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I want to solve electrostatic problem for potential. Charge density and medium permittivity are known, so is the potential of a grounded surface. I know how I can implement that.

But I would like to add an ideal conductor (of unknown potential) to the system. How can I introduce an equipotential surface/volume? I guess setting permittivity to infinity is not a feasible option?

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This does not easily fit into a PDE formulation because it is a nonlocal constraint. But for all practical aspects, choosing a very large permittivity is usually good enough. Just choose it several orders larger than the rest of the domain.

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  • $\begingroup$ I thought that should be something simple as all it requires is merging appropriate columns of the stiffness matrix. :/ Wouldn't such high difference in permittivity lead to numerical errors? $\endgroup$
    – abukaj
    Jun 24, 2022 at 8:01
  • $\begingroup$ It increases the condition number and that increases the error. But if you choose a permittivity that is, say, $10^6$ larger than elsewhere, you should still be fine. $\endgroup$
    – Wolfgang Bangerth
    Jun 27, 2022 at 3:24

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