HR job title
- Retired Professor
- Contact Info
- 1 786 202 1878
Lazarov, Raytcho Professor
Positions
- Professor, Mathematics, College of Arts and Sciences
- Overview
- Publications
- Research
- Teaching
- Works By Students
- Background
- Contact
- Other
- View All
Overview
Publications
selected publications
-
academic article
-
Harizanov, S., Lazarov, R., Margenov, S., & Marinov, P.
(2020).
Numerical solution of fractional diffusion-reaction problems based on BURA. Computers and Mathematics with Applications.
80(2), 316-331.
-
Moon, M., Lazarov, R., & Jun, H. K.
(2019).
Multiscale HDG model reduction method for flows in heterogeneous porous media. Applied Numerical Mathematics.
140, 115-133.
-
Jin, B., Lazarov, R., & Zhou, Z.
(2019).
Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview. Computer Methods in Applied Mechanics and Engineering.
346, 332-358.
-
Lazarov, R., & Takhirov, A.
(2018).
A note on the uniform inf-sup condition for the Brinkman problem in highly heterogeneous media. Journal of Computational and Applied Mathematics.
340, 537-545.
-
Harizanov, S., Lazarov, R., Margenov, S., Marinov, P., & Vutov, Y.
(2018).
Optimal solvers for linear systems with fractional powers of sparse SPD matrices. Numerical Linear Algebra with Applications.
25(5), e2167-e2167.
-
Duan, B., Jin, B., Lazarov, R., Pasciak, J., & Zhou, Z.
(2018).
Space-Time Petrov-Galerkin FEM for Fractional Diffusion Problems. Computational Methods in Applied Mathematics.
18(1), 1-20.
-
Lazarov, R., & Vabishchevich, P.
(2017).
A NUMERICAL STUDY OF THE HOMOGENEOUS ELLIPTIC EQUATION WITH FRACTIONAL BOUNDARY CONDITIONS. Journal of Fractional Calculus and Applied Analysis.
20(2), 337-351.
-
Kanschat, G., Lazarov, R., & Mao, Y.
(2017).
Geometric Multigrid for Darcy and Brinkman models of flows in highly heterogeneous porous media: A numerical study. Journal of Computational and Applied Mathematics.
310, 174-185.
-
Jin, B., Lazarov, R., Thomee, V., & Zhou, Z.
(2017).
ON NONNEGATIVITY PRESERVATION IN FINITE ELEMENT METHODS FOR SUBDIFFUSION EQUATIONS. Mathematics of Computation.
86(307), 2239-2260.
-
Jin, B., Lazarov, R., & Vabishchevich, P.
(2017).
Preface: Numerical Analysis of Fractional Differential Equations. Computational Methods in Applied Mathematics.
17(4), 643-646.
-
Jin, B., Lazarov, R., & Zhou, Z.
(2016).
A PETROV-GALERKIN FINITE ELEMENT METHOD FOR FRACTIONAL CONVECTION-DIFFUSION EQUATIONS. SIAM Journal on Numerical Analysis.
54(1), 481-503.
-
Jin, B., Lazarov, R., Lu, X., & Zhou, Z.
(2016).
A simple finite element method for boundary value problems with a Riemann-Liouville derivative. Journal of Computational and Applied Mathematics.
293, 94-111.
-
Jin, B., Lazarov, R., & Zhou, Z.
(2016).
An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data. IMA Journal of Numerical Analysis.
36(1), 197-221.
-
Jin, B., Lazarov, R., Sheen, D., & Zhou, Z.
(2016).
ERROR ESTIMATES FOR APPROXIMATIONS OF DISTRIBUTED ORDER TIME FRACTIONAL DIFFUSION WITH NONSMOOTH DATA. Journal of Fractional Calculus and Applied Analysis.
19(1), 69-93.
-
Srinivasan, S., Lazarov, R., & Minev, P.
(2016).
Multiscale direction-splitting algorithms for parabolic equations with highly heterogeneous coefficients. Computers and Mathematics with Applications.
72(6), 1641-1654.
-
Kraus, J., Lazarov, R., Lymbery, M., Margenov, S., & Zikatanov, L.
(2016).
PRECONDITIONING HETEROGENEOUS H(div) PROBLEMS BY ADDITIVE SCHUR COMPLEMENT APPROXIMATION AND APPLICATIONS. SIAM Journal on Scientific Computing.
38(2), A875-A898.
-
Jin, B., Lazarov, R., & Zhou, Z.
(2016).
TWO FULLY DISCRETE SCHEMES FOR FRACTIONAL DIFFUSION AND DIFFUSION-WAVE EQUATIONS WITH NONSMOOTH DATA. SIAM Journal on Scientific Computing.
38(1), A146-A170.
-
Efendiev, Y., Lazarov, R., & Shi, K. e.
(2015).
A MULTISCALE HDG METHOD FOR SECOND ORDER ELLIPTIC EQUATIONS. PART I. POLYNOMIAL AND HOMOGENIZATION-BASED MULTISCALE SPACES. SIAM Journal on Numerical Analysis.
53(1), 342-369.
-
Efendiev, Y., Lazarov, R., Moon, M., & Shi, K. e.
(2015).
A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems. Computer Methods in Applied Mechanics and Engineering.
292, 243-256.
-
Bazhlekova, E., Jin, B., Lazarov, R., & Zhou, Z.
(2015).
An analysis of the Rayleigh-Stokes problem for a generalized second-grade fluid. Numerische Mathematik.
131(1), 1-31.
-
Jin, B., Lazarov, R., Pasciak, J., & Zhou, Z.
(2015).
Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion. IMA Journal of Numerical Analysis.
35(2), 561-582.
-
Jin, B., Lazarov, R., Liu, Y., & Zhou, Z.
(2015).
The Galerkin finite element method for a multi-term time-fractional diffusion equation. Journal of Computational Physics.
