[Node Name]#

Module: maddening.nodes.[module] Stability: [experimental | provisional | stable | deprecated] Algorithm ID: MADD-NODE-[XXX] Version: [semantic version of this algorithm implementation]

Summary#

[1-2 sentence description of what this node simulates.]

Governing Equations#

[Full mathematical formulation. Use LaTeX math blocks.]

$$ \frac{\partial T}{\partial t} = \alpha \nabla^2 T + S $$

Discretization#

[How the continuous equations are discretized. Explicit/implicit, finite difference/finite element/lattice Boltzmann, order of accuracy.]

Implementation Mapping#

[Trace every term in the governing equations and discretization to the specific Python/JAX function that implements it. This is mandatory for IEC 62304 Class C detailed design traceability (Clause 5.4).]

Equation Term	Implementation	Notes
$\alpha \nabla^2 T$ (diffusion)	`HeatNode.update()`	2nd-order central FD stencil
$S$ (source term)	`HeatNode.update()`	Added after diffusion
Time integration ($\partial T / \partial t$)	Forward Euler in `HeatNode.update()`	1st-order explicit
Boundary conditions	`state.at[0].set(left_T)`	JAX primitive: `jax.numpy.ndarray.at[].set()`

[If a term is handled by a JAX primitive or third-party function for which no explicit MADDENING function exists, document the primitive and its calling convention. Every governing equation term must appear in this table — silent omissions are not acceptable.]

[Code-driven generation of this table is recommended but not mandated. The table may be maintained manually provided it is complete and reviewed at each release. See scripts/check_impl_mapping.py for CI verification.]

Assumptions and Simplifications#

[Numbered list of every physical and mathematical assumption.]

[e.g., “Incompressible flow (Mach number << 1)”]

Validated Physical Regimes#

Parameter	Verified Range	Notes

Known Limitations and Failure Modes#

[Specific conditions where this model is known to produce incorrect or unreliable results. This section feeds directly into IEC 62304 SOUP anomaly assessment.]

[e.g., “CFL > 1 causes numerical instability”]

Stability Conditions#

[Analytical or empirical stability bounds for the numerical scheme.]

State Variables#

Field	Shape	Units	Description

Parameters#

Parameter	Type	Default	Units	Description

Boundary Inputs#

Field	Shape	Default	Description

References#

[Cite using Pandoc-style [@Key] syntax, where Key matches an entry in docs/bibliography.bib. Multiple citations: [@Key1; @Key2]. CI validates all cited keys exist via scripts/check_citations.py.]

[@ExampleKey] Author, A. (Year). Title. Publisher. — Brief note on relevance to this node.

Verification Evidence#

[Link to verification report and test files.]

Changelog#

Version	Date	Change
1.0.0	YYYY-MM-DD	Initial implementation