30-Jul-2021 15:22:01
stochastic_heat2d_test():
MATLAB/Octave version 9.9.0.1467703 (R2020b)
Test stochastic_heat2d().
STOCHASTIC_HEAT2D_TEST01
Consider steady heat equation in the unit square,
with 0 Dirichlet boundary conditions,
and a heat source term that is a Gaussian centered at (0.60,0.80).
Model the diffusivity coefficient as spatially varying,
with a stochastic dependence on parameters Omega1 through Omega4,
as described in Babuska, Nobile, Tempone (BNT).
Compute a solution for sample values of OMEGA.
Example omega: 1.07533 3.66777 -4.51769 1.72435
Plotfile saved as "example_solution.png".
Mean value of example solution is 0.00208993
STOCHASTIC_HEAT2D_TEST02
Consider steady heat equation in the unit square,
with 0 Dirichlet boundary conditions,
and a heat source term that is a Gaussian centered at (0.60,0.80).
Model the diffusivity coefficient as spatially varying,
with a stochastic dependence on parameters Omega1 through Omega4,
as described in Babuska, Nobile, Tempone (BNT).
Fix Omega3 = 4, Omega4 = 0, and
examine dependence of average temperature on Omega1 and Omega2
over the range [-10,+10].
Now fix OMEGA(3) and OMEGA(4), and compute U
for a range of OMEGA(1) and OMEGA(2) values,
keeping track of mean solution value each time.
Omega(3) fixed at 4
Omega(4) fixed at 0
Plot file saved as "mean_temperature.png".
U_Mean_Max= 0.641953
stochastic_heat2d_test():
Normal end of execution.
30-Jul-2021 15:22:08