281, 825-843.
-
Jin, B., Lazarov, R., Pasciak, J., & Rundell, W.
(2015).
VARIATIONAL FORMULATION OF PROBLEMS INVOLVING FRACTIONAL ORDER DIFFERENTIAL OPERATORS. Mathematics of Computation.
84(296), 2665-2700.
-
Jin, B., Lazarov, R., Pasciak, J., & Zhou, Z.
(2014).
ERROR ANALYSIS OF A FINITE ELEMENT METHOD FOR THE SPACE-FRACTIONAL PARABOLIC EQUATION. SIAM Journal on Numerical Analysis.
52(5), 2272-2294.
-
Jin, B., Lazarov, R., & Zhou, Z.
(2013).
ERROR ESTIMATES FOR A SEMIDISCRETE FINITE ELEMENT METHOD FOR FRACTIONAL ORDER PARABOLIC EQUATIONS. SIAM Journal on Numerical Analysis.
51(1), 445-466.
-
Efendiev, Y., Galvis, J., Lazarov, R., Moon, M., & Sarkis, M.
(2013).
Generalized multiscale finite element method. Symmetric interior penalty coupling. Journal of Computational Physics.
255, 1-15.
-
Chatzipantelidis, P., Lazarov, R., & Thomee, V.
(2013).
Some Error Estimates for the Finite Volume Element Method for a Parabolic Problem. Computational Methods in Applied Mathematics.
13(3), 251-279.
-
Efendiev, Y., Galvis, J., Lazarov, R., & Willems, J.
(2012).
ROBUST DOMAIN DECOMPOSITION PRECONDITIONERS FOR ABSTRACT SYMMETRIC POSITIVE DEFINITE BILINEAR FORMS. 46(5), 1175-1199.
-
Efendiev, Y., Galvis, J., Kang, S. K., & Lazarov, R. D.
(2012).
Robust Multiscale Iterative Solvers for Nonlinear Flows in Highly Heterogeneous Media. Numerical Mathematics Theory Methods and Applications.
5(3), 359-383.
-
Efendiev, Y., Galvis, J., Lazarov, R., Margenov, S., & Ren, J.
(2012).
Robust Two-level Domain Decomposition Preconditioners for High-contrast Anisotropic Flows in Multiscale Media. Computational Methods in Applied Mathematics.
12(4), 415-436.
-
Chatzipantelidis, P., Lazarov, R. D., & Thomee, V.
(2012).
SOME ERROR ESTIMATES FOR THE LUMPED MASS FINITE ELEMENT METHOD FOR A PARABOLIC PROBLEM. Mathematics of Computation.
81(277), 1-20.
-
Chapko, R., Dryja, M., Gavrilyuk, I., Gulin, A., Khlobystov, V., Kutniv, M., ... Yanovich, L.
(2011).
ACADEMICIAN V. L. MAKAROV IS 70 !. 2(105), 1-3.
-
Iliev, O., Lazarov, R., & Willems, J.
(2011).
VARIATIONAL MULTISCALE FINITE ELEMENT METHOD FOR FLOWS IN HIGHLY POROUS MEDIA. SIAM: Multiscale Modeling and Simulation.
9(4), 1350-1372.
-
Iliev, O., Lazarov, R., & Willems, J.
(2010).
Fast numerical upscaling of heat equation for fibrous materials. Computing and Visualization in Science.
13(6), 275-285.
-
Douglas, C., Efendiev, Y., Ewing, R., Ginting, V., Lazarov, R., Cole, M., & Jones, G.
(2010).
Least squares approach for initial data recovery in dynamic data-driven applications simulations. Computing and Visualization in Science.
13(8), 365-375.
-
Ewing, R., Iliev, O., Lazarov, R., Rybak, I., & Willems, J.
(2009).
A SIMPLIFIED METHOD FOR UPSCALING COMPOSITE MATERIALS WITH HIGH CONTRAST OF THE CONDUCTIVITY. SIAM Journal on Scientific Computing.
31(4), 2568-2586.
-
Lazarov, R., Repin, S., & Tomar, S. K.
(2009).
Functional A Posteriori Error Estimates for Discontinuous Galerkin Approximations of Elliptic Problems. Numerical Methods for Partial Differential Equations.
25(4), 952-971.
-
Sinha, R. K., Ewing, R. E., & Lazarov, R. D.
(2009).
MIXED FINITE ELEMENT APPROXIMATIONS OF PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS WITH NONSMOOTH INITIAL DATA. SIAM Journal on Numerical Analysis.
47(5), 3269-3292.
-
Chatzipantelidis, P., Lazarov, R. D., & Thomee, V.
(2009).
Parabolic Finite Volume Element Equations in Nonconvex Polygonal Domains. Numerical Methods for Partial Differential Equations.
25(3), 507-525.
-
Cockburn, B., Gopalakrishnan, J., & Lazarov, R.
(2009).
UNIFIED HYBRIDIZATION OF DISCONTINUOUS GALERKIN, MIXED, AND CONTINUOUS GALERKIN METHODS FOR SECOND ORDER ELLIPTIC PROBLEMS. SIAM Journal on Numerical Analysis.
47(2), 1319-1365.
-
Chapko, R., Hermann, M., Jovanovich, B., V.Khlobystov, V., Kutniv, M., Lazarov, R., ... Vasylyk, V.
(2008).
Ivan Gavrilyuk 60. Computational Methods in Applied Mathematics.
8(4), 311-314.
-
Lazarov, R. D., & Margenov, S. D.
(2007).
CBS constants for multilevel splitting of graph-Laplacian and application to preconditioning of discontinuous Galerkin systems. Journal of Complexity.
23(4-6), 498-515.
-
Douglas, C. C., Efendiev, Y., Ewing, R., Lazarov, R., Cole, M. J., Jones, G., & Johnson, C. R.
(2007).
