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Validation issue
Posted 3 déc. 2009, 03:35 UTC−5 3 Replies
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Hi there,
my inquiry is regarding the validation of FE solution. i have the analytical solution of the potential distribution on the surface of a sphere of radius 0.1m having a dipole in the center with source (current) and sink 0.005 m apart from the center of the sphere. the closed form analytical solution,attached, based on "Electric Potential by Two Point Current Sources in a Homogeneous Conducting Sphere" by ERNEST FRANK produces max potential of 0.1329 and min potential of -.1329 volts. which i have also confirmed from "An Improved Method for Localizing Electric Brain Dipoles" 's analytical solution.
when i compare those analytical solutions with the solution generated by FEMlab there is a huge disparity. the femlab file is attached. the V max and V min extracted by femlab are 8.909e-3 volts and -0.0265e-3 volts, respectively.
i do not understand as why there is such a big difference.
i am using conductive media DC to replicate poisson's equation for quasi-stationary(electrostatic) mode.
thanks
my inquiry is regarding the validation of FE solution. i have the analytical solution of the potential distribution on the surface of a sphere of radius 0.1m having a dipole in the center with source (current) and sink 0.005 m apart from the center of the sphere. the closed form analytical solution,attached, based on "Electric Potential by Two Point Current Sources in a Homogeneous Conducting Sphere" by ERNEST FRANK produces max potential of 0.1329 and min potential of -.1329 volts. which i have also confirmed from "An Improved Method for Localizing Electric Brain Dipoles" 's analytical solution.
when i compare those analytical solutions with the solution generated by FEMlab there is a huge disparity. the femlab file is attached. the V max and V min extracted by femlab are 8.909e-3 volts and -0.0265e-3 volts, respectively.
i do not understand as why there is such a big difference.
i am using conductive media DC to replicate poisson's equation for quasi-stationary(electrostatic) mode.
thanks
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3 Replies Last Post 4 déc. 2009, 17:23 UTC−5
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Posted:
2 decades ago
What happens when you add more mesh ? If adding more mesh gets you closer to the true solution, you have set up the problem, you just need more nodes to increase your accuracy. If adding more mesh does not get you closer to the solution, you have set up your problem wrong.
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Posted:
2 decades ago
Hi there,
I have already tried this option, though the results are better than the previous attempts but still long way from the analytical results. It is suppose to be a simple 2D electrostatic/DC conductive media problem and even with coarse mesh it should have give accurate results. My model is attached in my previous post, you can check it.
As mentioned earlier, i am using the poisson’s equation capable of handling current sources i.e.
-del.(sigma delV-Je)=Qj
I do not see any problem with the setup.
Point source and sink are assigned 1A/m and -1A/m respectively. The distance between them is very very small, when compared with the radius of the circle.
The boundary of the sphere/circle has electric-insulation boundary condition i.e.
n.J=0 (no current flows across the boundary)
When FD method is used, instead of the FEMlab, with SOR iterative method the result converges to the desired results.
I would be really grateful if you could direct me in the right direction.
Regards
Salman
I have already tried this option, though the results are better than the previous attempts but still long way from the analytical results. It is suppose to be a simple 2D electrostatic/DC conductive media problem and even with coarse mesh it should have give accurate results. My model is attached in my previous post, you can check it.
As mentioned earlier, i am using the poisson’s equation capable of handling current sources i.e.
-del.(sigma delV-Je)=Qj
I do not see any problem with the setup.
Point source and sink are assigned 1A/m and -1A/m respectively. The distance between them is very very small, when compared with the radius of the circle.
The boundary of the sphere/circle has electric-insulation boundary condition i.e.
n.J=0 (no current flows across the boundary)
When FD method is used, instead of the FEMlab, with SOR iterative method the result converges to the desired results.
I would be really grateful if you could direct me in the right direction.
Regards
Salman
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Posted:
2 decades ago
Salman, your model is not a 3D sphere, but rather, a 2D cylinder. The cylinder is of radius 0.1 m like you want for the sphere, but it is a depth (or height) of 1.0 m which is the default depth for the model you have chosen. Also, the solution is quite mesh sensitive and required a nonlinear solver to converge. You had it set up using a linear solver, but my guess is that the problem required a bit more work to solve. I like to set the nonlinear solvers for a damping factor initially at 0.1, then multiply by 2.0 to force at least 5 iterations. Also, I looked at the peaks inside your model where the potential points are set which drives the problem. You had a denser mesh there, but I think that should be the focus on whether you converge or not. with the mesh you provided, I looked at linear, quadratic, and cubic element basis and the peak-2-peak values there of about .77, .885, and .94 respectively. So, it is sensitive to the mesh/interpolate resolution, and it is solving the wrong problem. Also, I am using comsol v3.5a, and you mentioned femlab and your file extension is .fl, so perhaps you are using an earlier version that may give different results than what I have.