specifyCoefficientsThis section describes how to write the coefficient f in
the equation
or in similar equations. The question is how to write the coefficient f for
inclusion in the PDE model via specifyCoefficients.
N is the number of equations, see Equations You Can Solve Using PDE Toolbox.
Give f as either of the following:
If f is constant, give a column
vector with N components. For example, if N = 3, f could be:
f = [3;4;10];
If f is not constant, give a function
handle. The function must be of the form
fcoeffunction(location,state)
solvepde passes the location and
state structures to fcoeffunction. The
function must return a matrix of size N-by-Nr,
where Nr is the number of points in the location that
solvepde passes. Nr is equal to the
length of the location.x or any other location
field. The function should evaluate f at these points.
Pass the coefficient to specifyCoefficients as
a function handle, such as
specifyCoefficients(model,'f',@fcoeffunction,...)
location is a structure with these fields:
location.x
location.y
location.z
location.subdomain
The fields x, y, and
z represent the x-,
y-, and z- coordinates of points
for which your function calculates coefficient values. The
subdomain field represents the subdomain numbers,
which currently apply only to 2-D models. The location fields are row
vectors.
state is a structure with these
fields:
state.u
state.ux
state.uy
state.uz
state.time
The state.u field represents the current value of the solution
u. The state.ux,
state.uy, and state.uz fields are
estimates of the solution’s partial derivatives
(∂u/∂x,
∂u/∂y, and
∂u/∂z) at the corresponding points
of the location structure. The solution and gradient estimates are
N-by-Nr matrices. The
state.time field is a scalar representing time for
time-dependent models.
For example, if N = 3, f could be:
function f = fcoeffunction(location,state) N = 3; % Number of equations nr = length(location.x); % Number of columns f = zeros(N,nr); % Allocate f % Now the particular functional form of f f(1,:) = location.x - location.y + state.u(1,:); f(2,:) = 1 + tanh(state.ux(1,:)) + tanh(state.uy(3,:)); f(3,:) = (5 + state.u(3,:)).*sqrt(location.x.^2 + location.y.^2);
This represents the coefficient function