[Gmsh] gmsh/getdp magnetostatics

[Gordon West]

Hello Profs Christophe Geuzaine and Jean-François Remacle, or others

I have been experimenting with gmsh-getdp electromagnetic simulation, 
focusing on magnetostatic cases involving 3D solenoidal inductors with 
permeable cores. Overall, I am greatly impressed with gmsh/getdp's 
capabilities and organization, but I have run into some difficulties I 
can't seem to get past.

My objective is to design a complicated magnetic flux collector for an 
alternating magnetic field sensor in a borehole. I am working only with 
your compiled software, as I am not a C programmer. Since there is no 
built-in provision in gmsh-getdp for creating an external (uniform) 
field and observing the voltage it induces in the solenoid, I have been 
trying to do the inverse EM problem of finding the distant b magnetic 
field generated by current in the inductor (as modified by the core).

*Problem 1*     I can run your Inductor (3d) model with no difficulty, 
and also a very simple test model (SensTest) of a cylindrical inductor 
with cylindrical core.  However, when I have tried to incorporate a more 
complicated flux collector system (my model sensor), the model seems to 
mesh and display properly, but getdp provides a physically wrong source 
current /js/ even though /js0/ is correct.

Although the stranded inductor current density /js0/ is (correctly) a 
simple, unidirectional, cylindrical current, along the inner boundary of 
the inductor, the /js/ derived from it is directed in the correct 
annular direction but flows in the wrong (opposite) direction in all 
outer parts of the inductor. The resulting b field seems correct for 
this/js/, but it is incorrect for the provided /js0/.

I have likely caused this problem by some misunderstanding or simple 
coding error; but I cannot find the bugafter many hours of 
experimenting. Can you give me any suggestions?

*Problem 2*  In both sensor and senstest, I have used the spherical 
extension to infinity of the external field that is employed in your 
Inductor example. I have no difficult in displaying the vector field 
using your graphics GUI, but I want quantitatively to analyze the b 
vector flux density near the radius of the inner sphere. I can read the 
/_.res/, /_.pre/ and /_.pos/ output files in Matlab, but have had 
difficulty interpreting the vector components in the file; especially in 
relating them exactly to what I see in the gmsh GUI vector plots and to 
the mesh nodal coordinates. Are the gmsh-plotted vectors already 
interpolated from the edge element values of *A* onto a different grid?  
The GUI/b/ vector plots seem to provide one vector per tetrahedron, (as 
best I can tell), but the data output file/b.pos/ etc., provides 6 
components per tetrahedron, suggesting something different.

Can you direct me to any documentation about how to relate the field 
values in /b.pos/ to the mesh node location for the EM case where edge 
elements are employed in the analysis.

I feel badly asking for this much support from a freeware provider. If 
what I am asking is too onerous, I might be able to provide modest 
remuneration to a person, or make a contribution to an organization for 
this effort. Please don't hesitate to ask.

I append the file tree I have used with gmsh-getdp. I have worked with 
versions 2.14 to 2.16.

With sincere thanks

Gordon West
Retired Prof of Physics (geophysics), Univ of Toronto
Consulting geophysicist

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