Browsing by Author "Bialecki, B."
Now showing items 113 of 13

Article
Finite Difference Schemes for the Cauchy–Navier Equations of Elasticity with Variable Coefficients
Bialecki, B.; Karageorghis, Andreas (2015)We solve the variable coefficient Cauchy–Navier equations of elasticity in the unit square, for Dirichlet and DirichletNeumann boundary conditions, using second order finite difference schemes. The resulting linear systems ...

Article
Legendre Gauss spectral collocation for the Helmholtz equation on a rectangle
Bialecki, B.; Karageorghis, Andreas (2004)A spectral collocation method with collocation at the Legendre Gauss points is discussed for solving the Helmholtz equation Δu+κ(x,y)u=f(x,y) on a rectangle with the solution u subject to inhomogeneous Robin boundary ...

Article
A legendre spectral collocation method for the biharmonic Dirichlet problem
Bialecki, B.; Karageorghis, Andreas (2000)A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which ...

Article
A Legendre spectral Galerkin method for the biharmonic Dirichlet problem
Bialecki, B.; Karageorghis, Andreas (2001)A Legendre spectral Galerkin method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which ...

Article
A Legendre spectral quadrature Galerkin method for the CauchyNavier equations of elasticity with variable coefficients
Bialecki, B.; Karageorghis, Andreas (2017)We solve the Dirichlet and mixed DirichletNeumann boundary value problems for the variable coefficient CauchyNavier equations of elasticity in a square using a Legendre spectral Galerkin method. The resulting linear ...

Article
Matrix decomposition algorithms for elliptic boundary value problems: A survey
Bialecki, B.; Fairweather, G.; Karageorghis, Andreas (2011)We provide an overview of matrix decomposition algorithms (MDAs) for the solution of systems of linear equations arising when various discretization techniques are applied in the numerical solution of certain separable ...

Article
Matrix decomposition algorithms for modified spline collocation for Helmholtz problems
Bialecki, B.; Fairweather, G.; Karageorghis, Andreas (2003)We consider the solution of various boundary value problems for the Helmholtz equation in the unit square using a nodal cubic spline collocation method and modifications of it which produce optimal (fourth) order ...

Article
Modified nodal cubic spline collocation for threedimensional variable coefficient second order partial differential equations
Bialecki, B.; Karageorghis, Andreas (2013)We formulate a fourth order modified nodal cubic spline collocation scheme for variable coefficient second order partial differential equations in the unit cube subject to nonzero Dirichlet boundary conditions. The approximate ...

Article
A nonoverlapping domain decomposition method for Legendre spectral collocation problems
Bialecki, B.; Karageorghis, Andreas (2007)We consider the Dirichlet boundary value problem for Poisson's equation in an Lshaped region or a rectangle with a crosspoint. In both cases, we approximate the Dirichlet problem using Legendre spectral collocation, that ...

Article
Optimal superconvergent one step nodal cubic spline collocation methods
Bialecki, B.; Fairweather, G.; Karageorghis, Andreas (2006)We formulate new optimal (fourth) order one step nodal cubic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the respective ...

Article
Optimal superconvergent one step quadratic spline collocation methods
Bialecki, B.; Fairweather, G.; Karageorghis, Andreas; Nguyen, Q. N. (2008)We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved ...

Article
Spectral Chebyshev collocation for the poisson and biharmonic equations
Bialecki, B.; Karageorghis, Andreas (2010)This paper is concerned with the spectral Chebyshev collocation solution of the Dirichlet problems for the Poisson and biharmonic equations in a square. The collocation schemes are solved at a cost of 2N3 + O(N2 logN) ...

Article
Spectral ChebyshevFourier collocation for the Helmholtz and variable coefficient equations in a disk
Bialecki, B.; Karageorghis, Andreas (2008)The paper is concerned with the spectral collocation solution of the Helmholtz equation in a disk in the polar coordinates r and θ. We use spectral Chebyshev collocation in r, spectral Fourier collocation in θ, and a simple ...