PCE_LEGENDRE is a MATLAB library which sets up the system matrix for a polynomial chaos expansion, using Legendre polynomials with a linear factor, applied to a 2D PDE with a stochastic diffusion coefficient.
We wish to analyze a stochastic PDE of the form:
-div A(X,Y) grad U(X,Y) = F(X)where
We let X be a space of finite element functions generated by piecewise linear functions associated with a particular triangular dissection of the unit square.
We let Y be the space of polynomials over R^N with total degree at most P.
We seek solutions U in XxY using a polynomial chaos expansion approach.
[ nxy, bxy, fxy ] = pce_legendre_linear_assemble ( n, p )where the input is:
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
PCE_LEGENDRE is available in a MATLAB version.
CNOISE, a MATLAB library which generates samples of noise obeying a 1/f^alpha power law, by Miroslav Stoyanov.
LEGENDRE_POLYNOMIAL, a MATLAB library which evaluates the Legendre polynomial and associated functions.
LEGENDRE_RULE, a MATLAB program which computes a Gauss-Legendre quadrature rule.
PCE_BURGERS, a MATLAB program which defines and solves a version of the time-dependent viscous Burgers equation, with uncertain viscosity, using a polynomial chaos expansion, by Gianluca Iaccarino.
PCE_ODE_HERMITE, a MATLAB program which sets up a simple scalar ODE for exponential decay with an uncertain decay rate, using a polynomial chaos expansion in terms of Hermite polynomials.
POLPAK, a MATLAB library which evaluates a variety of mathematical functions.
STOCHASTIC_DIFFUSION, a MATLAB library which implements several versions of a stochastic diffusivity coefficient.
SUBSET, a MATLAB library which enumerates combinations, partitions, subsets, index sets, and other combinatorial objects.
[nxy,bxy,fxy]=pce_legendre_linear_assemble(3,2)
[nxy,bxy,fxy]=pce_legendre_linear_assemble(4,1)
[nxy,bxy,fxy]=pce_legendre_linear_assemble(4,2)
[nxy,bxy,fxy]=pce_legendre_linear_assemble(4,3)
[nxy,bxy,fxy]=pce_legendre_linear_assemble(4,4)
You can go up one level to the MATLAB source codes.