MATLAB PARTIAL DIFFERENTIAL EQUATION TOOLBOX 1 Manuel d'utilisateur télécharger pdf (Page 8)

Solving PDEs Programatically

Although the PDE Toolbox GUI is a useful way to solve PDEs, the flexibility of using

command-line functions is sometimes useful for automating calculations, such as for

convergence studies. The easiest way to do this is to still use the PDE Toolbox GUI to define the

geometry and boundary conditions and export the decomposed geometry and boundary condition

matrices to the MATLAB environment as described above. Then, from the MATLAB

environment (or a script file) use the following functions

fid = wgeom(g, 'file_g'); % create geometry file from matrix g

fid = wbound(b, 'file_b'); % create boundary condition file from matrix b

Next, to create, refine, and jiggle a mesh use the following functions

[p, e, t] = initmesh('file_g', 'Hmax', Hm);

[p, e, t] = refinemesh('file_g', p, e, t);

p = jigglemesh(p, e, t);

One option for the initmesh function is shown that sets the minimum size, Hm, for the edge

spacing for the mesh. Use the online help to see additional options for each of these functions.

To solve an elliptic PDE defined as

€

−∇⋅ c ∇u

( )

+ a u = f

(6)

where the values of the coefficients c, a, and f must be set as string variables, use the following

function for a linear equation

u = assempde('file_b', p, e, t, c, a, f);

Alternatively, use the following function to solve a nonlinear elliptic PDE equation

[u, res] = pdenonlin('file_b', p, e, t, c, a, f, 'Jacobian', 'full', 'U0', 100);

where the options to use the full Jacobian and to specify an initial guess are set. To solve the

parabolic PDE defined as

€

∂

− ∇⋅ c ∇u

( )

+ a u = f

(7)

where the values of the coefficients d, c, a, and f must again be set as string variables and the

initial condition and number of time steps must also be set using

u0 = T0*ones(size(p, 2), 1); % initial condition, T0 is the initial temperature

1 2 3 4 5 6 7 8 9 10 11 12 13 ... 17 18

Pas de commentaire

MATLAB PARTIAL DIFFERENTIAL EQUATION TOOLBOX 1 Manuel d'utilisateur Page 8