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Krylov subspace techniques in harmonic balance simulations become increasingly ineffective when applied to strongly nonlinear circuits. This limitation is particularly important in the simulation if the circuit has components being operated in a very nonlinear region. Even if the circuit contains only a few very nonlinear components, Krylov methods using standard preconditioners can become ineffective. To overcome this problem, we present two adaptive preconditioners that dynamically exploit the properties of the harmonic balance Jacobian. With these techniques we have been able to retain the advantages of Krylov methods even for strongly nonlinear circuits. Some numerical experiments illustrating the techniques are presented.

The enchancing of efficiency of the harmonic balance analysis by adaptation of preconditioner to circuit nonlinearity