Interpolation and update in dynamic data-driven application simulations. NATO Security through Science Series C: Environmental Security.
235-+.
-
Kachiashvili, K., Gordeziani, D., Lazarov, R., & Melikdzhanian, D.
(2007).
Modeling and simulation of pollutants transport in rivers. Applied Mathematical Modelling: simulation and computation for engineering and environmental systems.
31(7), 1371-1396.
-
Iliev, O., Lazarov, R., & Willems, J.
(2007).
Numerical Study of Two-grid Preconditioners for 1-d Elliptic Problems with Highly Oscillating Discontinuous Coefficients. Computational Methods in Applied Mathematics.
7(1), 48-67.
-
Ewing, R. E., Iliev, O. P., Lazarov, R. D., & Naumovich, A.
(2007).
On convergence of certain finite volume difference discretizations for 1D poroelasticity interface problems. Numerical Methods for Partial Differential Equations.
23(3), 652-671.
-
Lazarov, R. D., Lu, S., & Pereverzev, S. V.
(2007).
On the balancing principle for some problems of Numerical Analysis. Numerische Mathematik.
106(4), 659-689.
-
Lazarov, R., & Ye, X.
(2007).
Stabilized discontinuous finite element approximations for Stokes equations. Journal of Computational and Applied Mathematics.
198(1), 236-252.
-
Douglas, C., Efendiev, Y., Ewing, R., Ginting, V., & Lazarov, R.
(2006).
Dynamic data driven simulations in stochastic environments. Computing.
77(4), 321-333.
-
Lazarov, R., Pasciak, J., & Qin, G.
(2006).
On the occasion of the sixtieth birthday of Richard E. Ewing. Numerical Linear Algebra with Applications.
13(9), 675-676.
-
Chatzipantelidis, P., Lazarov, R. D., Thomee, V., & Wahlbin, L. B.
(2006).
Parabolic finite element equations in nonconvex polygonal domains. BIT Numerical Mathematics.
46(Suppl 1), S113-S143.
-
Chapko, R., Gavriljuk, I., Jovanovich, B., Hermann, M., Lazarov, R., Lukovsky, I., ... Vabishchevich, P.
(2006).
Professor V. L.Makarov 65. Computational Methods in Applied Mathematics.
6(4), 347-348.
-
Sinha, R. K., Ewing, R. E., & Lazarov, R. D.
(2006).
Some new error estimates of a semidiscrete finite volume element method for a parabolic integro-differential equation with nonsmooth initial data. SIAM Journal on Numerical Analysis.
43(6), 2320-2343.
-
Dobrev, V. A., Lazarov, R. D., Vassilevski, P. S., & Zikatanov, L. T.
(2006).
Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations. Numerical Linear Algebra with Applications.
13(9), 753-770.
-
Chatzipantelidis, P., Ginting, V., & Lazarov, R. D.
(2005).
A finite volume element method for a non-linear elliptic problem. Numerical Linear Algebra with Applications.
12(5-6), 515-546.
-
Chatzipantelidis, P., & Lazarov, R. D.
(2005).
Error estimates for a finite volume element method for elliptic PDES in nonconvex polygonal domains. SIAM Journal on Numerical Analysis.
42(5), 1932-1958.
-
Carstensen, C., Lazarov, R., & Tomov, S.
(2005).
Explicit and averaging a posteriori error estimates for adaptive finite volume methods. SIAM Journal on Numerical Analysis.
42(6), 2496-2521.
-
Andreev, A. B., Lazarov, R. D., & Racheva, M. R.
(2005).
Postprocessing and higher order convergence of the mixed finite element approximations of biharmonic eigenvalue problems. Journal of Computational and Applied Mathematics.
182(2), 333-349.
-
Chatzipantelidis, P., Lazarov, R. D., & Thomee, V.
(2004).
Error estimates for a finite volume element method for parabolic equations in convex polygonal domains. Numerical Methods for Partial Differential Equations.
20(5), 650-674.
-
Ginting, V., Ewing, R., Efendiev, Y., & Lazarov, R.
(2004).
Upscaled modeling in multiphase flow applications. Computational and Applied Mathematics.
23(2-3), 213-233.
-
Lazarov, R. D., Pasciak, J. E., Schoberl, J., & Vassilevski, P. S.
(2003).
Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids. Numerische Mathematik.
96(2), 295-315.
-
Lazarov, R., & Tomov, S.
(2002).
A posteriori error estimates for finite volume element approximations of convection-diffusion-reaction equations. Computational Geosciences: modeling, simulation and data analysis.
6(3-4), 483-503.
-
Edwards, M. G., Lazarov, R. D., & Yotov, I.
(2002).
Special issue on locally conservative numerical methods for flow in porous media - Introduction. Computational Geosciences: modeling, simulation and data analysis.
6(3-4), 225-225.
-
Ewing, R., Iliev, O., & Lazarov, R.
(2001).
A modified finite volume approximation of second-order elliptic equations with discontinuous coefficients. SIAM Journal on Scientific Computing.
23(4), 1334-1350.
-
Lazarov, R. D., Pasciak, J. E., & Vassilevski, P. S.
(2001).
Iterative solution of a coupled mixed and standard Galerkin discretization method for elliptic problems. Numerical Linear Algebra with Applications.
8(1), 13-31.
-
Lazarov, R. D., Tomov, S. Z., & Vassilevski, P. S.
(2001).
Interior Penalty Discontinuous Approximations of Elliptic Problems. Computational Methods in Applied Mathematics.
1(4), 367-382.
-
Lazarov, R. D., Pasciak, J. E., & Vassilevski, P. S.
(2001).
Iterative solution of a coupled mixed and standard Galerkin discretization method for elliptic problems. Numerical Linear Algebra with Applications.
8(1), 13-31.
-
Bramble, J. H., Lazarov, R. D., & Pasciak, J. E.
