanced Applications; Springer Verlag, Berlin, 2004, 298-307., 2004 | I. Faragó: Splitting methods for abstract Cauchy problems, in: Numerical Analysis and Its Application, , Lect. Notes Comp.Sci. 3401, Springer Verlag, Berlin, 2005, 35-45., 2004 | B. M. Garay, L. Lóczi: Monotone delay equations and Runge-Kutta discretization, Functional Differential Equations, Vol. 11, (2004) 59-67., 2004 | I. Lagzi, F. Izsák: Stabilization and destabilization effects of the electric field on stochastic precipitate pattern formation, Chem. Phys., V.303 (2004) 151-155., 2004 | I. Lagzi, F. Izsák, S.C. Muller, J. Ross: , Comment on ``Precipitate pattern formation in fluctuating media\'\', J. Chem. Phys., V. 121(2004) 3943-3943., 2004 | L. Lóczi: Az ötödfokú egyenlet megoldása, POLYGON folyóirat (közlésre elfogadva), 2007 | J. Karátson, S.Korotov: Continuous and discrete maximum principles for nonlinear elliptic problems, Computational and Mathematical Methods in Science and Engineering, (2004) 191-200., 2004 | I. Faragó, Á. Havasi: On the convergence and local splitting error of different splitting schemes, Progress in Computational Fluid Dynamics, 5 (2005) 495-504., 2005 | P. Csomós: Analysis of a transport model applying operator splitting and semi-Lagrangian method, International Journal of Computational Science and Engineering (közlésre elfogadva), 2007 | P. Csomós: Analyticcal solutions and numerical experiments for optimizing operator splitting procedures, Időjárás, Quarterly Journal of Hungarian Meteorological Service (közlésre elfogadva), 2007 | I. Faragó: New operator splittings and their applications, Lect. Notes Comp. Sci. 4310, Springer Verlag, Berlin, 443-450., 2007 | P. Csomós: Operator splitting procedures for air pollution transport models, Proceedings of the 5th International Conference on Large-Scale Scientific Computations, June 6-10, Sozopol (2005) (to appear)., 2005 | I. Faragó, J. Karátson: Variable preconditioning for nonlinear elliptic problems via inexact Newton methods in Hilbert spaces, SIAM J. Numer. Anal. 41, 1242-1262., 2003 | F. Izsák: An existence theorem for a type of functional differential equation with infinite delay, Acta Mathematica Hungarica, 108 (2005) 137-153., 2005 | I. Faragó, R. Horváth, S. Korotov: Discrete maximum principle for linear parabolic problems solved on hybrid meshes, Appl. Numer. Math. 43, 249-264., 2005 | J. Karátson: Sobolev regularity of the second biharmonic problem on a rectangle, Acta Math. Hung., 109 (2005) 269-273., 2005 | M. Ripszam, D. Nagy, A. Wolford, I. Lagzi, F. Izsák: The Liesegang eyes phenomenon, Chemical Physics Letters, 414 (2005).384-388., 2005 | I. Faragó, S. Korotov, P. Neittaanmäki: Galerkin approximations for the linear parabolic equation with the third boundary condition, Appl. Math. 48, 111-128., 2003 | J. Karátson, S. Korotov: Discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions, Numer. Math., 99 (2005) 669-698., 2005 | L. Lóczi: Conjugacy in the discretized transcritical bifurcation, Preprint 05/016, DFG research group ''Spectral analysis, asymptotic distributions and stochastic dynamics'', Univ. of Bielefeld, www.mathematik.uni-b, 2005 | I. Faragó, R. Horváth, W. Schilders: Investigation of numerical time integrations of the Maxwell equations using the staggered grid spatial discretization, Int. J. Num. Modelling, 18, 149-169., 2005 | I. Faragó: Lax equivalence theorem in Banach spaces with parameter, Tübinger Berichte zur Funktionalanalysis, 14, Univesität Tübingen 89-95., 2005 | I. Faragó: Splitting methods for abstract Cauchy problems, in: Z. Li, L. Vulkov, J. Wa¶niewski eds. Numerical Analysis and Its Application, Lect. Notes Comp. Sci. 3401, Springer Verlag, Berlin, 35-45., 2005 | Á. Havasi: Dispersion analysis of operator splittings in the linearized shallow water equations, Proceedings of the 5th International Conference on Large-Scale Scientific Computations, June 6-10, 2005, Sozopol (2005) (to appear), 2005 | R. Horváth: On the Sign-Stability of the Finite Difference Solutions of One-Dimensional Parabolic Problems, Lecture Notes in Computer Science (közlésre elfogadva), 2007 | F. Izsák: Discontinuous Galerkin Methods for Partial Differential Equations in the Atmospheric Modeling, Időjárás, Quarterly Journal of Hungarian Meteorological Service (közlésre elfogadva), 2007 | J.J.W. van der Vegt, F. Izsák, O. Bokhove: Error analysis of a continuous-discontinous Galerkin finite element model for generalized 2D