THE UNIVERSITY OF BIRMINGHAM

THE SCHOOL OF MATHEMATICS

THE APPLIED MATHEMATICS GROUP

N.B.PETROVSKAYA

Refereed papers

  N.B.Petrovskaya, N.L.Embleton.   Evaluation of Peak Functions on Ultra-Coarse Grids.   Proc. R. Soc. A, 2013, vol.469 (article in press) doi: 10.1098/rspa.2012.0665   abstract

  N.L.Embleton, N.B.Petrovskaya.   On Numerical Uncertainty in Evaluation of Pest Population Size.   Ecol. Complex., 2013, vol.14(2), pp.117-131 doi: 10.1016/j.ecocom.2012.11.004   abstract

  S.V.Petrovskii, N.B.Petrovskaya.   Computational Ecology as an Emerging Science.   J.R.Soc. Interface Focus, 2012, vol.2(2), pp.241-254, doi:10.1098/rsfs.2011.0083   abstract

  N.B.Petrovskaya, S.V.Petrovskii, A.K.Murchie.   Challenges of Ecological Monitoring: Estimating Population Abundance From Sparse Trap Counts.   J.R.Soc.Interface, 2012, vol.9(68), pp.420-435, doi:10.1098/rsif.2011.0386   abstract ,   pdf file

  N.B.Petrovskaya, E.Venturino.   Numerical Integration of Sparsely Sampled Data.   Simulat. Modell. Pract. Theory, 2011, vol.19(9), pp.1860–1872, doi:10.1016/j.simpat.2011.05.003   abstract ,   pdf file

  A. V. Wolkov, Ch. Hirsch, N.B.Petrovskaya.   Application of a Higher Order Discontinuous Galerkin Method in Computational Aerodynamics.   Mathematical Modeling of Natural Phenomena, 2011, vol.6(3) (invited issue on computational aerodynamics), pp.237-263, doi:10.1051/mmnp/20116310   abstract ,   pdf file

  N.B.Petrovskaya.   Data Dependent Weights in Discontinuous Weighted Least-Squares Approximation with Anisotropic Support.   Calcolo, 2011, vol.48(1), pp.127-143, doi: 10.1007/s10092-010-0032-7   abstract ,   pdf file

  N.B.Petrovskaya, S. V. Petrovskii.   The Coarse-Grid Problem in Ecological Monitoring.   Proc. R. Soc. A, 2010, vol.466, pp. 2933-2953, doi: 10.1098/rspa.2010.0023.   abstract ,   pdf file

  A.V.Wolkov, N.B.Petrovskaya.   Higher Order Discontinuous Galerkin Method for Acoustic Pulse problem.   Comput. Phys. Commun., 2010, vol.181, pp. 1186–1194.   abstract ,   pdf file

  N.B.Petrovskaya, A.V.Wolkov.   The Impact of Grid Geometry on the Accuracy of Higher Order Finite-Volume and Finite Element Schemes.   J. Math. Mod., 2010, vol.22(3), pp.145-160, in Russian.   abstract ,   pdf file

  N.B.Petrovskaya.   Quadratic Least-Squares Solution Reconstruction in a Boundary Layer Region.   Commun. Numer.Meth. Engng., 2010, vol.26(12), pp.1721-1735, doi: 10.1002/cnm.1259.   abstract ,   pdf file

  N.B.Petrovskaya.   Discontinuous Weighted Least-Squares Approximation on Irregular Grids.   CMES: Computer Modeling in Engineering & Sciences, 2008, vol.32(2), pp.69-84, doi: 10.3970/cmes.2008.032.069   abstract ,   pdf file

  N.B.Petrovskaya.   The Accuracy of Least-Squares Approximation on Highly Stretched Meshes. Int. J. Comput. Methods, 2008, vol.5(3), pp.449 - 462.   abstract   pdf file

  N.B.Petrovskaya, A.V.Wolkov, S.V.Lyapunov.   Modification of Basis Functions in High Order Discontinuous Galerkin Schemes for Advection Equation. Appl. Math. Model., 2008, vol.32(5), pp.826-835.   abstract ,   pdf file

  N.B.Petrovskaya, A.V.Wolkov.   The Issues of Solution Approximation in Higher Order Schemes on Distorted Grids. Int. J. Comput. Methods, 2007, vol.4(2), pp.367-382.   abstract ,   pdf file