(2001).
Least-squares methods for linear elasticity based on a discrete minus one inner product. Computer Methods in Applied Mechanics and Engineering.
191(8-10), 727-744.
-
Kim, C., Lazarov, R. D., Pasciak, J. E., & Vassilevski, P. S.
(2001).
Multiplier spaces for the mortar finite element method in three dimensions. SIAM Journal on Numerical Analysis.
39(2), 519-538.
-
Ewing, R., Iliev, O., & Lazarov, R.
(2001).
A Modified Finite Volume Approximation of Second-Order Elliptic Equations with Discontinuous Coefficients. SIAM Journal on Scientific Computing.
23(4), 1335-1351.
-
Ewing, R. E., Lazarov, R. D., & Lin, Y. P.
(2000).
Finite volume element approximations of nonlocal in time one-dimensional plows in porous media. Computing.
64(2), 157-182.
-
Ewing, R., Lazarov, R., & Lin, Y. P.
(2000).
Finite volume element approximations of nonlocal reactive flows in porous media. Numerical Methods for Partial Differential Equations.
16(3), 285-311.
-
Ewing, R., Lazarov, R., Lin, T., & Lin, Y.
(2000).
Mortar finite volume element approximations of second order elliptic problems. East West Journal of Numerical Mathematics.
8(2), 93-110.
-
Ewing, R. E., Lazarov, R. D., Lyons, S. L., Papavassiliou, D. V., Pasciak, J., & Qin, G.
(1999).
Numerical well model for non-Darcy flow through isotropic porous media. Computational Geosciences: modeling, simulation and data analysis.
3(3-4), 185-204.
-
Bramble, J. H., Lazarov, R. D., & Pasciak, J. E.
(1998).
Least-squares for second-order elliptic problems. Computer Methods in Applied Mechanics and Engineering.
152(1-2), 195-210.
-
Chen, H. S., Ewing, R., & Lazarov, R.
(1998).
Superconvergence of mixed finite element methods for parabolic problems with nonsmooth initial data. Numerische Mathematik.
78(4), 495-521.
-
Lazarov, R. D., Tobiska, L., & Vassilevski, P. S.
(1997).
Streamline diffusion least-squares mixed finite element methods for convection-diffusion problems. East West Journal of Numerical Mathematics.
5(4), 249-264.
-
Bramble, J. H., Lazarov, R. D., & Pasciak, J. E.
(1997).
A least-squares approach based on a discrete minus one inner product for first order systems. Mathematics of Computation.
66(219), 935-955.
-
Konijnenberg, A., van der Post, J. A., Mol, B. W., Schaap, M. C., Lazarov, R., Bleker, O. P., Boer, K., & Sturk, A.
(1997).
Can flow cytometric detection of platelet activation early in pregnancy predict the occurrence of preeclampsia? A prospective study. AMERICAN JOURNAL OF OBSTETRICS AND GYNECOLOGY.
177(2), 434-442.
-
Chen, H., & Lazarov, R. D.
(1996).
Domain splitting algorithm for mixed finite element approximations to parabolic problems. East West Journal of Numerical Mathematics.
4(2), 121-135.
-
Chen, Z. X., Ewing, R. E., & Lazarov, R.
(1996).
Domain decomposition algorithms for mixed methods for second order elliptic problems. Mathematics of Computation.
65(214), 467-490.
-
Lazarov, R. D., Mishev, I. D., & Vassilevski, P. S.
(1996).
Finite volume methods for convection-diffusion problems. SIAM Journal on Numerical Analysis.
33(1), 31-55.
-
Chen, Z. X., Ewing, R. E., Lazarov, R. D., Maliassov, S., & Kuznetsov, Y. A.
(1996).
Multilevel preconditioners for mixed methods for second order elliptic problems. Numerical Linear Algebra with Applications.
3(5), 427-453.
-
Vassilevski, P. S.
(1996).
Preconditioning mixed finite element saddle-point elliptic problems. Numerical Linear Algebra with Applications.
3(1), 1-20.
-
CAI, Z., LAZAROV, R., MANTEUFFEL, T. A., & MCCORMICK, S. F.
(1994).
1ST-ORDER SYSTEM LEAST-SQUARES FOR 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS .1. SIAM Journal on Numerical Analysis.
31(6), 1785-1799.
-
EWING, R. E., & LAZAROV, R. D.
(1994).
APPROXIMATION OF PARABOLIC PROBLEMS ON GRIDS LOCALLY REFINED IN TIME AND SPACE. Applied Numerical Mathematics.
14(1-3), 199-211.
-
EWING, R. E., LAZAROV, B. D., & VASSILEV, A. T.
(1994).
FINITE-DIFFERENCE SCHEME FOR PARABOLIC PROBLEMS ON COMPOSITE GRIDS WITH REFINEMENT IN TIME AND SPACE. SIAM Journal on Numerical Analysis.
31(6), 1605-1622.
-
LAZAROV, R. D., MISHEV, I. D., & VASSILEVSKI, P. S.
(1994).
FINITE-VOLUME METHODS WITH LOCAL REFINEMENT FOR CONVECTION-DIFFUSION PROBLEMS. Computing.
53(1), 33-57.
-
PEHLIVANOV, A. I., CAREY, G. F., & LAZAROV, R. D.
(1994).
LEAST-SQUARES MIXED FINITE-ELEMENTS FOR 2ND-ORDER ELLIPTIC PROBLEMS. SIAM Journal on Numerical Analysis.
31(5), 1368-1377.
-
Ewing, R. E., Lazarov, R. D., & Vassilevski, P. S.
(1994).
Local Refinement Techniques for Elliptic Problems on Cell-centered Grids; II. Optimal Order Two-grid Iterative Methods. Numerical Linear Algebra with Applications.
1(4), 337-368.
-
Cai, Z., Lazarov, R., Manteuffel, T. A., & McCormick, S. F.
