Bernard Bialecki

Publication Activity (10 Years)

Years Active: 1994-2022
Publications (10 Years): 5

Top Topics

Image Denoising

Rectangular Regions

Finite Difference

Top Venues

Numer. Algorithms

J. Sci. Comput.

J. Comput. Phys.

Publications

Bernard Bialecki, Graeme Fairweather, Andreas Karageorghis
An optimal two-step quadratic spline collocation method for the Dirichlet biharmonic problem. Numer. Algorithms 91 (3) (2022)
Bernard Bialecki, Maksymilian Dryja, Ryan I. Fernandes
Convergence analysis of the finite difference ADI scheme for the heat equation on a convex set. Math. Comput. 90 (332) (2021)
Bernard Bialecki, Graeme Fairweather, Andreas Karageorghis, Jonathan Maack
A quadratic spline collocation method for the Dirichlet biharmonic problem. Numer. Algorithms 83 (1) (2020)
Bernard Bialecki, Andreas Karageorghis
A Legendre spectral quadrature Galerkin method for the Cauchy-Navier equations of elasticity with variable coefficients. Numer. Algorithms 77 (2) (2018)
Bernard Bialecki, Ryan I. Fernandes
Alternating direction implicit orthogonal spline collocation on some non-rectangular regions with inconsistent partitions. Numer. Algorithms 74 (4) (2017)
Bernard Bialecki, Graeme Fairweather, Juan C. López-Marcos
The Extrapolated Crank-Nicolson Orthogonal Spline Collocation Method for a Quasilinear Parabolic Problem with Nonlocal Boundary Conditions. J. Sci. Comput. 62 (1) (2015)
Bernard Bialecki, Lyndsey Wright
A fast direct solver for a fourth order finite difference scheme for Poisson's equation on the unit disc in polar coordinates. Numer. Algorithms 70 (4) (2015)
Bernard Bialecki, Andreas Karageorghis
Finite Difference Schemes for the Cauchy-Navier Equations of Elasticity with Variable Coefficients. J. Sci. Comput. 62 (1) (2015)
Ryan I. Fernandes, Bernard Bialecki, Graeme Fairweather
An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains. J. Comput. Phys. 299 (2015)
Bernard Bialecki, Andreas Karageorghis
Modified nodal cubic spline collocation for three-dimensional variable coefficient second order partial differential equations. Numer. Algorithms 64 (2) (2013)
Bernard Bialecki
A fourth order finite difference method for the Dirichlet biharmonic problem. Numer. Algorithms 61 (3) (2012)
Bernard Bialecki, Graeme Fairweather, Andreas Karageorghis
Matrix decomposition algorithms for elliptic boundary value problems: a survey. Numer. Algorithms 56 (2) (2011)
Bernard Bialecki, Andreas Karageorghis
Spectral Chebyshev Collocation for the Poisson and Biharmonic Equations. SIAM J. Sci. Comput. 32 (5) (2010)
Bernard Bialecki, Javier de Frutos
ADI spectral collocation methods for parabolic problems. J. Comput. Phys. 229 (13) (2010)
Bernard Bialecki, R. Baker Kearfott, Krzysztof A. Sikorski, Masaki Sugihara
Guest editors' preface: Issue dedicated to Professor Frank Stenger. J. Complex. 25 (3) (2009)
Bernard Bialecki, Ryan I. Fernandes
An Alternating Direction Implicit Backward Differentiation Orthogonal Spline Collocation Method for Linear Variable Coefficient Parabolic Equations. SIAM J. Numer. Anal. 47 (5) (2009)
Bernard Bialecki, Graeme Fairweather, David B. Knudson, D. Abram Lipman, Que N. Nguyen, Weiwei Sun, Gadalia M. Weinberg
