Browsing by Subject "Matrix decomposition"

Now showing items 1-9 of 9

    • Article  

      Conformal Mapping for the Efficient Solution of Poisson Problems with the Kansa-RBF Method 

      Liu, X. -Y; Chen, C. S.; Karageorghis, Andreas (2017)
      We consider the solution of Poisson Dirichlet problems in simply-connected irregular domains. These domains are conformally mapped onto the unit disk and the resulting Poisson Dirichlet problems are solved efficiently using ...
    • Article  

      Efficient MFS algorithms for inhomogeneous polyharmonic problems 

      Karageorghis, Andreas (2011)
      In this work we develop an efficient algorithm for the application of the method of fundamental solutions to inhomogeneous polyharmonic problems, that is problems governed by equations of the form Δ ℓ u=f, ℓ ε ℕ, in circular ...
    • Article  

      Efficient MFS algorithms for problems in thermoelasticity 

      Karageorghis, Andreas; Marin, L. (2013)
      We propose efficient fast Fourier transform (FFT)-based algorithms using the method of fundamental solutions (MFS) for the numerical solution of certain problems in planar thermoelasticity. In particular, we consider ...
    • 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 Dirichlet-Neumann boundary conditions, using second order finite difference schemes. The resulting linear systems ...
    • Article  

      Kansa-RBF algorithms for elliptic problems in axisymmetric domains 

      Karageorghis, Andreas; Chen, C. S.; Liu, X. -Y (2016)
      We employ a Kansa-radial basis function method for the numerical solution of elliptic boundary value problems in three-dimensional axisymmetric domains. We consider problems governed by the Poisson equation, the inhomogeneous ...
    • Conference Object  

      Matrix decomposition MFS algorithms 

      Karageorghis, Andreas; Smyrlis, Yiorgos-Sokratis (2006)
      We describe the application of the Method of Fundamental Solutions (MFS) to elliptic boundary value problems in rotationally symmetric problems. In particular, we show how efficient matrix decomposition MFS algorithms can ...
    • Article  

      Matrix decomposition RBF algorithm for solving 3D elliptic problems 

      Karageorghis, Andreas; Chen, C. S.; Smyrlis, Yiorgos-Sokratis (2009)
      In this study, we propose an efficient algorithm for the evaluation of the particular solutions of three-dimensional inhomogeneous elliptic partial differential equations using radial basis functions. The collocation points ...
    • 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  

      The plane waves method for axisymmetric Helmholtz problems 

      Karageorghis, Andreas (2016)
      The plane waves method is employed for the solution of Dirichlet and Neumann boundary value problems for the homogeneous Helmholtz equation in two- and three-dimensional domains possessing radial symmetry. The appropriate ...