How can i define PDE coefficient which is scalar matrix inside the boundary

Hello wonderful people in the MathWorks!!

I'm relativelly new to this, so forgive me if I'm missing the basics.

I'm trying to solve a 2D PDE problem, which is defined as follows, described in PDE model coefficients .

specifyCoefficients(model, 'm', 0, 'd', 0, 'c', @cfunc, 'a', 0, 'f', @ffunc);

So it is a (time independent) elliptic 2nd order PDE.

So my problem is defining cfunc and ffunc.

c and f are time-independent scalar field, mapped inside the boundaries as a matrix.

They are not caculated values which can be described as f(location.x, location.y), but obseved values. (c requires information from 2 matrices)

How can i define c and f in this case?

Here are the schematics of codes I've been trying to pull off

NoE=1; % number of equation 

% generate boundary 
R= [2; 4; min(xv); max(xv); max(xv); min(xv); max(-yv); max(-yv); min(-yv); min(-yv)]; % 4 rectangular edges, xv and yv are vectors for points  
g= decsg(R, 'R', 'R');

%generate mesh: I need to designate specific mesh that suits my interest, since diff(xv) << diff(yv) 
[mesh_p, mesh_e, mesh_t]=poimesh(g, length(xv)-1, length(yv)-1);

% create pdemodel
model=createpde(NoE)

%set mesh
mesh_t(4, :)=[]; %for some reason the supproted format seems to be different 
[geomet2, mesh]=geometryFromMesh(model, mesh_p, mesh_t);

%boundary condition 
applyBoundaryCondition(model,'dirichlet','Edge',[1 2 3 4],'u',0);

%specify coefficients 
specifyCoefficients(model, 'm', 0, 'd', 0, 'c', @cfunc, 'a', 0, 'f', @ffunc);

%solve, but neither works, displaying error messages that differs accoding to cfunc and ffunc i make 
result1=assembleFEMatrices(model, 'nullspace')
result2=solvepde(model)

for specify coefficients, I tried various functions, ex)

I tried scatteredInterpolant function inside cffunc, (and ffunc)

function ccoeff=cfunc(location, status)
ccoeff=zeros(4*NoE,numel(location.x));
ccoeff(1, :)=N2scat(location.x, location.y); %N2scat and f2scat is scatteredInterpolant object, global
ccoeff(4, :)=f2scat(location.x, location.y);
end 

or

it1=mesh_t(1,:);
it2=mesh_t(2,:);
it3=mesh_t(3,:);
xpts = (mesh_p(1,it1) + mesh_p(1,it2) + mesh_p(1,it3))/3;
ypts = (mesh_p(2,it1) + mesh_p(2,it2) + mesh_p(2,it3))/3;
for i=1:length(location.x)
    [~, id(i)]=min((location.x(i)-xpts).^2 +(location.y(i)-ypts).^2);
end
N2inside=N2scat(xpts, ypts);
f2inside=f2scat(xpts, ypts);
ccoeff(1, :)=N2inside(id);
ccoeff(4, :)=f2inside(id);

returns error

================================================

Warning: Matrix is singular to working precision.

> In pde.EquationModel/solveStationaryNonlinear (line 21)

In pde.PDEModel/solvepde (line 77)

Error using pde.EquationModel/solveStationaryNonlinear (line 27)

Unsuitable initial guess U0 (default: U0=0).

Error in pde.PDEModel/solvepde (line 77)

u = self.solveStationaryNonlinear(coefstruct, u0);

=================================================

or

=================================================

Error using pde.EquationModel/assembleFEMatricesInternal (line 22)

PDE coefficients cannot be function of solution or time.

Error in assembleFEMatrices (line 73)

FEMatricesOut = assembleFEMatricesInternal(pdem,BCEnforcementOption);

=================================================

I'm not sure where this errors come from, or have i completely gone sidetrack?

any suggestions?

Thanks in advance,

SJ Kim

Answer 1

[Ravi Kumar]

Hi Kim,

Is your ffunc depends on solution, i.e., using state.u? Can you provide sample data, also xv and yv?

Regards,

Ravi