(1994).
First-order system least squares for second-order partial differential equations: Part I. SIAM Journal on Numerical Analysis.
31(6), 1785-1799.
-
PEHLIVANOV, A. I., CAREY, G. F., LAZAROV, R. D., & SHEN, Y.
(1993).
CONVERGENCE ANALYSIS OF LEAST-SQUARES MIXED FINITE-ELEMENTS. Computing.
51(2), 111-123.
-
EWING, R. E., LAZAROV, R. D., PASCIAK, J. E., & VASSILEVSKI, P. S.
(1993).
DOMAIN DECOMPOSITION TYPE ITERATIVE TECHNIQUES FOR PARABOLIC PROBLEMS ON LOCALLY REFINED GRIDS. SIAM Journal on Numerical Analysis.
30(6), 1537-1557.
-
EWING, R. E., LAZAROV, R. D., & VASSILEV, A. T.
(1992).
ADAPTIVE TECHNIQUES FOR TIME-DEPENDENT PROBLEMS. Computer Methods in Applied Mechanics and Engineering.
101(1-3), 113-126.
-
VASSILEVSKI, P. S., PETROVA, S. I., & LAZAROV, R. D.
(1992).
FINITE-DIFFERENCE SCHEMES ON TRIANGULAR CELL-CENTERED GRIDS WITH LOCAL REFINEMENT. SIAM Journal on Scientific and Statistical Computing.
13(6), 1287-1313.
-
PEHLIVANOV, A. I., LAZAROV, R. D., CAREY, G. F., & CHOW, S. S.
(1992).
SUPERCONVERGENCE ANALYSIS OF APPROXIMATE BOUNDARY-FLUX CALCULATIONS. Numerische Mathematik.
63(4), 483-501.
-
Ewing, R. E., Lazarov, R. D., & Vassilevski, P. S.
(1991).
Local refinement techniques for elliptic problems on cell-centered grids. I. Error analysis. Mathematics of Computation.
56(194), 437-461.
-
EWING, R. E., LAZAROV, R. D., & VASSILEVSKI, P. S.
(1991).
LOCAL REFINEMENT TECHNIQUES FOR ELLIPTIC PROBLEMS ON CELL-CENTERED GRIDS .1. ERROR ANALYSIS. Mathematics of Computation.
56(194), 437-461.
-
EWING, R. E., LAZAROV, R. D., & VASSILEVSKI, P. S.
(1991).
LOCAL REFINEMENT TECHNIQUES FOR ELLIPTIC PROBLEMS ON CELL-CENTERED GRIDS .3. ALGEBRAIC MULTILEVEL BEPS PRECONDITIONERS. Numerische Mathematik.
59(5), 431-452.
-
EWING, R. E., LAZAROV, R. D., & WANG, J.
(1991).
SUPERCONVERGENCE OF THE VELOCITY ALONG THE GAUSS LINES IN MIXED FINITE-ELEMENT METHODS. SIAM Journal on Numerical Analysis.
28(4), 1015-1029.
-
Chow, S., Carey, G. F., & Lazarov, R. D.
(1991).
Natural and postprocessed superconvergence in semilinear problems. Numerical Methods for Partial Differential Equations.
7(3), 245-259.
-
EWING, R. E., LAZAROV, R. D., & VASSILEVSKI, P. S.
(1990).
FINITE-DIFFERENCES SCHEMES ON GRIDS WITH LOCAL REFINEMENT IN TIME AND SPACE FOR PARABOLIC PROBLEMS .1. DERIVATION, STABILITY, AND ERROR ANALYSIS. Computing.
45(3), 193-215.
-
EWING, R. E., LAZAROV, R. D., LU, P., & VASSILEVSKI, P. S.
(1990).
PRECONDITIONING INDEFINITE SYSTEMS ARISING FROM MIXED FINITE-ELEMENT DISCRETIZATION OF 2ND-ORDER ELLIPTIC PROBLEMS. Lecture Notes in Mathematics.
1457, 28-43.
-
PASHEVA, V., & LAZAROV, R.
(1989).
BOUNDARY ELEMENT METHOD FOR 2D PROBLEMS OF IDEAL FLUID-FLOWS WITH FREE BOUNDARIES. Advances in Water Resources.
12(1), 37-45.
-
MANOLOV, V. K., YOTOVA, A. I., LAZAROV, R. D., & RASHEV, T. V.
(1989).
INVESTIGATION OF TEMPERATURE-FIELDS OF STEEL METALLURGICAL BLOCK BY THE FINAL ELEMENTS METHOD. Comptes Rendus- Acade¿¿?mie Bulgare des Sciences.
42(4), 51-54.
-
CHOW, S. S., & LAZAROV, R. D.
(1989).
SUPERCONVERGENCE ANALYSIS OF FLUX COMPUTATIONS FOR NONLINEAR PROBLEMS. Bulletin of the Australian Mathematical Society.
40(3), 465-479.
-
Godev, K. N., Lazarov, R. D., Makarov, V. L., & Samarski, A. A.
(1988).
HOMOGENEOUS DIFFERENCE SCHEMES FOR ONE-DIMENSIONAL PROBLEMS WITH GENERALIZED SOLUTIONS. Sbornik: Mathematics.
59(1), 155-179.
-
Andreev, A. B., & Lazarov, R. D.
(1988).
Superconvergence of the gradient for quadratic triangular finite elements. Numerical Methods for Partial Differential Equations.
4(1), 15-32.
-
GODEV, K. N., LAZAROV, R. D., MAKAROV, V. L., & SAMARSKII, A. A.
(1986).
HOMOGENEOUS DIFFERENCE-SCHEMES FOR ONE-DIMENSIONAL PROBLEMS WITH GENERALIZED SOLUTIONS. Sbornik: Mathematics.
131(1-2), 155-179.