  N.B.Petrovskaya.   On Oscillations in Discontinuous Galerkin Discretization Schemes for Steady State Problems. SIAM J. Sci. Comput., 2006, vol.27(4), pp.1329-1346.   abstract ,   pdf file

  N.B.Petrovskaya, S.V. Petrovskii, B.-L. Li.   Biodiversity Measures Revisited. Ecol. Complex., 2006, vol.3, pp.13-22.   abstract ,   pdf file

  N.B.Petrovskaya.   Two Types of Solution Overshoots in Discontinuous Galerkin Discretization Schemes.   Comm. Math. Sci., 2005, vol.3(2), pp.235-249.   abstract ,   pdf file

  N.B.Petrovskaya.   Implementation of Newton's Method in High Order Schemes for Steady State Problems.   Comput. Tech., 2005, vol.10(2), pp.106-113, in Russian.

  N.B.Petrovskaya.   Approximation of Discontinuous Solutions in High Order Discontinuous Galerkin Schemes.   J. Math. Mod., 2005, vol.17(1), pp.79 - 92, in Russian.   abstract ,   pdf file

  N.B.Petrovskaya.   The Analysis of the Grid Refinement Procedure for Vector Functions.  Comput. Tech., 2004, vol.9(4), pp.3-14.   abstract ,   pdf file

  N.B.Petrovskaya.  The Choice of Weight Coefficients for the Least-Squares Gradient Approximation.   J. Math. Mod., 2004, vol.16(5), pp.83-93, in Russian.   abstract ,   pdf file

  N.B.Petrovskaya.  Modification of a Finite Volume Scheme for Laplace's Equation.   SIAM J. Sci. Comput., 2001, vol.23(3), pp.891-909.   abstract ,   pdf file

  K.V.Brushlinsky, M.S. Mikhailova, A.I.Morozov, N.B.Petrovskaya, V.D.Pustovitov, N.M. Zueva.  Computer Simulation of "Galatea -Stellarator",  Problems of Atomic Science and Technology (ser. Plasma Phys.), 1999, vol.2(2). pp.24-29.

  K.V.Brushlinsky, A.I.Morozov, N.B.Petrovskaya.   Numerical Simulation of Equilibrium Helical Configuration with Plasma on the Separatrix.  J. Math. Mod., 1998, vol.10(11), pp.29-36, in Russian (transl. Eng.)

  K.V.Brushlinsky, N.M.Zueva, M.S.Mikhaylova, N.B.Petrovskaya.   On Uniqueness and Stability of Solutions to 2-D Plasmastatics Problems.  J. Math. Mod., 1995, vol.4(7), pp.73-86, in Russian (transl. Eng.)

  K.V.Brushlinsky, N.M.Zueva, M.S.Mikhaylova, N.B.Petrovskaya.  Dependence of Properties of Helical Plasma Sheaths on Helix Lead.   Plasma Phys. Rep., 1995, vol.21(3), pp.209-214.

  K.V.Brushlinsky, N.M.Zueva, M.S.Mikhaylova, A.I.Morozov, V.D.Pustovitov, N.B.Tuzova (Petrovskaya).  Numerical Simulation of Straight Helical Sheaths with Conductors Immersed in Plasma.   Plasma Phys. Rep., 1994, vol.20(3), pp.256-264.

  K.V.Brushlinsky, V.S.Ryabenky, N.B.Tuzova (Petrovskaya).  The Transfer of Boundary Conditions Across a Vacuum in Axisymmetric Problems.  J. Comput. Math. and Math. Phys., 1992, vol.32(12), pp.1757-1767.

  K.V.Brushlinsky, A.I.Morozov, T.A.Ratnikova, N.B.Tuzova(Petrovskaya).  Dissipative Evolution of the Magnetic Configuration of an Autonomic Probe ("Microgalatea").  Sov. J. Plasma Phys., 1992, vol.18(8), pp.1047-1058, in Russian (transl. Eng.)

  K.V.Brushlinsky, T.A.Ratnikova, N.B.Tuzova(Petrovskaya).  Calculation of the Evolution of the Magnetic Field and Temperature in a Conducting Hoop with Current in an Applied Uniform Field.  J.Math. Mod., 1991, vol.2(11), pp.45-54, in Russian (transl. Eng.)

Refereed book chapters

  N.B.Petrovskaya, N.L.Embleton, S.V.Petrovskii.   Numerical Study of Pest Population Size at Various Diffusion Rates.   M.A. Lewis et al. (eds.), Dispersal, Individual Movement and Spatial Ecology, Lecture Notes in Mathematics 2071, Springer-Verlag Berlin Heidelberg 2013, pp. 355-386.  

