Solver Verification by Manufactured Solutions
The breeder's numerical solvers are verified with the method of manufactured solutions and convergence studies — checks that need no machine and can be reproduced today.
Checking the solver against known answers
Before trusting a solver on a problem with no known answer, you check it on problems that do. The method of manufactured solutions (MMS) constructs an exact solution by design, inserts the matching source term into the equations, and confirms the solver recovers it at the expected order of accuracy. The breeder (Hyperion) code applies MMS to its core solvers.
# Method of manufactured solutions (schematic)
# 1. Pick an exact u*(x): e.g. u* = sin(pi x)
# 2. Insert into operator L: compute forcing f = L[u*]
# 3. Solve L[u]=f numerically -> u_h
# 4. error = ||u_h - u*||; refine grid; check order p:
# error ~ C * h^p (p should match the scheme's design order)Convergence and conservation
- Convergence: refining the grid should shrink error at the scheme's design order; a wrong order signals a bug.
- Conservation: quantities that should be conserved (particles, energy) must not drift.
- Limiting cases: the solver must reproduce known analytic limits.
Verification is not validation
Passing MMS means the code solves its equations correctly. It says nothing about whether those equations describe a real breeder plasma — that is validation, which awaits FOAK. But verification is a real, reproducible result available now, and it is part of what an independent reproducer can confirm from the deposit.
The two also fail independently. A perfectly verified code can encode a wrong physical model and confidently produce wrong answers; a sound model can be undone by a coding error a verification suite would catch. Because the breeder is verified in places but validated nowhere in hardware, the honest present-tense status is that the arithmetic can be trusted to the extent it has been verified, and the physics awaits the machine.
This page describes a design-and-simulation study, not a built machine. Construction of the breeder (Hyperion) begins Q2 2027; first-of-a-kind first tritium is targeted near 2030. No hardware net-gain claim is made before FOAK.