stochastic_diffusion
stochastic_diffusion,
a Python code which
implements several versions of a stochastic diffusivity coefficient.
In the 1D stochastic version of the problem, the diffusivity function DC()
includes the influence of stochastic parameters:
- d/dx ( DC(X;OMEGA) d/dx U(X;OMEGA) ) = F(X).
In the 2D stochastic version of the problem, the diffusivity function DC()
includes the influence of stochastic parameters:
- Del ( DC(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 MIT 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:
black_scholes,
a Python code which
implements some simple approaches to
the Black-Scholes option valuation theory;
Reference:
-
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.
-
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.
-
Roger Ghanem, Pol Spanos,
Stochastic Finite Elements: A Spectral Approach,
Revised Edition,
Dover, 2003,
ISBN: 0486428184,
LC: TA347.F5.G56.
-
Xiang Ma, Nicholas Zabaras,
An adaptive hierarchical sparse grid collocation algorithm for the solution
of stochastic differential equations,
Journal of Computational Physics,
Volume 228, pages 3084-3113, 2009.
-
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.
-
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:
-
diffusivity_1d_pwc.png,
a 1D piecewise constant stochastic diffusivity function.
-
diffusivity_1d_xk.png,
a 1D stochastic diffusivity function from Xiu and Karniadakis.
-
diffusivity_2d_bnt.png,
a 2D stochastic diffusivity function from Babuska, Nobile, and Tempone.
-
diffusivity_2d_elman.png,
a 2D stochastic diffusivity function from Elman.
-
diffusivity_2d_jvb.png,
a 2D stochastic diffusivity function that generalizes the
Babuska, Nobile, and Tempone, by allowing an arbitrary number of
coefficients in the KL expansion.
-
diffusivity_2d_ntw.png,
a 2D stochastic diffusivity function from Nobile, Tempone, and Webster.
-
diffusivity_2d_pwc.png,
a 2D piecewise constant stochastic diffusivity function.
Last modified on 24 March 2019.