16-May-2025 08:31:43

stochastic_heat2d_test():
  MATLAB/Octave version 6.4.0
  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:  -3.55781  -0.235392  3.97004  -0.38614

  Plotfile saved as "example_solution.png".
  Mean value of example solution is 0.337377

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.

16-May-2025 08:32:15