Numerical Methods

This document summarizes the numerical methods used in the Resonance Substrate Model simulations.

Quicklinks#

• docs README
• docs api integration examples
• docs api README
• docs api schema overview
• docs api using the schemas
• docs experiments faraday paradox experiment
• docs experiments README
• docs experiments replication checklist
• docs experiments resonance alignment tests
• docs experiments rotating conductor tests
• docs methods dimensional layers
• docs methods field equations
• docs methods operator definitions
• docs methods README
• docs methods substrate dynamics
• docs methods triadic fields
• docs onboarding model map
• docs onboarding reading guide
• docs onboarding triadic quickstart
• docs onboarding verification tests
• docs overview comparison to gr models
• docs overview glossary
• docs overview introduction
• docs overview README
• docs overview resonance primitives
• docs overview theoretical background
• docs simulations boundary conditions
• docs simulations README
• docs simulations solver_architecture
• docs simulations validation metrics
• docs simulations core README
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1. Discretization#

• finite difference schemes for scalar and vector fields
• finite volume methods for flux-based operators
• optional spectral methods for smooth domains

2. Time Integration#

• explicit Euler for rapid prototyping
• Runge–Kutta methods for improved stability
• semi-implicit schemes for stiff operators

3. Stability Considerations#

• CFL conditions for diffusion and advection
• timestep adaptivity
• error estimation and correction

4. Grid Structures#

• uniform Cartesian grids
• support for multi-resolution or nested grids