stochastic_diffusion


stochastic_diffusion, a MATLAB code which implement several versions of a diffusivity coefficient whose value depends on parameters that may be chosen stochastically.

In the 1D stochastic version of the problem, the diffusivity function rho() includes the influence of a stochastic parameter vector OMEGA:

        - d/dx ( rho(X;OMEGA) d/dx U(X;OMEGA) ) = F(X).
      

In the 2D stochastic version of the problem, the diffusivity function rho() includes the influence of a stochastic parameter vector OMEGA:

        - Del ( rho(X,Y;OMEGA) Del U(X,Y;OMEGA) ) = F(X,Y).
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

stochastic_diffusion is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

stochastic_diffusion_test

Reference:

  1. Ivo Babuska, Fabio Nobile, Raul Tempone,
    A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data,
    SIAM Journal on Numerical Analysis,
    Volume 45, Number 3, 2007, pages 1005-1034.
  2. Howard Elman, Darran Furnaval,
    Solving the stochastic steady-state diffusion problem using multigrid,
    IMA Journal on Numerical Analysis,
    Volume 27, Number 4, 2007, pages 675-688.
  3. Fabio Nobile, Raul Tempone, Clayton Webster,
    A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data,
    SIAM Journal on Numerical Analysis,
    Volume 46, Number 5, 2008, pages 2309-2345.
  4. Dongbin Xiu, George Karniadakis,
    Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos,
    Computer Methods in Applied Mechanics and Engineering,
    Volume 191, 2002, pages 4927-4948.

Source Code:


Last modified on 07 March 2019.