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3D and 1D integration
Posted 8 juil. 2010, 11:49 UTC−4 1 Reply
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Hi everybody,
I try since two weeks to integrate a multivariable functions on a multi-domain.
I have to integrate the function f(x,y,z,t,x_0,y_0,z_0) = exp(sqrt((x-x_0)^2+(y-y_0)^2+(z-z_0)^2))*t) for t = [0 , 10] (time-integration 1D) and for (x,y,z) on a surface defined by a geometry (surface-integration 3D-the surface of a cube for example). The final result is the function g(x_0 , y_0 , z_0) with x_0 , y_0 and z_0 are spatial variables.
Unfortunateny, the method using integration coupling variable and extrusion coupling variable (and coupling a 1D geometry for the integration domain of t and 3D geometry for the surface integration of (x,y,z)) do not give good results...
Really, I don't know how COMSOL can solve such a problem. The COMSOL book is very useful but does not mention this problem completely.
Have you already achieve such a problem with COMSOL ?
Thank you for your help.
Sébastien and Pierre
I try since two weeks to integrate a multivariable functions on a multi-domain.
I have to integrate the function f(x,y,z,t,x_0,y_0,z_0) = exp(sqrt((x-x_0)^2+(y-y_0)^2+(z-z_0)^2))*t) for t = [0 , 10] (time-integration 1D) and for (x,y,z) on a surface defined by a geometry (surface-integration 3D-the surface of a cube for example). The final result is the function g(x_0 , y_0 , z_0) with x_0 , y_0 and z_0 are spatial variables.
Unfortunateny, the method using integration coupling variable and extrusion coupling variable (and coupling a 1D geometry for the integration domain of t and 3D geometry for the surface integration of (x,y,z)) do not give good results...
Really, I don't know how COMSOL can solve such a problem. The COMSOL book is very useful but does not mention this problem completely.
Have you already achieve such a problem with COMSOL ?
Thank you for your help.
Sébastien and Pierre
1 Reply Last Post 12 juil. 2010, 12:52 UTC−4
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Posted:
1 decade ago
Hi
I have been looking into your issue, an interesting one. On the forum there is a trick how to derive a variable w.r.t time, but not how to integrate ? see www.comsol.eu/community/forums/general/thread/401/
I have also tested in V4.0 the derivative of a surface integration by setting a Global Varaible Probe equal to
d(intop1(T),t)
for a time Dependent solver case, and this gives me the derivative., but NOT the integral.
In V4 you get the table with the surface integration, so you can at least copy it to Excel and to the time integration there, but this is not really handy for using the variable in the COMSOL solver process.
perhaps by combining the idea above, creating a new variable, initialise to 0 and being iteratively itself + new value divided by the timestep, this should give a triangular integration, already a start
But so far I have not found any better solution yet: BUT I should have, have you checked the Knowledg base ?:
www.comsol.eu/support/knowledgebase/1042/
www.comsol.eu/support/knowledgebase/913/
I also only suggest to ask comsol support when you have tricky problems and nobody on the Forum can help, support does their best too, provided you have the correct maintenance
Good luck
Ivar
I have been looking into your issue, an interesting one. On the forum there is a trick how to derive a variable w.r.t time, but not how to integrate ? see www.comsol.eu/community/forums/general/thread/401/
I have also tested in V4.0 the derivative of a surface integration by setting a Global Varaible Probe equal to
d(intop1(T),t)
for a time Dependent solver case, and this gives me the derivative., but NOT the integral.
In V4 you get the table with the surface integration, so you can at least copy it to Excel and to the time integration there, but this is not really handy for using the variable in the COMSOL solver process.
perhaps by combining the idea above, creating a new variable, initialise to 0 and being iteratively itself + new value divided by the timestep, this should give a triangular integration, already a start
But so far I have not found any better solution yet: BUT I should have, have you checked the Knowledg base ?:
www.comsol.eu/support/knowledgebase/1042/
www.comsol.eu/support/knowledgebase/913/
I also only suggest to ask comsol support when you have tricky problems and nobody on the Forum can help, support does their best too, provided you have the correct maintenance
Good luck
Ivar