Matrix decomposition algorithms for the finite element Galerkin method with piecewise Hermite cubics. Numer. Algorithms 52 (1) (2009)
Bernard Bialecki, Andreas Karageorghis
Spectral Chebyshev-Fourier collocation for the Helmholtz and variable coefficient equations in a disk. J. Comput. Phys. 227 (19) (2008)
Bernard Bialecki, Maksymilian Dryja
Nonoverlapping domain decomposition with cross points for orthogonal spline collocation. J. Num. Math. 16 (2) (2008)
Bernard Bialecki, Andreas Karageorghis
A Nonoverlapping Domain Decomposition Method for Legendre Spectral Collocation Problems. J. Sci. Comput. 32 (2) (2007)
Abeer Ali Abushama, Bernard Bialecki
Modified Nodal Cubic Spline Collocation For Poisson's Equation. SIAM J. Numer. Anal. 46 (1) (2007)
Bernard Bialecki, Ryan I. Fernandes
An Alternating-Direction Implicit Orthogonal Spline Collocation Scheme for Nonlinear Parabolic Problems on Rectangular Polygons. SIAM J. Sci. Comput. 28 (3) (2006)
Abeer Ali Abushama, Bernard Bialecki
Modified nodal cubic spline collocation for biharmonic equations. Numer. Algorithms 43 (4) (2006)
Bernard Bialecki, Graeme Fairweather, Andreas Karageorghis
Optimal Superconvergent One Step Nodal Cubic Spline Collocation Methods. SIAM J. Sci. Comput. 27 (2) (2005)
Bernard Bialecki, Andreas Karageorghis
Legendre Gauss Spectral Collocation for the Helmholtz Equation on a Rectangle. Numer. Algorithms 36 (3) (2004)
Bernard Bialecki, Maksymilian Dryja
A Nonoverlapping Domain Decomposition Method for Orthogonal Spline Collocation Problems. SIAM J. Numer. Anal. 41 (5) (2003)
Bernard Bialecki, Graeme Fairweather, Andreas Karageorghis
Matrix Decomposition Algorithms for Modified Spline Collocation for Helmholtz Problems. SIAM J. Sci. Comput. 24 (5) (2003)
Rakhim Aitbayev, Bernard Bialecki
A Preconditioned Conjugate Gradient Method for Nonselfadjoint or Indefinite Orthogonal Spline Collocation Problems. SIAM J. Numer. Anal. 41 (2) (2003)
Bingkun Li, Graeme Fairweather, Bernard Bialecki
Discrete-Time Orthogonal Spline Collocation Methods for Vibration Problems. SIAM J. Numer. Anal. 39 (6) (2002)
Bernard Bialecki, Andreas Karageorghis
A Legendre Spectral Galerkin Method for the Biharmonic Dirichlet Problem. SIAM J. Sci. Comput. 22 (5) (2001)
Rakhim Aitbayev, Bernard Bialecki
Orthogonal Spline Collocation for Nonlinear Dirichlet Problems. SIAM J. Numer. Anal. 38 (5) (2000)
Zhou-Ming Lou, Bernard Bialecki, Graeme Fairweather
Orthogonal spline collocation methods for biharmonic problems. Numerische Mathematik 80 (2) (1998)
Bernard Bialecki, Karin A. Remington
Fourier Matrix Decomposition Methods for the Least Squares Solution of Singular Neumann and Periodic Hermite Bicubic Collocation Problems. SIAM J. Sci. Comput. 16 (2) (1995)
Bernard Bialecki, Graeme Fairweather
Matrix Decomposition Algorithms in Orthogonal Spline Collocation for Separable Elliptic Boundary Value Problems. SIAM J. Sci. Comput. 16 (2) (1995)
Bernard Bialecki
Preconditioned Richardson and Minimal Residual Iterative Methods for Piecewise Hermite Bicubic Orthogonal Spline Collocation Equations. SIAM J. Sci. Comput. 15 (3) (1994)
Bernard Bialecki
Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation. Numer. Algorithms 8 (2) (1994)