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Implementation of mixed derivatives in PDE

Posted 12 apr 2021, 04:45 GMT-4 Piezoelectric Devices, Structural & Acoustics, Modeling Tools & Definitions Version 5.5 4 Replies

Akshay Manthekar
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Hi guys, I am working on the mathematical modelling of piezoelectric sensor and I developed system of 4 PDEs in which there are 2 independent variables (viz. r,z) and 4 dependent variables (viz. ur, u_theta, uz and phi) as shown below. The problem is axisymmetric so I will be using 2D axisymmetric module instead of 3D.

I need to implement it in the coefficient form PDE in COMSOL but the coefficient form of PDE doesn't take mixed derivatives. Is there any other way I can solve this system of equations in COMSOL? Any help is much appreciated. Thank you.

4 Replies Last Post 15 apr 2021, 05:59 GMT-4
Jeff Hiller COMSOL Employee

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Posted: 4 years ago 12 apr 2021, 08:50 GMT-4

Hello Akshay,

By specifying a non-diagonal c (Diffusion coefficient) matrix, you'll be able to have mixed derivatives in acoefficient form PDE interface.

Best regards,

Jeff

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Jeff Hiller
Hello Akshay, By specifying a non-diagonal c (Diffusion coefficient) matrix, you'll be able to have mixed derivatives in acoefficient form PDE interface. Best regards, Jeff
Akshay Manthekar
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Posted: 4 years ago 13 apr 2021, 02:31 GMT-4

Hi Jeff, Thanks for the response. As I have 2 independent variables (r and z), so the non-diagonal elements of c (Diffusion matrix) will be coefficients of and right?

Hi Jeff, Thanks for the response. As I have 2 independent variables (r and z), so the non-diagonal elements of c (Diffusion matrix) will be coefficients of \frac{\partial^2}{\partial r\partial z} and \frac{\partial^2}{\partial z\partial r} right?
Jeff Hiller COMSOL Employee

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Posted: 4 years ago 13 apr 2021, 09:02 GMT-4

More or less, yes. To be more accurate, I would need to point out that the elements of c can be functions of r and z, so when you take the divergence of c grad(whatever) you can also end up with terms from the differentiation of the terms of c.

Best,

Jeff

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Jeff Hiller
More or less, yes. To be more accurate, I would need to point out that the elements of c can be functions of r and z, so when you take the divergence of c grad(whatever) you can also end up with terms from the differentiation of the terms of c. Best, Jeff
Akshay Manthekar
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Posted: 4 years ago 15 apr 2021, 05:59 GMT-4

Thanks Jeff

Thanks Jeff

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