Simulation Engine

The MetoSim engine solves Maxwell's equations on 3D Yee grids using GPU-accelerated FDTD. It handles mesh generation, material assignment, field propagation, convergence detection, and HDF5 serialisation.

Supported Solvers

Solver	Method	Version	Use Case
FDTD	Finite-Difference Time-Domain	V1 ✅	General EM propagation, broadband
RCWA	Rigorous Coupled-Wave Analysis	V2	Periodic structures, metasurfaces
FEM	Finite Element Method	V3+	Complex geometries, eigenmode analysis

FDTD Solver

The core solver implements the standard Yee algorithm with:

• 3D Yee grid — staggered electric and magnetic field components
• PML boundaries — absorbing layers to truncate the computational domain
• Courant stability — automatic time-step sizing from dt ≤ dx / (c × √3)
• Convergence detection — early stopping when relative field change drops below threshold
• GPU acceleration — JAX backend for NVIDIA B200/A100 execution

Configuration

from metosim.simulation import FDTDSettings

settings = FDTDSettings(
    time_steps=20000,               # max iterations
    courant_factor=0.99,            # stability factor (0 < cf ≤ 1)
    convergence_threshold=1e-6,     # relative change for early stop
    check_every_n=1000,             # convergence check interval
)

Resolution Guidelines

Structure	Recommended	Points per λ
Bulk dielectric	λ / (10n)	10
Waveguide mode	λ / (20n)	20
Metallic nanostructure	λ / (30n)	30
Plasmonic hotspot	λ / (40n)	40+

Example: Silicon (n=3.48) at 1550 nm → minimum feature 220 nm → resolution ≤ 22 nm.

Geometry Primitives

Structures are defined as geometric primitives painted onto the Yee grid:

# Rectangular slab
metosim.Box(center=(0, 0, 0), size=(2e-6, 2e-6, 0.22e-6), material="Si")

# Nano-pillar
metosim.Cylinder(center=(0, 0, 0), radius=150e-9, height=600e-9, axis="z", material="TiO2")

# Nanoparticle
metosim.Sphere(center=(0, 0, 0), radius=50e-9, material="Au")

Structures are applied in list order — later entries overwrite earlier ones at overlapping grid cells.

Materials Library

Built-in wavelength-dependent permittivity at telecom wavelengths:

Formula	Name	n @ 1550 nm	Type
Si	Silicon	3.476	Semiconductor
SiO2	Silica	1.444	Dielectric
TiO2	Titanium Dioxide	2.270	High-index dielectric
Si3N4	Silicon Nitride	1.994	Dielectric
Au	Gold	0.56 + 11.2i	Plasmonic metal
Al	Aluminium	1.44 + 16.0i	UV plasmonic
Air	Vacuum	1.000	Background

Lookup is case-insensitive with aliases: glass → SiO₂, silicon → Si, vacuum → Air.

Custom Materials

custom = metosim.Material(
    name="PMMA",
    formula="PMMA",
    permittivity_fn=lambda wl: complex(1.49**2, 1e-4),
    wavelength_range=(0.4e-6, 2.0e-6),
)
lib = metosim.MaterialLibrary()
lib.register(custom)

Boundary Conditions

Type	Keyword	Use Case
PML	pml	Open boundaries (default)
Periodic	periodic	Unit cells, photonic crystals
Bloch	bloch	Oblique incidence on periodic structures
Symmetric	symmetric	Exploit mirror symmetry (2× speedup)
Anti-symmetric	antisymmetric	TE/TM symmetry exploitation

from metosim.simulation import SimulationDomain, BoundaryCondition

domain = SimulationDomain(
    size=(4e-6, 4e-6, 4e-6),
    resolution=20e-9,
    boundary_conditions=(
        BoundaryCondition.PML,
        BoundaryCondition.PERIODIC,
        BoundaryCondition.PML,
    ),
    pml_layers=16,
)

Result Format (HDF5)

results.hdf5
├── fields/
│   ├── Ex, Ey, Ez          # Electric field (3D float64)
│   ├── Hx, Hy, Hz          # Magnetic field (3D float64)
├── structure/
│   └── permittivity         # 3D complex128
├── convergence/
│   ├── steps                # 1D int
│   └── residuals            # 1D float64
└── metadata/
    ├── @config              # Full input config (JSON)
    ├── @solver_version      # Engine version string
    ├── @sha256_checksum     # File integrity hash
    ├── @wall_time           # Seconds
    ├── @converged           # Boolean
    └── @performance         # Grid-points × steps / s

All field arrays use gzip compression (level 4) with HDF5 chunking.

Performance

Typical simulation times on NVIDIA B200:

Grid Size	Steps	Wall Time	Cost
100³	10,000	~30s	~$0.20
200³	20,000	~4min	~$1.50
400³	20,000	~25min	~$10
500³	50,000	~2hrs	~$50

GPU pricing: 1 credit = $25 = 1 hour B200 compute.