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Time Differential equation

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Hello users !

From two years, I try to learn COMSOL (the license from my university) by using some personal models but the last result is not like I want...

In fact, I try to solve a very quick differential equation (COMSOL's notations) :

utt = exp(-(x^2+y^2+z^2))*exp(-t)
with the initial conditions : u(x,y,z,t=0)=0 and ut(x,y,z,t=0)=0

where u(x,y,z,t) is a spatio-temporal function and the second derivative (utt) is performed with respect to the time only.

*To find the solution u(x,y,z,t), I used the "PDE, coefficient form" with the coefficients "e_a = 1" and "f = exp(-(x^2+y^2+z^2))*exp(-t)" in the menu "Physics / subdomain Settings" (in this problem, my subdomain is simply a solid cylinder). All the others coefficients appearing in this menu are zero.

*Also, I took the initial values u(t_0)=0 and ut(t_0)=0 in the "init" menu.

Finally, I solved my model by using the solver "Direct UMFPACK" in the solver manager menu but the final result is not depends on the solver used.

Unfortunately, the result obtained is really wrong ! It is very different of the analytical solution...For example, the true solution gives u = 3.46 for x=y=z=0 and t=4.45. The solution given by COMSOL is 1.28...

You will find my model in attachement...Can COMSOL solve such a problem ? An experimented user can help me to find the problem ?

Thank you.

Sébastien






3 Replies Last Post Dec 29, 2011, 7:28 a.m. EST

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Posted: 1 decade ago Dec 17, 2011, 12:32 p.m. EST
Thank you all for your answer !
Thank you all for your answer !

Lechoslaw Krolikowski

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Posted: 1 decade ago Dec 17, 2011, 12:40 p.m. EST
Hi,
You have the so-called spatially distributed ODE. Such equations are solved in Comsol starting with version 4.2.
Best regards
Andrzej
Hi, You have the so-called spatially distributed ODE. Such equations are solved in Comsol starting with version 4.2. Best regards Andrzej

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Posted: 1 decade ago Dec 29, 2011, 7:28 a.m. EST
Thank you Lechoslaw for your answer ! I found the solution of my problem...

See you

Sébastien
Thank you Lechoslaw for your answer ! I found the solution of my problem... See you Sébastien

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