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Optional DASSL-Class Variable-Step EMT

AIMORA provides an optional DASSL-class variable-step, variable-order implicit DAE mode for a deliberately narrow set of admitted instantaneous-EMT owners. Existing projects and APIs continue to select fixed-step EMT unless the caller explicitly constructs EMTIntegrationSelection(DASSLClassEMTSettings(...)). Fixed-step execution remains the reference for switching detail, convergence comparisons, and real-time/HIL workflows.

Numerical formulation

For differential and algebraic state x = [y; z], the selected mode solves F(t, x, xdot; p) = 0. At candidate time t_n, derivative weights are the derivatives of the Lagrange basis through the candidate and accepted history, so each differential component uses xdot_n = sum(w_j x_(n-j)); algebraic derivative slots remain zero. Newton correction uses the effective Jacobian F_x + w_0 F_xdot. Orders one through five and step size are selected only from accepted smooth history. A rejected trial cannot modify physical owners, accepted numerical history, events, tasks, outputs, or checkpoint state.

Each component uses ewt_i = atol_i + rtol_i max(abs(x_i), abs(x_pred_i)); correction and residual tests use a weighted root-mean-square norm. Requested output inside one smooth accepted segment uses the accepted interpolation polynomial. The interpolant never crosses a task, root, topology transition, reset, or consistency restart. Exact transition output is labelled left or right.

Selection and preparation

using AIMORA

settings = DASSLClassEMTSettings(
    initial_step_s=2e-6,
    minimum_step_s=1e-10,
    maximum_step_s=2e-4,
    maximum_order=5,
    relative_tolerance=1e-8,
)
selection = EMTIntegrationSelection(settings)

DASSLClassEMTNetworkRequest declares exact owner identities, node count, interval, initial voltages, SI absolute tolerances and residual scales, requested output times, directed roots, and exact tasks. dassl_class_emt_readiness(request) returns a sorted typed disposition for every physical owner before runtime allocation. prepare_dassl_class_emt(request) and execute_dassl_class_emt!(prepared) use only an explicitly activated backend; without one they return SolverUnavailableResult rather than loading a private package or falling back to fixed step.

Initially admitted owners

The released slice admits canonical finite-conductance ideal sources, current injection, conductance, series R-L, series R-L-C, capacitor, memoryless exponential and cubic current laws with analytic Jacobians, exact time-switch resistance changes without current-extinction history, and one wound-field synchronous-machine electromagnetic/shaft realization with its sampled control owner. Validation-only manufactured residuals are not production physical owners.

Preparation refuses every exact type, fidelity, state, event, delay, topology, or snapshot intersection outside that matrix. Important refused owners include fixed-coefficient or frequency-dependent history elements without a variable-time reconstruction certificate, switch-detailed PWM and semiconductor owners with fixed-step trial state, unsupported transformer/hysteresis realizations, partitioned/local-subcycling execution, arbitrary native extensions, stochastic mutation, and real-time/HIL.

Public example and outputs

The emt_dassl_class_variable_step catalog entry executes four inspectable boundaries:

  • A passive Thevenin/series-RLC system publishes requested-grid dense output, KVL and charge residuals, nonnegative stored energy, and exact split/restart state identity.
  • A nonlinear cubic-current/capacitor system closes and opens a resistance switch at exact boundaries and publishes both left and right transition states.
  • A wound-field synchronous machine executes its electromagnetic flux, shaft, one source event, and two sampled-control releases.
  • An unsupported ideal-transformer constraint returns owner_type_not_admitted before numerical allocation.

The runner writes deterministic CSV and SVG products for all three admitted trajectories, a result-contract table with state/work/signature data, and a summary with the refusal and unsupported boundary. Set AIMORA_SOLVER_PATH explicitly to generate these artifacts; no private path is serialized into them.

Measured scale and crossover

On Julia 1.12.6/Linux/skylake with one Julia and BLAS thread, the equal-output fixed-step crossover has two deliberately different boundaries. For a constant algebraic Thevenin-source/load problem with 41 requested outputs, direct fixed evaluation required 0.000000742 s, while DASSL-class execution required 0.000331845 s; the maximum voltage difference was 6.91e-10 V, so fixed execution was about 447 times faster. For the stiff passive RLC trajectory at the same 41 requested times, DASSL-class execution required 0.002486814 s, while the independently implemented fixed BDF reference required 6.334348791 s and a 3.0517578125e-9 s step to meet or exceed the DASSL trajectory accuracy over the full output grid. This establishes one measured crossover from algebraic overhead to stiffness-driven adaptive benefit; it does not establish a universal crossover for other models, tolerances, event densities, hardware, or fixed-step implementations.

The canonical scale tier executed 100,000 total states—33,338 differential and 66,662 algebraic—with 200,088 sparse nonzeros, one root, four exact tasks, and seven outputs. Admission required 0.693864860 s, setup 18.529590169 s, first execution 31.666119924 s, warmed execution 32.279843721 s, and checkpointing 1.289381425 s; peak resident memory was 2,021,896,192 bytes. It accepted 44 steps across BDF orders one through five with zero rejected steps, localized the root, performed five consistency restarts, and ended with residual WRMS 4.69e-5, machine-decomposition error 1.50e-7, and endpoint-voltage errors below 4.4e-15 V. This scale result has no equal-fidelity fixed-step timing and therefore supports readiness and resource bounds, not a speedup claim.

Validity and evidence boundary

Native-Linux qualification covers deterministic index-one systems within the state, step, tolerance, output, and boundary ceilings declared by the accepted requirement and each admitted owner. Independent Julia formulations cover passive RLC, wound-field machine, stiff nonlinear and manufactured index-one problems, interpolation, events, conservation/passivity, restart, uncertainty, and refinement. Exact pinned SUNDIALS IDA 7.8.0 and OpenModelica 1.27.0 executions cover only their declared Robertson and nonlinear-root overlaps. External agreement does not establish algorithm identity.

This capability does not claim arbitrary high-index DAE support, every EMT owner, unrestricted stepping through switch detail, exact DASSL/DASPK/IDA/OpenModelica behavior, ATP/PSCAD compatibility, universal speedup, guaranteed convergence, standard conformance, certification, or native private macOS/Windows execution. The accepted fixed-step behavior and default remain unchanged.