NPSS Cycle Deck Element Configuration for Missing Analytic Jacobian Boundary Conditions

NPSS exposes an element-development framework for user-defined components inside cycle decks, but the solver integration contract does not specify whether analytic Jacobians are required or under what boundary conditions numerical differentiation is substituted when a partial derivative is omitted.

When a custom element introduces an implicit constraint without full derivative information, solver convergence depends on internal perturbation defaults that are not exposed as configurable parameters in the standard cycle-deck interface. The variable-scoping model for nested submodels also leaves the interaction between locally declared solver variables and outer-scope names undefined when the same element is instantiated multiple times in a single cycle.

Because these fallback policies and scoping rules are implementation-defined rather than contractual, observed behavior is not guaranteed to be uniform across NPSS distributions or platform builds.

What boundary conditions govern the solver's substitution of numerical differentiation for a missing analytic partial derivative in a user-defined element? How do locally declared solver variables interact with outer-scope names when a custom element is instantiated more than once? Are the internal perturbation defaults and step-size policies discoverable through solver logs or convergence reports under default strategy settings?