How to get AssembleFEMatrices for a nonlinear and Time dependent PDE problem in PDEtool box

In MATLAB pde tool box, To get the assemble matrices for time dependent pde or nonlinear pde - ''FEM = assembleFEMatrices(___,state) '' this command is used. But how to get a assemble matrices for a pde with time dependent and nonlinear.

, k = 0.7 + 0.003*T, tlist = linespace(0,0.5,20); therefore my pde coefficients wills be d = 1, m = a = 0, c = k, f = 1; since c coefficent is non linear (dependent on T, temperature); How am i going to get AssembleFEMtrices at tlist(1) i.e. at t = 0 ?

clear,clc,close all;

model = createpde();

%% Geometry
R1 = [3;4;-1;1;1;-1;-1;-1;1;1];
g = decsg(R1);
heatmodel_geom = geometryFromEdges(model,g);

%% Mesh
msh = generateMesh(model,'GeometricOrder','linear');
[P,E,T] = meshToPet( msh );

%% Specify Coefficients

c = @(~,state) 0.7+0.003*state.u; % nonlinear coefficient

specifyCoefficients(model,'m',0,'d',1,'c',c,'a',0,'f',1);

%% Spacial BC

applyBoundaryCondition(model,'dirichlet','edge',[1 2 3 4],'u',0);

%% Initial guess
setInitialConditions(model,0);

%% assemble the finite elements matrices with imposed spacial BC
tlist = linspace(0,0.1,20);
Rnonlin = solvepde(model,tlist);
state.u = Rnonlin.NodalSolution;
state.time = tlist(1);
FEMn = assembleFEMatrices(model,'nullspace',state);

    

I could see lot of errors when i run this code. Am not sure if this approch is correct or not to get assemble FEMatrices... Please help me with a way to get assemble matrices for a pde which is nonlinear and time dependent?

My commands are based on the link given below

https://in.mathworks.com/help/pde/ug/assemblefematrices.html

Thank you

Answer 1

[Ravi Kumar]

Solution matrix must of of the size NumPDEs x NumNodes. In your case, you are providing several solutions at all the time-steps as inputs. Change the line:.

state.u = Rnonlin.NodalSolution;

to

state.u = Rnonlin.NodalSolution(:,1)';

If you want matrices at multuple time steps, you need to updated state struct with corresponding solution and time values and call assembleFEMatrices.

Regards,

Ravi