-
GODEV, K. N., & LAZAROV, R. D.
(1984).
ERROR-ESTIMATES OF FINITE-DIFFERENCE SCHEMES IN LP-METRICS FOR PARABOLIC BOUNDARY-VALUE-PROBLEMS. Comptes Rendus- Acade¿¿?mie Bulgare des Sciences.
37(5), 565-568.
-
LAZAROV, R. D., MAKAROV, V. L., & WEINELT, W.
(1984).
ON THE CONVERGENCE OF DIFFERENCE-SCHEMES FOR THE APPROXIMATION OF SOLUTIONS U IS-AN-ELEMENT-OF W2M(M LESS-THAN 0.5) OF ELLIPTIC-EQUATIONS WITH MIXED DERIVATIVES. Numerische Mathematik.
44(2), 223-232.
-
VAINELT, V., LAZAROV, R. D., & SHTRAIT, U.
(1984).
ORDER OF CONVERGENCE OF FINITE-DIFFERENCE SCHEMES FOR WEAK SOLUTIONS OF THE HEAT-CONDUCTION EQUATION FOR AN ANISOTROPIC NONUNIFORM MEDIUM. DIFFERENTIAL EQUATIONS.
20(7), 828-834.
-
VAINELT, V., LAZAROV, R. D., & MAKAROV, V. L.
(1983).
CONVERGENCE OF FINITE-DIFFERENCE SCHEMES FOR ELLIPTIC-EQUATIONS WITH MIXED DERIVATIVES HAVING GENERALIZED SOLUTIONS. DIFFERENTIAL EQUATIONS.
19(7), 838-843.
-
GAVRILYUK, I. P., LAZAROV, R. D., MAKAROV, V. L., & PIRNAZAROV, S. I.
(1983).
ESTIMATES OF THE RATE OF CONVERGENCE OF DIFFERENCE-SCHEMES FOR FOURTH-ORDER ELLIPTIC-EQUATIONS. USSR Computational Mathematics and Mathematical Physics.
23(2), 64-70.
-
LAZAROV, R. D.
(1983).
FINITE-DIFFERENCE NUMERICAL-SOLUTION OF SOME AXIALLY-SYMMETRIC PROBLEMS IN THE MATHEMATICAL-THEORY OF ELASTICITY. DIFFERENTIAL EQUATIONS.
19(3), 383-389.
-
LAZAROV, R. D., & MOKIN, I. I.
(1983).
THE CALCULATION OF LOGARITHMIC POTENTIAL. DOKLADY AKADEMII NAUK SSSR.
272(1), 27-30.
-
LAZAROV, R. D., MAKAROV, V. L., & SAMARSKII, A. A.
(1982).
APPLICATION OF EXACT DIFFERENCE-SCHEMES TO THE CONSTRUCTION AND STUDY OF DIFFERENCE-SCHEMES FOR GENERALIZED SOLUTIONS. Sbornik: Mathematics.
117(4), 461-471.
-
LAZAROV, R. D., & MAKAROV, V. L.
(1982).
DIFFERENCE-SCHEMES OF 2ND-ORDER ACCURACY FOR AXISYMMETRIC POISSON EQUATIONS ON GENERALIZED SOLUTIONS FROM W2(2). DOKLADY AKADEMII NAUK SSSR.
262(1), 22-26.
-
LAZAROV, R. D.
(1982).
EVALUATION OF CONVERGENCE OF DIFFERENTIAL SCHEMES FOR PARABOLIC EQUATIONS WITH GENERALIZED SOLUTIONS. Comptes Rendus- Acade¿¿?mie Bulgare des Sciences.
35(1), 7-10.
-
LAZAROV, R. D.
(1981).
CONVERGENCE OF DIFFERENCE-SCHEMES FOR SOME AXISYMMETRIC PROBLEMS OF MATHEMATICAL PHYSICS IN CLASSES OF GENERALIZED SOLUTIONS. DOKLADY AKADEMII NAUK SSSR.
258(6), 1301-1304.
-
LAZAROV, R. D.
(1981).
CONVERGENCE OF FINITE-DIFFERENCE SCHEMES FOR GENERALIZED SOLUTIONS OF POISSONS-EQUATION. DIFFERENTIAL EQUATIONS.
17(7), 829-836.
-
LAZAROV, R. D.
(1981).
CONVERGENCE OF FINITE-DIFFERENCE SOLUTIONS TO GENERALIZED SOLUTIONS OF A BIHARMONIC EQUATION IN A RECTANGLE. DIFFERENTIAL EQUATIONS.
17(7), 836-843.
-
LAZAROV, R. D., & MAKAROV, V. L.
(1981).
CONVERGENCE OF THE NET METHOD AND STRAIGHT-LINE METHOD FOR MULTIDIMENSIONAL PROBLEMS OF THE MATHEMATICAL PHYSICS IN CLASSES OF GENERALIZED SOLUTIONS. DOKLADY AKADEMII NAUK SSSR.
259(2), 282-286.
-
Lazarov, R. D., & Makarov, V. L.
(1981).
Difference scheme of second order of accuracy for the axisymmetric poisson equation in generalized solutions. USSR Computational Mathematics and Mathematical Physics.
21(5), 95-107.
-
LAZAROV, R. D., & MOKIN, I. I.
(1981).
THE CONVERGENCE OF DIFFERENCE-SCHEMES FOR POISSON EQUATIONS IN LP METRICS. DOKLADY AKADEMII NAUK SSSR.
261(4), 796-801.
-
LAZAROV, R. D.
(1979).
FACTORIZED DIFFERENCE SCHEMES OF 2ND ORDER ACCURACY FOR SOME DYNAMIC AXYSYMMETRIC PROBLEMS OF ELASTICITY. Comptes Rendus- Acade¿¿?mie Bulgare des Sciences.
32(1), 7-10.
-
Ganev, K., & Lazarov, R.
