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Support restarting multistep integration schemes using a single-step warm-up #58

Description

@arfazeli

Summary

OpenCMP currently rejects restarting history-dependent multistep schemes because a restart loads only one checkpoint, while schemes such as CNLF, SBDF, and adaptive IMEX require multiple consecutive previous solutions.

Saved .sol files cannot reliably provide this history because save_frequency may skip time steps.

Proposed solution

After loading the restart checkpoint, use a single-step method such as implicit Euler to generate the missing solution history. Once enough accepted warm-up steps have been completed, switch back to the configured multistep scheme.

The warm-up should use an appropriate time step, respect the simulation end time, and correctly populate the solution and time-step histories. IMEX schemes may need Euler IMEX as their warm-up method.

Acceptance criteria

  • Restart works for CNLF, SBDF, and adaptive IMEX from one checkpoint.
  • The solver switches to the configured multistep scheme after warm-up.
  • Existing single-step restart behavior remains unchanged.
  • Tests and restart documentation cover the new behavior.

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