vorticity dynamics, SIAM Journal on Numerical Analysis (közlésre elfogadva), 2007 | F. Izsák, I. Lagzi: A new universal law for the Liesegang pattern formation, Journal of Chemical Physics, 122 (2005) (184707 – Article number)., 2005 | F. Izsák, I. Lagzi: Simulation of a crossover from the precipitation wave to moving Liesegang pattern formation, Journal of Physical Chemistry A, 109 (2005) 730-733., 2005 | J. Karátson, L. Lóczi: Sobolev gradient preconditioning for the electrostatic potential equation, Comput. Math. Appl., 50 (2005) 1093-1104., 2005 | J. Karátson, I. Faragó: Preconditioning operators and Sobolev gradients for nonlinear elliptic problems, Comput. Math. Appl. 50, 1077-1092., 2005 | J. Karátson: Mesh independent superlinear convergence estimates of the conjugate gradient method for some equivalent self-adjoint operators, Appl. Math. (Prága) 50 (2005) 277-290., 2005 | L. Lóczi: Construction of a conjugacy and closeness estimates in the discretized fold bifurcation, Preprint 04/022, DFG research group ''Spectral analysis, asymptotic distributions and stochastic dynamics'', Univ. of Bielefeld, www.mathematik.uni-b, 2004 | I. Faragó, Á. Havasi, K. Georgiev: Advances in Air Pollution Modeling for Environmental Security, NATO Science Series, 54, Springer Verlag, 2005 | O. Axelsson, J. Karátson,: Superlinearly convergent CG methods via equivalent preconditioning for nonsymmetric elliptic operators, Numer. Math., 99, 197-223., 2004 | J. Karátson, S. Korotov: Discrete maximum principles for finite element solutions of mixed nonlinear elliptic problems using quadratures, J. Comp. Appl. Math. 192, No. 1, pp. 75-88, 2006 | J. Karátson, T. Kurics: On Superlinear PCG Methods for FDM Discretizations of Convection-Diffusion Equations, Lecture Notes Comp Sci (közlésre elküldve), preprint: ELTE Dept. Appl. Anal., www.cs.elte.hu/applanal/preprints, 2006-13, 2006 | O. Axelsson, J. Karátson: Mesh independent superlinear PCG rates via compact-equivalent operators, SIAM J Numer Anal (közlésre elfogadva), 2007 | I. Antal, J. Karátson: A mesh independent superlinear algorithm for some nonlinear nonsymmetric elliptic systems, Comput. Math. Appl. (közlésre elfogadva), 2007 | J. Karátson, S. Korotov: Discrete maximum principles for FEM solutions of some nonlinear elliptic interface problems, Helsinki University of Technology, Institute of Mathematics, Research Report A510, 2006 | J. Karátson, S. Korotov, M. Krizek: On Discrete Maximum Principles for Nonlinear Elliptic Problems, Math. Comp. Simul. (közlésre elfogadva), 2006 | O. Axelsson, J. Karátson,: Symmetric part preconditioning of the CGM for Stokes type saddle-point systems, Numer. Funct. Anal. (közlésre elküldve), preprint: Technical reports from the Dept. of Inf. Tech., Uppsala, No. 2006-004, 2006 | J. Karátson,: On the superlinear convergence rate of the preconditioned CGM for some nonsymmetric elliptic problems, Numer. Funct. Anal. (közlésre elküldve), preprint: ELTE Dept. Appl. Anal., www.cs.elte.hu/applanal/preprints, 2006-11, 2006 | P. Csomós. I. Faragó: Error analysis of the numerical solution of split differential equations, Mathematical and Computer Modelling (közlésre elfogadva), 2007 | I. Faragó, J. Geiser: Iterative operator- splitting methods for linear problems, Weierstass Institute für Angewandte Analysis, 1043, 1-18., 2005 | I. Dimov, I. Faragó, Á. Havasi, Z. Zlatev: Different splitting techniques with application to air pollution models, Int. J. Environmental. Pollution (közlésre elfogadva), 2007 | I. Faragó: On the efficiency of the operator splitting method, Problems in Programming 7, 654-658., 2006 | A. Dorosenko, I. Faragó, Á. Havasi, V. Prussov: On the numerical solution of the three-dimensional advection-diffusion equation, Problems in Programming 7, 641-647., 2006 | I. Faragó, Á. Havasi: Consistency analysis of operator splitting methods for C0-semigroups, Semigroup Forum, online at http://www.springerlink.com/content/u0h415q559527u6x/fulltext.pdf., 2006 | I. Faragó, R. Horváth: A review of reliable numerical models for three-dimensional linear parabolic problems, Int.. J. Numer. Meth. Engng. (közlésre elfogadva), 2007 | I. Faragó, R. Horváth: On the connections between the qualitative properties of the numerical solutions of linear parabolic problems, SIAM Scientific Computing 28, 2313-2336., 2006 | I. Faragó: Application of the operator splitting method for real-life problems, Időjárás, Quarterly Journal of Hungarian Meteorological