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Adding nonlinear eigensolver capability to Palace to enable eigenmode simulations with frequency-dependent boundary conditions such as WavePort, Conductivity, or second-order Absorbing.

Specifically, two nonlinear eigensolver options are introduced:

  • Hybrid (default): a hybrid approach where the nonlinear term is (coarsely) approximated with a second-order polynomial, the quadratic EVP is solved with the existing SLEPc or ARPACK polynomial eigensolvers, and the resulting eigenmodes are used as initial guesses for a (deflated) quasi-Newton eigenvalue solver.
  • SLP: SLEPc's Successive Linear Problem (SLP) solver from the NEP interface.

Three eigenmode regression tests are added:

  • CPW with lumped ports and second-order absorbing BCs.
  • CPW with wave ports.
  • Adapter waveguide (rectangle at one end, ellipse at the other)

Closes #422.

@hughcars hughcars self-requested a review August 28, 2025 14:27
@simlapointe simlapointe force-pushed the simlapointe/nonlinear-eigen branch from a7a6ae0 to 71b7912 Compare August 29, 2025 21:06
@simlapointe simlapointe marked this pull request as ready for review August 29, 2025 21:27
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Nonlinear eigensolver
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