Model reduction Project

Write a matlab code to create a reduced model for the transient diffusion equation

Use PGD with 3 variables: k,x,t

The space-time-diffusivity domain is x t k = (0, 1) (0, 0.1) [1, 5].

For the the source term, take f = 1.

Regarding the initial and boundary conditions, take: u(x, t = 0) = u(x = 0, t) = u(x = 1, t) = 0,

Use uniform grids with 61 points for the space domain, 151 points for the time domain and 101 points for the diffusivity domain.

Generate plots for the normalized functions Xi (x), Ti (t) and Ki (k) for i = 1, . . . , 4. (Fig 5.1, 5.2 and 5.3 in the book)

Use Finite element difference to solve the differential equations in the alternating strategy loop

Make use of the 2 matlab code provided for Poisson equation (PGD_Poisson_2D.m and Section_2_1_3.m)