Numerical methods

The chapters below inventory every numerical method currently built into Magnelio, in the order a simulation passes through them: spatial discretisation, mesh generation and conformal geometry, boundary conditions, port models, lumped circuit elements, dispersive materials, conductor losses, sources and monitors, far-field computation, and the eigenmode solver. A final chapter covers implementation-level engineering (backends, precision) that is not itself a research method.

Every method that originates in published research carries a citation; in-house derivations are marked as such in the text.

• Spatial discretisation and time integration
  • Finite Integration Technique (FIT)
  • Leapfrog time integration
  • Stability (CFL condition)
  • Selectable precision
  • Simulation duration and energy stopping
• Mesh generation and conformal geometry
  • Geometry kernel and material filling
  • Graded Cartesian mesh
  • Conformal sub-cell material matrices (partially filled cells)
  • Thin conducting sheets
  • Thin-wire sub-cell model
  • Mesh quality safeguards
• Boundary conditions
  • Absorbing boundary: CPML
  • PEC, PMC and periodic walls
  • Symmetry planes
  • Boundary-condition interaction with ports
• Waveguide ports and S-parameter extraction
  • 2D port-mode solvers
  • Exact discrete transparent boundary conditions (DTBC)
  • Excitation and recording
  • S-parameters
• Discrete ports and lumped circuit elements
  • Semi-implicit Thévenin discrete port
  • Trapezoidal RLC companion models
  • Lumped devices on symmetry planes
  • Edge-path rasterisation
• Dispersive and lossy materials
  • Pole-residue material model
  • Auxiliary differential equation (ADE) update
  • Magnetic loss \(\sigma^*\)
  • Vector fitting of measured data
• Conductor losses
  • Perturbative wall losses (post-processing)
  • Surface roughness
  • Broadband time-domain SIBC
• Sources, monitors and post-processing
  • Plane-wave source (TF/SF)
  • Field, flux and frequency monitors
  • Signal processing
  • Project store, checkpointing, resume
• Far-field computation
  • Surface equivalence on a Huygens box
  • Ground planes, walls and symmetry planes
  • Normalisation, gain and radiated power
  • Plots
• Eigenmode analysis
  • 3D cavity eigenmode solver
  • 2D mode solver
• Implementation engineering (non-method)
  • Kernel dispatch and backends
  • Precision
  • Parallel mesh building
  • Dependencies with numerical relevance