Numerical methods

The chapters below inventory every numerical method currently built into Magnelio, in the order a simulation passes through them: spatial discretisation, geometry and board input, 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. Four final chapters cover numerical precision, the progress a run reports, the 3D viewer and implementation-level engineering (backends, kernel dispatch) that are not themselves research methods.

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
• Geometry construction
  • Bodies, sheets and curves
  • Lofts: between profiles, and between faces
  • From a map to a reflector: parametric surfaces
  • What the mesher sees
• CAD import
  • What an exchange format carries, and what it does not
  • Only solids are imported
  • Assigning materials by name
  • Assemblies
  • Colours
  • Healing
  • Limits
• Board import
  • What a fabrication export carries
  • The stackup is taken literally
  • Meshing a board
  • Materials
  • Limits
• 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
  • Paths: any direction, at a measured price
• 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)
  • The surface current
  • Surface roughness
  • Broadband time-domain SIBC
• Sources, monitors and post-processing
  • Sources, waveforms and excitations
  • The general time-domain analysis
  • Incident fields on a total-field/scattered-field box
  • Initial fields
  • Field sources: reusing what a model radiates
  • Impressed currents on a path
  • Field containers
  • Field, flux and frequency monitors
  • Signal processing
  • Project store, checkpointing, resume
  • ParaView export
• Projects and runs
  • Vocabulary
  • Reading a project
  • A project that is still being written
  • Time
  • Checkpoints and resume
  • What prints
• Far-field computation
  • Surface equivalence on a Huygens box
  • Ground planes, walls and symmetry planes
  • Feed guides crossing the box
  • Normalisation, gain and radiated power
  • Power balance: how close the box may sit to the radiator
  • Plots
• Eigenmode analysis
  • 3D cavity eigenmode solver
  • 2D mode solver
• Numerical precision
  • The switch
  • What the switch reaches
  • What single precision buys
  • What single precision costs
  • Recognising a word-length-limited result
  • Choosing
• Progress output
  • The switch
  • What the phases mean
  • Short phases
  • Terminals, notebooks and logs
• 3D viewer
  • What is drawn
  • The cutting plane
  • Fields on the cut
  • Fields in the volume
  • Rendering modes
  • Requirements
  • Limitations
• Implementation engineering (non-method)
  • Kernel dispatch and backends
  • Precision
  • Parallel mesh building
  • Dependencies with numerical relevance