Service (közlésre elfogadva), 2007 | Csomós, I. Dimov, I. Faragó, Á. Havasi, Tz. Ostromsky: Computational complexity of weighted splitting scheme on parallel computers, International Journal of Parallel, Emergent and Distributed Systems (közlésre elfogadva), 2007 | I. Faragó, B. Gnandt, Á. Havasi: Additive and iterative splitting methods and their numerical investigation, Comput. Math. Appl. (közlésre elfogadva), 2007 | P. Csomós, I. Faragó, Á. Havasi: Operator splitting and global error analysis, NATO Advenced Research Workshop "Air Pollution Processes in Regional Scale", Kallithea, Greece, NATO Science Series, Kluwer Academic Publishers 37-44., 2003 | I. Faragó, R. Horváth: Qualitative analysis of discrete mesh operators, Lect. Notes Comp. Sci. (közlésre elküldve), 2007 | I. Faragó: Modified iterated operator splitting method, Applied Mathematical Modelling (közlésre elküldve), 2007 | I. Faragó, P. Thomsen, Z. Zlatev: On the additive splitting procedures and their computer realization, Applied Mathematical Modelling (közlésre elküldve), 2007 | I. Faragó: Operator splitting procedures and their analysis, Alkalmazott Matematikai Lapok (közlésre elküldve), 2007 | I. Faragó, Á. Havasi: Higher order adaptive operator splitting schemes, J. Comp. Appl. Math. (közlésre elküldve), 2007 | Á. Havasi: Dispersion analysis of operator splittings in the linearized shallow water equations, Lecture Notes in Computer Science, Springer 3743/2006, 355-362., 2006 | J. Karátson, J. W. Neuberger: Newton's method in the context of gradients, Trans. AMS (közlésre elküldve), 2006 | O. Axelsson, J. Karátson,: Symmetric part preconditioning for the conjugate gradient method, Numer Funct Anal 24 (2003), No. 5-6, 455-474, 2003 | J. Karátson, P.L.Simon: Exact multiplicity for degenerate two-point boundary value problems with p-convex nonlinearity, Nonlin. Anal 52 (2003), No. 6., 1569-1590., 2003 | J. Karátson, T. Kurics: Superlinearly convergent PCG algorithms for some nonsymmetric elliptic systems, J. Comp. Appl. Math (közlésre elfogadva), 2006 | I. Lagzi, F. Izsák: Stochastic description of precipitate pattern formation in an electric field, PHYSICAL CHEMISTRY CHEMICAL PHYSICS 5 (19): 4144-4148, 2003 | R. Horváth: Uniform Treatment of the Numerical Time-Integration of the Maxwell Equations, Lect. Notes Comp. Sci., 2003 | F. Izsak, I. Lagzi: Simulation of Liesegang pattern formation using a discrete stochastic model, CHEMICAL PHYSICS LETTERS 371 (3-4): 321-326, 2003 | I. Lagzi, F. Izsak: Regular Liesegang patterns and precipitation waves in an open system, PHYSICAL CHEMISTRY CHEMICAL PHYSICS 7 (22): 3845-3850, 2005 | R. Horváth: On the Maximum-Minimum Principle for Advection-Diffusion Equations, Problems in Programming, Nr. 2-3, 2006 | A. Volford, F. Izsak, M Ripszam: Systematic front distortion and presence of consecutive fronts in a precipitation system, JOURNAL OF PHYSICAL CHEMISTRY B 110 (10): 4535-4537, 2006 | F. Izsak: Maximum likelihood estimation for constrained parameters of multinomial distributions - Application to Zipf-Mandelbrot models, COMPUTATIONAL STATISTICS & DATA ANALYSIS 51 (3): 1575-1583, 2006 | R. Horváth: Operator Splittings for the Numerical Solution of Maxwell's Equations, Lect. Notes Comp. Sci., 2006 | A. Volford, F. Izsak, Ripszam, M., I. Lagzi: Pattern Formation and Self-Organization in a Simple Precipitation System, Langmuir; (Letter); 23(3); 961-964., 2007 | R. Horváth: New Unconditionally Stable Numerical Schemes for Maxwell's Equations, Int. J. Comput. Sci. Eng. (közlésre elfogadva), 2007 | F. Izsák, D. Harutyunyan, J.J.W. van der Vegt: Implicit a posteriori error estimates for the Maxwell equations, Memorandum 1816, Department of Applied Mathematics, University of Twente, Enschede. ISSN 0169-2690. http://eprints.eemcs.utwente.nl/8448/, 2007 | D. Harutyunyan, F. Izsák, M. A. Botchev, J.J.W. van der Vegt: Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates., Memorandum 1810, Department of Applied Mathematics, University of Twente, Enschede. ISSN 0169-2690. http://eprints.eemcs.utwente.nl/8541/, 2006 | R. Horváth: On the Sign-Stability of Numerical Solutions of One-Dimensional Parabolic Problems, Applied Mathematical Modelling (közlésre elküldve), 2007 | R. Horváth: Sufficient Conditions of the Discrete Maximum-Minimum Principle for Parabolic Problems on Rectangular Meshes, Int. J. Comput. Sci. Eng. (közlésre elfogadva), 2007 |
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