Discussion Closed This discussion was created more than 6 months ago and has been closed. To start a new discussion with a link back to this one, click here.

Jacobian Matrix of B with respect to H (Accessing External Material Models)

Please login with a confirmed email address before reporting spam

Dear all,
in the scope of research project, I'm checking out COMSOL's abilty of accessing external material models. There's an example code available via www.comsol.com/model/external-material-ac-dc-module-general-hb-bh-relation-32321 . What I'm trying to do now is to understand that referred example. I'm aware of what's happening during the interpolation routine, but I don't understand how the Jacobian Matrix is built:
// Write Jacobian of B with respect to H
if (normH>0) {
for (i=0; i<3; ++i) {
for (j=0; j<3; ++j) {
Jac[i*3+j] = dNormB*H[i]*H[j]/(normH*normEpsH)+normB*(-H[i]*H[j]/(normEpsH2*normEpsH)+(i==j ? 1.0/normEpsH : 0.0));
}
}
} else {
for (i=0; i<3; ++i) {
for (j=0; j<3; ++j) {
Jac[i*3+j] = (i==j ? dNormB : 0.0);
}
}
}
I know that a Jacobian Matrix contains the partial derivatives of a vector valued function, but I don't really understand the procedure in the code-snippet above. Can anyone help me out and explain it to me or post a link to a literature reference (with an explanation of the procedure)?


Thanks in advance and best regards

Michael

1 Reply Last Post 1 août 2017, 04:19 UTC−4

Please login with a confirmed email address before reporting spam

Posted: 7 years ago 1 août 2017, 04:19 UTC−4
Since I haven't recieved any answer yet, I can only guess that the procedure in the code-snippet above is some kind of formulation of the Newton-Raphson method using Jacobian Matrixes. Someone who's interested may find help in the paper referenced below ...
doi.org/10.1109/TASC.2009.2039787

Best regards
Since I haven't recieved any answer yet, I can only guess that the procedure in the code-snippet above is some kind of formulation of the Newton-Raphson method using Jacobian Matrixes. Someone who's interested may find help in the paper referenced below ... https://doi.org/10.1109/TASC.2009.2039787 Best regards

Note that while COMSOL employees may participate in the discussion forum, COMSOL® software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team.