[petsc-users] Conditional Constraints

[Jonathan Backs]

Hi,

I am trying to add a constraint feature to my first PETSc application, which uses the finite difference method to calculate the potential distribution produced by a collection of electrodes in a resistive medium. I would like to make this simulation more realistic by imposing a maximum electric current and a maximum potential difference that can be supplied to each electrode by the power supply. If the medium between the electrodes is very conductive, the current maximum would be exceeded by the maximum potential difference, so the potential difference should be decreased from maximum until it produces the maximum current. On the other hand, the potential difference between the electrodes should remain at maximum as long as the current remains below maximum (say, for a less conductive medium).

I added an extra degree of freedom (the electrode voltages) to my DMDA, and I developed a set of conditional expressions that describe the above constraints, but one problem is that the logic relies on if-then-else decisions that are made when forming the function/residual and the Jacobian. Once these decisions are made, of course, the conditions are not checked again until the next function or Jacobian evaluation. The non-linear solver then tends to oscillate between extreme solutions to the opposing conditions with each iteration, and never converges towards a reasonable solution.

Is there a better strategy for solving such problems? Does PETSc offer mechanisms to aid in their solution? I would very much appreciate any hints.

Thank you for your time,

Jon