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Numerical Derivative is Jagged

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Hello, I'm modeling the unsteady state diffusion of a protein out of a hollow cylinder. Two plots I'm interested in are the cumulative mass release and the release rate. I obtained the former by integrating concentration over the domains the protein had diffused into and the latter by taking the time derivative of the cumulative release curve. However, my release rate graph has become very jagged. I've tried both decreasing the time step and refining the mesh to very small values, and while it has helped some, the curve is remains jagged and noisey. I read that because comsol works with derivatives and integrals numerically, taking the numerical derivative of a numerical integration can introduce a lot of noise as seen in my graph.

I attached my cumulative mass release plot where the integration gives a smooth curve, and the release rate where the time derivative of the integration becomes jagged. Is there any way to get rid of the jaggedness/noise that's introduced with taking a numerical derivative of a numerical integration?


2 Replies Last Post 2015年4月22日 GMT-4 12:27
Edgar J. Kaiser Certified Consultant

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Posted: 10 years ago 2015年4月22日 GMT-4 11:37
Hi Craig,

first of all, it doesn't look too bad. Derivatives of numerical data always generate some noise.

You could try to tighten the convergence criterion, i.e. the tolerance factor in termination criteria to achieve higher precision.

Cheers
Edgar

--
Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
Hi Craig, first of all, it doesn't look too bad. Derivatives of numerical data always generate some noise. You could try to tighten the convergence criterion, i.e. the tolerance factor in termination criteria to achieve higher precision. Cheers Edgar -- Edgar J. Kaiser emPhys Physical Technology http://www.emphys.com

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Posted: 10 years ago 2015年4月22日 GMT-4 12:27
Thanks for the response Edgar,

Decreasing the tolerance did the trick for smoothing out the curves, which now seems obvious in hindsight.

That makes sense about the noise too, I'm probably still just used to analytical solutions that give perfectly smooth curves.

Thanks, Craig
Thanks for the response Edgar, Decreasing the tolerance did the trick for smoothing out the curves, which now seems obvious in hindsight. That makes sense about the noise too, I'm probably still just used to analytical solutions that give perfectly smooth curves. Thanks, Craig

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