I am working with an AC/DC, 3D, Stationary, Electric Currents model.
I am currently studying charge density between deep brain stimulation electrodes of different surface areas and geometries. To represent an oversimplified electrode, we created a cylinder with high conductivity (1e10 S/m) and a point current source at it's center. The cylinder was in a conductive medium similar to the brain, 0.2 S/m.
When evaluating this simplified problem, I encountered some error that seems violate current conservation. Specifically, I am finding 47% error between the point current source (0.001 A) and the integral of current density (ec.normJ) over the surface area of the cylinder.
Note: I did conduct a mesh convergence study - below the current mesh size (0.00002), the error does not notably improve.
I then explored this issue with different geometries (spheres, ellipsoids, cubes, rectangular boxes, etc). See page 1 of the attached TroubleshootingComsol.pdf for the results. To quickly summarize, symmetric geometries - spheres and cubes - integrate to a current within 2% error. However, non symmetric geometries, ellipsoids, cylinders, rectangular boxes - have unacceptable integration error (11-63%).
*****Question: Any ideas of the possible sources of error in the simple problem? Any suggestions to further troubleshoot?
An an alternative method, I also explored representing the electrode as a cylindrical shell with floating potential of 0.001 A. In this case, the integral of normJ is 0.0004- less than half than expected. The integral of nJ was closer - 0.0009. To troubleshoot this, I went back to a sphere, with similar results - integral of normJ was 0.00048 and integral of nJ was 0.00097. See page 2 of the TroubleshootingComsol.pdf for more details.
*****Question: I originally believed that normJ, the total current density norm, was the output of interest when studying charge density on a surface, but I am confused by the fact that it is substantially lower than nJ in the floating potential situation.
I greatly appreciate in advance any tips, explanations or corrections.
Sincerely,
Ashley
I am currently studying charge density between deep brain stimulation electrodes of different surface areas and geometries. To represent an oversimplified electrode, we created a cylinder with high conductivity (1e10 S/m) and a point current source at it's center. The cylinder was in a conductive medium similar to the brain, 0.2 S/m.
When evaluating this simplified problem, I encountered some error that seems violate current conservation. Specifically, I am finding 47% error between the point current source (0.001 A) and the integral of current density (ec.normJ) over the surface area of the cylinder.
Note: I did conduct a mesh convergence study - below the current mesh size (0.00002), the error does not notably improve.
I then explored this issue with different geometries (spheres, ellipsoids, cubes, rectangular boxes, etc). See page 1 of the attached TroubleshootingComsol.pdf for the results. To quickly summarize, symmetric geometries - spheres and cubes - integrate to a current within 2% error. However, non symmetric geometries, ellipsoids, cylinders, rectangular boxes - have unacceptable integration error (11-63%).
*****Question: Any ideas of the possible sources of error in the simple problem? Any suggestions to further troubleshoot?
An an alternative method, I also explored representing the electrode as a cylindrical shell with floating potential of 0.001 A. In this case, the integral of normJ is 0.0004- less than half than expected. The integral of nJ was closer - 0.0009. To troubleshoot this, I went back to a sphere, with similar results - integral of normJ was 0.00048 and integral of nJ was 0.00097. See page 2 of the TroubleshootingComsol.pdf for more details.
*****Question: I originally believed that normJ, the total current density norm, was the output of interest when studying charge density on a surface, but I am confused by the fact that it is substantially lower than nJ in the floating potential situation.
I greatly appreciate in advance any tips, explanations or corrections.
Sincerely,
Ashley