(1979).
Application of the method of splitting for solving the axisymmetric problem of mesometeorology. 5(4), 11-21.
-
LAZAROV, R. D.
(1976).
DIFFERENCE METHOD OF 2ND-ORDER ACCURACY FOR AXISYMMETRICAL PROBLEMS OF ELASTICITY. Comptes Rendus- Acade¿¿?mie Bulgare des Sciences.
29(1), 21-24.
-
Mokin, Y. I., & Lazarov, R. D.
(1973).
Stability of elliptic difference problems. USSR Computational Mathematics and Mathematical Physics.
13(2), 282-291.
-
Lazarov, R. D.
(1971).
Difference schemes for the second boundary value problem of elasticity theory for domains with curvilinear boundaries. USSR Computational Mathematics and Mathematical Physics.
11(4), 166-179.
-
Harizanov, S., Lazarov, R., Margenov, S., & Marinov, P.
(2020).
Numerical solution of fractional diffusion-reaction problems based on BURA. Computers and Mathematics with Applications.
80(2), 316-331.
-
chapter
-
Efendiev, Y., Galvis, J., Lazarov, R., Margenov, S., & Ren, J.
(2013).
Multiscale Domain Decomposition Preconditioners for Anisotropic High-Contrast Problems. Lecture Notes in Computational Science and Engineering.
Bank, R. E., Holst, M. J., Widlund, O. B., & Xu, J. (Eds.),
Domain Decomposition Methods in Science and Engineering XX.
(pp. 289-296).
Springer Nature.
-
Efendiev, Y., Galvis, J., Lazarov, R., Margenov, S., & Ren, J.
(2013).
Multiscale Domain Decomposition Preconditioners for Anisotropic High-Contrast Problems. Lecture Notes in Computational Science and Engineering.
Bank, R. E., Holst, M. J., Widlund, O. B., & Xu, J. (Eds.),
Domain Decomposition Methods in Science and Engineering XX.
(pp. 289-296).
Springer Nature.
-
conference paper
-
Harizanov, S., Lazarov, R., Margenov, S., Marinov, P., & Pasciak, J.
(2019).
Comparison Analysis of Two Numerical Methods for Fractional Diffusion Problems Based on the Best Rational Approximations of t on [0, 1]. Lecture Notes in Computational Science and Engineering.
165-185.
-
Efendiev, Y., Galvis, J., Lazarov, R., & Weisser, S.
(2014).
Mixed FEM for Second Order Elliptic Problems on Polygonal Meshes with BEM-Based Spaces. Lecture Notes in Artificial Intelligence.
331-338.
-
Jin, B., Lazarov, R., Pasciak, J., & Zhou, Z.
(2013).
Galerkin FEM for Fractional Order Parabolic Equations with Initial Data in H-s, 0 <= s <= 1. Lecture Notes in Artificial Intelligence.
24-37.
-
Efendiev, Y., Galvis, J., Lazarov, R., & Willems, J.
(2012).
Robust Solvers for Symmetric Positive Definite Operators and Weighted Poincar Inequalities. Lecture Notes in Artificial Intelligence.
43-51.
-
Lazarov, R., Mihaylova, I., Gesheva-Atanasova, N., & Bakardjiev, S.
(2011).
COMPARATIVE ANALYSIS OF TWO RADIOTHERAPY REGIMENS FOR THE TREATMENT OF PATIENTS WITH NON-SMALL CELL LUNG CANCER. RADIOTHERAPY AND ONCOLOGY.
S341-S341.
-
Mihaylova, I., Parvanova, V., Dimitrova, N., Kurteva, G., & Lazarov, R.
(2011).
PREOPERATIVE RADIOCHEMOTHERAPY WITH CAPECITABINE VERSUS RADIOTHERAPY ALONE IN PATIENTS WITH LOCALLY ADVANCED RECTAL CANCER. RADIOTHERAPY AND ONCOLOGY.
S398-S398.
-
Iliev, O. P., Lazarov, R. D., & Willems, J.
(2010).
Discontinuous Galerkin Subgrid Finite Element Method for Heterogeneous Brinkman's Equations. Lecture Notes in Artificial Intelligence.
14-+.
-
Dobrev, V. A., Lazarov, R. D., & Zikatanov, L. T.
(2008).
Preconditioning of Symmetric Interior Penalty Discontinuous Galerkin FEM for Elliptic Problems. Lecture Notes in Computational Science and Engineering.
33-44.
-
Parvanova, V., Gesheva, N., Klenova, A., Kurteva, G., Lazarow, R., Lazarov, R., Gueorguiev, I., & Staykova, V.
(2007).
Hypofractionation radiotherapy versus combined conventional radio-chemotherapy in advanced head and neck tumors. RADIOTHERAPY AND ONCOLOGY.
S59-S60.
-
Douglas, C. C., Harris, J. C., Iskandarani, M., Johnson, C. R., Lodder, R. J., Parker, S. G., ... Qin, G.
(2006).
Dynamic contaminant identification in water. Lecture Notes in Artificial Intelligence.
393-400.
-
Andreev, A., Lazarov, R., & Racheva, M.
(2006).
Postprocessing and improved accuracy of the lowest-order mixed finite element approximation for biharmonic eigenvalues. Lecture Notes in Artificial Intelligence.
613-620.
-
Douglas, C. C., Efendiev, Y., Ewing, R., Ginting, V., Lazarov, R., Cole, M. J., Jones, G., & Johnson, C. R.
(2005).
Multiscale interpolation, backward in time error analysis for data-driven contaminant simulation. Lecture Notes in Artificial Intelligence.
640-647.
-
Douglas, C. C., Efendiev, Y., Ewing, R., Ginting, V., Lazarov, R., Cole, M. J., Jones, G., & Johnson, C. R.
(2005).
Dynamic data-driven contaminant simulation. 25-36.
