Non-uniqueness of conductive media DC solution

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Non-uniqueness of conductive media DC solution

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Hi,

I am using conductive medium DC to simulated potential field in a four-probe measurement of resistance/resistivity of a material. I have a Jo through the first probe and -Jo through the last probe. The nalaysis will tell me the potential difference between the middle two probes. The calculation seems right becuase the potential difference makes sense. However, it looks like I cannot specify a proper boundary condition such that the calculated potential field has a constant shift and the constant varies everytime I run the same analysis (but with a slighly different mesh or a different solver). This is similar to running a elastic stress analysis without providing a fixed support such that a rigid body movement exists. I am not worried too much about the result, but I wonder if this lack of proper boundary condition would jepodize the solution. I am new to DC simulation, but I experience with stress analyses tells me that the stiffness matrix could be ill if I do not provide proper boundary condition to eliminate the regid-body movement. Please let me know how I would fix this problem. Thanks.

JZ
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Re: Non-uniqueness of conductive media DC solution

Precise Simulation
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The mathematical formulation of the problem leads to non-unique steady state solutions if only flux/Neumann boundary conditions are applied (the solution is only be known up to an arbitrary constant/offset level).

In order to get a unique and mathematically well posed problem one can do either of:

1) Add at least one fixed value/Dirichlet boundary constraint.
2) Fix the value of the dependent variable in at least one point.
3) Add an integral constraint for the mean value.
4) Switch to a time dependent solver/solution.