How can I calculate a volume integration of magnetic field including a divergence operator in Comsol derived values?

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Hao Tian

Hi Ehsan Mohseni,

I could offer a solution which may be helpful for you. Firstly, you could define a volume integration to the component by clicking definition--> component couplings---> Integration. Then you should point the integration domain of interest. Then you should define a variable, for example, Int. And then enter the expression of Integrand like this: Int=intop1(expression of integrand).

Then you should click update solution by right clicking study. You could then evaluate Int in the global evaluation which is the volume integration of your problem. Hope this will help you.

Sincerely,

Tian Hao

Ehsan Mohseni

Hi Dear Tian,

This was greatly helpful. Thanks to you. Infact I did'nt know even such a thing could be done in Comsol, However your solution just opened a horizon full of new questions for me :). So, I'd like to ask few more questions that im facing now.

In Results---> Derived velues, I am able to evaluate for example mf.Bx or mf.Ee which stand for x component of magnetic flux density and electric field, respectively. Im wondering how I can use them in intop1(expression of integrand). when I write them for example in form of mf.Bx*mf.Ex, the expression turns to yellow and it says the variable is unknown, although they shall be known as comsol inner variables!

It is possible to insert an outer product of vectors by expanded form but I dont have any idea how to write the divergence of the product in integrand expression.

hope I can use your helpful hints again.

Regards,

Hi Ehsan,

I am glad that my answer is helpful for you! As for your first question, I want to know how you evaluate mf.Bx and mf.Ex. If you evaluate them by global evaluation in the derived values, this means they are global value so they could not be used in the integration. Then you should find the expression of B and E of one point in the model. Could you let me know which study and physics you choose? Maybe I could find it for you.

As for your second question, I come up with two method and I hope they could work in your model. 1. if you want to calculate divergence of B*E, you could also expend the expression of divergence, since there is partial differential function in COMSOL which is pd(f,x). This function is used to calculate partial differential df/dx. or 2. you could change the volume integration of divergence of B*E into surface integration, so you could avoid calculating divergence.

Hope my answer is helpful for you.

Sincerely

Hello Hao,

Thanks for your quick responses .

about my first question, you are compeletly right, I made a mistake. Bx and Ex are not global values and I cant get them through global evaluation. these vectors could be evaluated by 3D plot ------> arrow volume -----> add plot data to export, using this method the number of points could be changed but using this method I am not sure that I can use exported vector values for integration, so I really dont know what should I do!

Regarding your question, Im using AC/DC ---> mf and a frequency domain solver is used for the study. I attach my model here but I shall delete the solutions due to file size, hope you have comsol 5.0 (In case you have older versions, I could change to older).

About the divergence, I guess you are right, I will arrive to that after finding out hoe to exploit B and E in integral. Thanks for your time.

I am sorry. I just have COMSOL 4.4, so I could not open your model. Could you please change it into old version? Actually, you do not have to export the data for integration. You can use B and E directly in the expression of the integration. and then global evaluate the integration. This is actually what I do, but I do not know what's wrong with your model.

I guess I learned how to use the H and E for integration (Thanks to you) but still dont know how to write the divergence expression for the outer product of E and H. I converted the file (recreated) in comsol 4.4. hope you could take a look and give your comments.

Ehsan

I am glad you have solved the first problem. As for the file you sent to me, I could not open it. I am sorry and do not know why. As for your question, maybe you can expend the expression of divergence by using the partial differential function pd(f,x) in COMSOL. In your case, the expression of div(H*E) may be: pd(Hy*Ez-Hz*Ey, x)+pd(Hz*Ex-Hx*Ez, y)+pd(Hx*Ey-Hy*Ex, z). You may use this expression for the integration. Hope this will work in your model. If you have any question please feel free to contact me.