PDE Toolkit - what is d when m is non-zero?

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Sattik Basu
Sattik Basu 2022-1-21
评论： Sattik Basu 2022-1-25
To solve the following equation
we need to input values of m,d,c,a and f.
I have been able to input m,c,a,f, however, for d, there is a special rule. The following is from Matlab's own support pages.
It says "Generally, d is either proportional to results results.M, or is a linear combination of results.M and results.K". M and K are matrices obtained after the assembleFEMatrices (i.e., after discretization).
Now, to say the least, this is confusing, as I do have the values of the d matrix (2x2 symmetric matrix in my case). Any insights would be appreciated.
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Torsten
Torsten 2022-1-21
If you have a valid MATLAB licence, I'd contact MATLAB support service.
Sattik Basu
Sattik Basu 2022-1-21
Thank you Torsten, I think that is indeed the final option.

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回答（1 个）

Ravi Kumar
Ravi Kumar 2022-1-21
When m is non-zero in a structural problem, d-matrix (coefficient) could represent a damping matrix. That is the most common use case. Hence, the documentation describes how to compute d, proportional damping matrix, as a combination of global mass and stiffness matrix.
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Torsten
Torsten 2022-1-25
Thank you for your feedback.
To see whether the reduction to a first-order system works, I'd test it for the acoustic wave equation
d^2u/dt^2 = omega^2 * d^2u/dx^2
and compare with the solution of the formulation as a PDE second order in time.
Sattik Basu
Sattik Basu 2022-1-25
Yes, I am working on validating the answers as we speak. It's always a "state-space" like approach that matlab is comfortable with.

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