How to apply the boundary conditons to the mass and stiffness matrices?
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Julian Henning
il 18 Giu 2019
Commentato: Sravan Kumar Putta
il 25 Feb 2021
I'm using the Partial Differential equation toolbox for getting the mass and stiffness matrices of a cube and liked to apply boundary conditions on the faces. My code looks like that:
gm = multicuboid(2,2,2);
model = createpde;
model.Geometry = gm;
specifyCoefficients(model,'m',0,'d',1,'c',1,'a',0,'f',1);
applyBoundaryCondition(model,'dirichlet','Face',1:6,'u',0);
mesh = generateMesh(model,'GeometricOrder','linear', ...
'Hmax', 2^-2);
FEM = asembleFEMatricess(model);
M = FEM.M; K = FEM.K;
How can I apply the boundary conditions to the matrices M and K. I know, that FEM also contains the matrices
FEM =
struct with fields:
K: [919×919 double]
A: [919×919 double]
F: [919×1 double]
Q: [919×919 double]
G: [919×1 double]
H: [452×919 double]
R: [452×1 double]
M: [919×919 double]
where G,H,R,M store some sort of information about the boundary conditions, but I'm not sure how to combine that with M and K. I'm also not sure if which matrices the 'nullspace' options returns.
PS: I need the matrices for solving the heat equation with a space-time-method, that is why a don't use the solve option from the model.
PPS: This should also work for quadratic meshs, thats why I can't just delete rows and columns.
6 Commenti
Sravan Kumar Putta
il 25 Feb 2021
I am in extreme need of help dear, can u pls look into this problem
https://in.mathworks.com/matlabcentral/answers/755649-how-to-solve-semi-discretized-pde-matrices-with-a-time-derivative-in-pde-tool-box-using-ode-solvers?s_tid=srchtitle
Sravan Kumar Putta
il 25 Feb 2021
did you use nullspace or stiff-spring to impose the boundary condition?
Risposta accettata
Ravi Kumar
il 18 Giu 2019
Use the 'nullspace' as second argument, you will get matrices with BC imposed by eleminating dirichlet DoFs.
Regards,
Ravi
3 Commenti
Sravan Kumar Putta
il 25 Feb 2021
Once you got matrices from nullspace or stiff-spring, How did you solve it using space - time method ? If you have used ODE solvers then how did you frame the ode function?
Can any one explain me?
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