MATLAB: Boundary conditions for pdenonlin

boundary conditionspdenonlin

In order to solve nonlinear system of pde's I need to supply, together with the pde specification, a boundary condition file or matrix:

pdenonlin(b,p,e,t,c,a,f)

where b is the Boundary condition input, p,e,t are the mesh input, and c,a,f are the coefficients.

Matlab enable us to get the boundary conditions matrix Q,G,H,R by

[Q,G,H,R]=assemb(b,p,e)

What are these matrix uses for? Are they an alternative input for pde solver? if so, how?

Thanks!

Best Answer

Q,G,H,R are alternative ways to specify boundary conditions for assempde() (static & linear case). Typically you would use them along with the matrix representations of the PDE coefficients such as: K,M,F.

pdenonlin doesn't read the matrix form. As to why one would use the matrix form even for linear cases, they are useful in some cases. I've used them for efficiently solving 4th order PDEs, applying periodic and other global BCs and also creating state space models.

for info on how to specify "b", check out http://www.mathworks.com/help/pde/ug/boundary-conditions-for-scalar-pde.html

Deepak

Related Solutions

MATLAB: How to specify boundary conditions on subdomain borders using the Partial Differential Equation (PDE) Toolbox 1.0.13 (R2008b)

One should be able to specify boundary conditions on all external boundaries of any geometry.

 For example, look at the “A scattering problem” example in the documentation. It has a Neumann condition at the outer boundary and a Dirichlet condition at the inner boundary (that is formed by the square sub-region).

Boundary conditions on internal boundaries such as boundaries across which material properties or governing equations might change are not required by Finite Element method.

MATLAB: How to use the function PDENONLIN from the The Partial Differential Equation (PDE) Toolbox 1.0.4 (R13)

The most commonly encountered problem when using PDENONLIN occurs by not passing the input arguments correctly.

In an equation such as the following:

-div(c*grad(u))+a*u=f

you can use PDENONLIN as follows:

[U,RES]=PDENONLIN(B,P,E,T,C,A,F)

The B matrix is a boundary matrix, not a geometry matrix. For more information, see the Related Solution at the botom of the page.

P,E,T are the usual quantities when dealing with a PDE. C,A,F in PDENONLIN may be functions of u, and so you can either enter them as scalar quantities or as character arrays.

As an example, to solve the following equation:

 -div(grad(u)) + u^3 = 0

you can use the following code:

% this is an example of how to use PDENONLIN
[p,e,t] = initmesh('circleg');
% this defines a unit circle as the surface we simulate the PDE on
% this also has the simple boundary condition u = 0, on the boundary
% you can view the details of the mfile, by typing "edit cricleg.m"
[p,e,t] = refinemesh('circleg',p,e,t);
[p,e,t] = refinemesh('circleg',p,e,t);
% refined the mesh twice (made the elements of FEM smaller)
% we're going to simulate the static problem
% so the equation is: -div(grad(u)) + u^3 = 0
% so the parameters that we will pass to PDENONLIN
% [U,RES]=PDENONLIN(B,P,E,T,C,A,F) solves the nonlinear
%  PDE problem -div(c*grad(u))+a*u=f
% so our c = 1, a = u^2 and f = 0;
% you can change these as you wish
[ U, R ] = pdenonlin('circleb1',p,e,t,1,['u.^2'],0,'U0',1);
% Note that we used the function 'circleb1' rather than 'circleg'
% here, this is because we need a boundary matrix b, not a geometry
% this is further explained at the following URL:
% <http://www.mathworks.com/support/solutions/data/1-19DTS.shtml>
% Also, note how we entered a, as a character array, if you simply type 
% u.^2 rather than ['u.^2'] you will receive an error
pdeplot(p,e,t,'xydata',u);
% we now plot the solution of the PDE

Best Answer

Related Solutions

MATLAB: How to specify boundary conditions on subdomain borders using the Partial Differential Equation (PDE) Toolbox 1.0.13 (R2008b)

MATLAB: How to use the function PDENONLIN from the The Partial Differential Equation (PDE) Toolbox 1.0.4 (R13)

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