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Partial differential operator

Posted Jun 3, 2020, 1:44 a.m. EDT 4 Replies

Ming Xu
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Hi,everyone! I have some question about partial differential operator. We know the ampere's law: J=curlH. So if we have a wire along Z axis, we have Jz=curl.Hz. In comsol Hyx means the x component of the gradient of Hy (is this sure? ), then we have curl.Hz=Hyx-Hxy. But in the result part, I make the expression to be : mfh.Jz-(Hyx-Hxy) , the output is not 0. What's wrong with it? In my opinion, Hyx doesn't mean the x component of the gradient of Hy, maybe it means the x component of the derivative of Hy. So, what's the partial differential operator in COMSOL?

Any suggestions you give will help me a lot.Thank you.

4 Replies Last Post Jun 5, 2020, 1:03 a.m. EDT
Alexandre Arsenault
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Posted: 5 years ago Jun 3, 2020, 2:53 p.m. EDT

Hi Ming,

The variable Hxy should indeed give the derivative of Hx with respect to y. Thus, the current density in the z direction should be Jz=Hyx-Hxy as you suggested. However, I am not sure why you are getting a non-zero value for the expression mentioned above. What kind of value are you getting for the expression? Also, are you using a moving mesh?

Cheers,

Alex

Hi Ming, The variable Hxy should indeed give the derivative of Hx with respect to y. Thus, the current density in the z direction should be Jz=Hyx-Hxy as you suggested. However, I am not sure why you are getting a non-zero value for the expression mentioned above. What kind of value are you getting for the expression? Also, are you using a moving mesh? Cheers, Alex
Ming Xu
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Posted: 5 years ago Jun 3, 2020, 9:18 p.m. EDT

Dear Alex,

Thank you for your suggestion.

Firetly, I just use a triangular mesh, it's not a moving mesh.

And, I use the mfh part. The expression: mfh.curlHz-mfh.Jz is zero, but the value of mfh.Jz-(Hyx-Hxy) is from -2.56e-13 to 2.34e-13.

Yours,

Ming

Dear Alex, Thank you for your suggestion. Firetly, I just use a triangular mesh, it's not a moving mesh. And, I use the mfh part. The expression: mfh.curlHz-mfh.Jz is zero, but the value of mfh.Jz-(Hyx-Hxy) is from -2.56e-13 to 2.34e-13. Yours, Ming
Alexandre Arsenault
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Posted: 5 years ago Jun 4, 2020, 9:25 a.m. EDT

Hi Ming,

This is probably due to numerical error rather than the definition of Hyx. Taking the derivative of the H field will lead to numerical error, and since the H field is usually on the order of 1e6 A/m, the error of 1e-13 seems reasonable. The reason why mfh.curlHz-mfh.Jz gives zero is that mfh.Jz is defined as mfh.curlHz, so Comsol recognizes that they are exactly equal.

Cheers,

Alex

Hi Ming, This is probably due to numerical error rather than the definition of Hyx. Taking the derivative of the H field will lead to numerical error, and since the H field is usually on the order of 1e6 A/m, the error of 1e-13 seems reasonable. The reason why mfh.curlHz-mfh.Jz gives zero is that mfh.Jz is defined as mfh.curlHz, so Comsol recognizes that they are exactly equal. Cheers, Alex
Ming Xu
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Posted: 5 years ago Jun 5, 2020, 1:03 a.m. EDT

Dear Alex

Thanks for your suggestion. This helps me a lot. I was confused for days, now I can have a good sleep. Haha

Yours,

Ming

Dear Alex Thanks for your suggestion. This helps me a lot. I was confused for days, now I can have a good sleep. Haha Yours, Ming

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