  N.B.Petrovskaya.   Solution Limiters and Flux Limiters in High Order Discontinuous Galerkin Schemes.   Lecture Notes in Computer Science (T. Boyanov et al, eds.), Springer, 2007, vol.4310, pp. 668-677.

  K.V.Brushlinsky, N.M.Zueva, M.S.Mikhaylova, N.B.Petrovskaya. Mathematical Model of "Stellarator - Galateya" and Boundary Value Problems with Grad-Shafranov Equation. Proceedings of European Physical Society (Controlled Fusion and Plasma Physics), Kiev, Ukraine, 1996, pp.119-126.

Other publications

  N.B.Petrovskaya.   Some Issues of Implementation of Higher Order Schemes in Computational Aerodynamics.   Boeing technical report 66-ZB-B001-10A-533,  The Boeing Company,   Seattle, WA, 2007.

  N.B.Petrovskaya.   Newton's Method for High Order Schemes: As Good As It Gets?   preprint N11,    Inst. Appl. Math., Rus.Ac.Sci., 2004.

  N.B.Petrovskaya.   A Least-Squares Approximation Problem on "Bad" Grids.   Boeing technical report 104AE, Boeing Operations International, Inc., Moscow, 2003.

  N.B.Petrovskaya.   Non-oscillating Discontinuous Galerkin Schemes for Steady State Problems.   Boeing technical report 104AE, Boeing Operations International, Inc., Moscow, 2003.

    N.B.Petrovskaya.   The Impact of Grid Cell Geometry on the Least - Squares Gradient Reconstruction.   preprint N21, Inst. Appl. Math., Rus.Ac.Sci., 2003.

  N.B.Petrovskaya.   Minimization of Interpolation Error Estimates for Vector Functions.   preprint N23, Inst. Appl. Math.,Rus.Ac.Sci., 2003.

  N.B.Petrovskaya.   A Modified Discontinuous Galerkin Discretization Scheme for One - Dimensional Conservation Laws.   Boeing technical report 104Z, Boeing Operations International, Inc., Moscow, 2002.

  N.B.Petrovskaya.   Treatment of a Shock for the Discontinuous Galerkin Discretization Scheme.   Boeing technical report 104Z, Boeing Operations International, Inc., Moscow, 2002.

  N.B.Petrovskaya.   A Choice of Adaptation Strategy for Vector Functions.   Boeing technical report 104Y, Boeing Operations International, Inc., Moscow, 2001.

  N.B.Petrovskaya.   Measuring Adaptive Grid Information.   Boeing technical report 104Y, Boeing   Operations International, Inc., Moscow, 2001.

  N.B.Petrovskaya.   Error Indicators and Analysis of Refinement Technology for Vector Functions.   Boeing technical report 104W, Boeing Operations International, Inc., Moscow, 2000.

  N.B.Petrovskaya.  Positive Finite Volume Scheme for Laplace's Equation on Arbitrary 2-D Unstructured Meshes.   In Proceedings of 16-th IMACS World Congress 2000, Lausanne, Switzerland, August 21-25, 2000.

  N.B.Petrovskaya.   Large Angles Tolerant Discretization.   Boeing technical report 104R, Boeing Operations International, Inc., Moscow, 1999.

  N.B.Petrovskaya.   Modified finite volume scheme for Laplace's equation.   Boeing technical report 104R, Boeing Operations International, Inc., Moscow, 1999.

  D.S.Kamenetskii, N.B.Petrovskaya.   Multiblock Surface Grid Generation Based on a Quasi - Isometric Functional.   Boeing technical report 104N, Boeing Operations International, Inc., Moscow, 1998

  S.K.Godunov, O.B.Feodoritova,A.V.Gusev, D.S.Kamenetskii, M.V.Mikchailuk, I.L.Petrouchenkov, N.B.Petrovskaya and       V.T. Zhukov.   Grid Generation System. User's guide.   Boeing technical report 104L, Boeing Operations International,Inc., Moscow, 1997

  N.B.Petrovskaya.   A Surface Grid Generation Problem in the Presence of Singular Points.   Boeing technical report 104G, Boeing Operations International, Inc., Moscow, 1996

  N.B.Petrovskaya.   A Bifurcation Model for Solutions to a One-Dimensional Plasmastatics Problem.   preprint N61, Inst. Appl. Math., Rus.Ac.Sci., 1994, in Russian.