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Helmholtz on a cylindrical surface (curved surface)

Posted Jun 29, 2022, 8:49 a.m. EDT 2 Replies

John Fusco
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The below post is related to an archived discussion

Hi

I intend to solve Helmholtz equation (Laplacian+ k^2)*psi =0 which is essentially the equation to solve for eigenmodes and eigenfrequencies. I understand that for 2D and 3D structures, this is quite simple by using EMW module and Eigenfrequency analysis. However, I intend to solve this equation on the surface of a cylinder for instance. A curved surface.

I understand from the Aforementioned topic that I have to do the following:

1- Find the modified Laplacian operator for this specific curved surface which embodies the curvature of the surface in itslef. Then I have the new helmholtz equation as a result, with a crazy new form. 2- Then for general PDE or Coeficient PDE format in COMSOL, use lower dimention option in comsol. This enables me to solve PDE on the surface of my 3D shape. 3- Based on the form of my new calculated Helmholtz euqation, I have to specify the coeficinet of the general PDE format in COMSOL and run the simulation.

Am I correct and is the any other solution for this kind of problem?

Thanks in advance

2 Replies Last Post Aug 30, 2022, 4:09 p.m. EDT
John Fusco
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Posted: 2 years ago Jul 2, 2022, 12:06 p.m. EDT

I think I figures it out

One should create a general coeficients PDE forom in "lower dimenion" mode and. Match the coeficients of PDE formula such that they match the ones of Helmholtz. Then an Eigenvalue study has to be added and executed. Done

I think I figures it out One should create a general coeficients PDE forom in "lower dimenion" mode and. Match the coeficients of PDE formula such that they match the ones of Helmholtz. Then an Eigenvalue study has to be added and executed. Done
Anurag Rajan
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Posted: 2 years ago Aug 30, 2022, 4:09 p.m. EDT

Hello John,

I am trying to solve a similar problem on curved surface. When you say match the coefficients, do you mean simply write the same PDE but in lower dimensions and let comsol do the rest? I mean, do we need to change anything, along the lines of point 1 in your original question: "Then I have the new helmholtz equation as a result, with a crazy new form".

Thanks, Anurag

Hello John, I am trying to solve a similar problem on curved surface. When you say match the coefficients, do you mean simply write the same PDE but in lower dimensions and let comsol do the rest? I mean, do we need to change anything, along the lines of point 1 in your original question: "Then I have the new helmholtz equation as a result, with a crazy new form". Thanks, Anurag

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