-
Douglas, C. C., Shannon, C. E., Efendiev, Y., Ewing, R., Ginting, V., Lazarov, R., ... Simpson, J.
(2004).
A note on data-driven contaminant simulation. Lecture Notes in Artificial Intelligence.
701-708.
-
Douglas, C. C., Efendiev, Y., Ewing, R., Lazarov, R., Cole, M. J., Jones, G., & Johnson, C. R.
(2003).
Virtual telemetry for dynamic data-driven application simulations. Lecture Notes in Artificial Intelligence.
279-288.
-
Lazarov, R. D., & Margenov, S. D.
(2003).
On a two-level parallel MIC(0) preconditioning of Crouzeix-Raviart non-conforming FEM systems. Lecture Notes in Artificial Intelligence.
192-201.
-
Lazarov, R. D., & Tomov, S. Z.
(2001).
Adaptive finite volume element method for convection-diffusion-reaction problems in 3-D. 91-106.
-
Lazarov, R. D., Pasciak, J. E., & Tomov, S. Z.
(2000).
Error control, local grid refinement, and efficient solution algorithms for singularly perturbed problems. 71-82.
-
Lazarov, R. D., & Vassilevski, P. S.
(2000).
Least-squares streamline diffusion finite element approximations to singularly perturbed convection-diffusion problems. 83-94.
-
Chernogorova, T., Ewing, R. E., Iliev, O., & Lazarov, R.
(2000).
On the discretization of interface problems with perfect and imperfect contact. Lecture Notes in Physics.
93-103.
-
Ewing, R. E., & Lazarov, R. D.
(1998).
Adaptive local grid refinement. 643-651.
-
EWING, R. E., LAZAROV, R. D., & VASSILEVSKI, P. S.
(1991).
FINITE-DIFFERENCE SCHEMES ON GRIDS WITH LOCAL REFINEMENT IN TIME AND IN SPACE FOR PARABOLIC PROBLEMS - OPTIMAL ORDER 2-GRID ITERATIVE METHODS. 70-93.
-
EWING, R. E., LAZAROV, R. D., & VASSILEVSKI, P. S.
(1991).
MIXED FINITE-ELEMENT SOLUTIONS OF 2ND-ORDER ELLIPTIC PROBLEMS ON GRIDS WITH REGULAR LOCAL REFINEMENT. 206-212.
-
EWING, R. E., LAZAROV, R. D., RUSSELL, T. F., & VASSILEVSKI, P. S.
(1990).
LOCAL REFINEMENT VIA DOMAIN DECOMPOSITION TECHNIQUES FOR MIXED FINITE-ELEMENT METHODS WITH RECTANGULAR RAVIART-THOMAS ELEMENTS. 98-114.
-
EWING, R. E., LAZAROV, R. D., LU, P., & VASSILEVSKI, P. S.
(1990).
PRECONDITIONING INDEFINITE SYSTEMS ARISING FROM MIXED FINITE-ELEMENT DISCRETIZATION OF 2ND-ORDER ELLIPTIC PROBLEMS. 28-43.
-
LAZAROV, R. D., VASSILEVSKI, P. S., & MARGENOV, S. D.
(1988).
SOLVING ELLIPTIC PROBLEMS BY THE DOMAIN DECOMPOSITION METHOD USING PRECONDITIONING MATRICES DERIVED BY MULTILEVEL SPLITTINGS OF THE FINITE-ELEMENT MATRIX. Lecture Notes in Artificial Intelligence.
826-835.
-
Harizanov, S., Lazarov, R., Margenov, S., Marinov, P., & Pasciak, J.
(2019).
Comparison Analysis of Two Numerical Methods for Fractional Diffusion Problems Based on the Best Rational Approximations of t on [0, 1]. Lecture Notes in Computational Science and Engineering.
165-185.
Research
principal investigator on
co-principal investigator on
- Adaptive Multiscale Simulation Framework for Reduced-Order Modeling in Perforated Domains awarded by National Science Foundation - (Arlington, Virginia, United States) 2016 - 2020
- Advanced Discretization Techniques and Applications (ADTA) awarded by National Science Foundation - (Arlington, Virginia, United States) 2015
Teaching
teaching activities
- MATH221 Hnr-sev Variable Calculus Instructor
- MATH417 Numerical Methods Instructor
- MATH610 Num Meth In Diff Equa Instructor
- MATH685 Directed Studies Instructor
- MATH691 Research Instructor
Works By Students
chaired theses and dissertations
-
Dobrev, Veselin Asenov (2007-12). Preconditioning of discontinuous Galerkin methods for second order elliptic problems.
-
Ginting, Victor Eralingga (2003-05). Computational upscaled modeling of heterogeneous porous media flow utilizing finite volume method.
-
Kang, Seul Ki (2012-08). Multiscale Simulation and Uncertainty Quantification Techniques for Richards' Equation in Heterogeneous Media.
-
Mao, Youli (2014-08). Geometric Multigrid Methods for Flow Problems in Highly Heterogeneous Porous Media.
-
Moon, Minam (2015-08). Generalized Discontinuous Multiscale Methods for Flows in Highly Heterogeneous Porous Media.
-
Zhou, Zhi (2015-08). Numerical Analysis of Fractional-Order Differential Equations with Nonsmooth Data.
Background
education and training
- D.Sc. in Applied Mathematics, Sofia University - (Palo Alto, California, United States) 1982
- Ph.D. in Physics and Mathematics, Moscow State University - (Moscow, Russia) 1972
- M.Sc. in Mathematics, Wroclaw University of Economics - (WrocLaw, Poland) 1966
awards and honors
- IMI-BAS Medal with Ribbon, conferred by Bulgarian Academy of Sciences - (Sofia, Bulgaria), 2007
Contact
first name
- Raytcho
has last name
- Lazarov
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- r-lazarov@tamu.edu