Geometry and Materials

This page lists the calls that define what is in the domain: materials, shapes, metal sheets and dispersive media. The guide Materials and Geometry explains how shapes land on the grid and which kind of conductor to use. All lengths are in metres and conductivity is in S/m.

Simulation.add_material(name, *, eps_r=1.0, sigma=0.0, mu_r=1.0,
                        debye_poles=None, lorentz_poles=None, chi3=0.0)
    -> Simulation

Registers a named, isotropic material. Use the name in add(...).

import numpy as np
from rfx import (Box, Cylinder, DebyePole, PolylineWire, Simulation, Sphere,
                 Via, drude_pole, lorentz_pole)

sim = Simulation(freq_max=5e9, domain=(0.04, 0.03, 0.02), dx=1e-3,
                 boundary="cpml", cpml_layers=6)

sim.add_material("substrate", eps_r=4.3, sigma=0.02)
sim.add_material("lossy_block", sigma=5.0e5)            # below the PEC threshold
sim.add_material("water_body", eps_r=4.9,
                 debye_poles=[DebyePole(delta_eps=74.1, tau=8.3e-12)])
sim.add_material("resonant", lorentz_poles=[
    lorentz_pole(delta_eps=2.0, omega_0=2 * np.pi * 10e9, delta=1e8)])
sim.add_material("plasma",                              # 10 GHz plasma frequency
                 lorentz_poles=[drude_pole(omega_p=2 * np.pi * 10e9, gamma=2 * np.pi * 1e9)])

Library materials need no add_material call: "vacuum", "air", "fr4", "rogers4003c", "rogers4350b", "rt_duroid_5880", "alumina", "silicon", "ptfe", "water_20c", "copper", "aluminum" and "pec". The values are in rfx.MATERIAL_LIBRARY. The dielectric losses there are a constant conductivity matched at one frequency, so use your laminate’s data for real designs.

The conductor threshold. Any material with sigma >= 1e6 S/m is treated as PEC: tangential E is forced to zero and the conductivity is not used. So "copper" and "aluminum" are lossless PEC, and their skin depth is not resolved. Keep sigma below 1e6 for a lossy bulk medium. For conductor loss on a metal sheet, use add_thin_conductor(..., surface_impedance_f0=f0).

Fitting measured data. fit_debye(freqs, eps_measured, n_poles=1, *, eps_inf=None) and fit_lorentz(...) fit poles to complex permittivity data; load_material_csv(path, ...) reads it from a CSV file. See the generated reference.

Simulation.add(shape, *, material) -> Simulation

Fills the shape with a registered or library material. Shapes are rasterized in the order you add them. Where dielectrics overlap, the later one wins. Metal accumulates: a later shape cannot cut a hole in a conductor.

sim.add(Box((0.005, 0.005, 0.004), (0.035, 0.025, 0.0056)), material="substrate")
sim.add(Sphere((0.020, 0.015, 0.012), radius=0.003), material="alumina")
sim.add(Cylinder((0.010, 0.010, 0.0048), radius=0.0005, height=0.0016, axis="z"),
        material="pec")
sim.add(PolylineWire(((0.028, 0.010, 0.008), (0.028, 0.020, 0.008)),
                     radius=0), material="pec")
sim.add(Via(center=(0.015, 0.020), drill_radius=0.3e-3, pad_radius=0.6e-3,
            layers=[(0.004, 0.0056)]), material="pec")

sim.fidelity_report() prints where every shape actually landed next to what you drew. Run it before a long solve.

MeshShape.from_file reads a watertight STL, OBJ or PLY mesh, or STEP/STP with the cad extra installed (pip install "rfx-fdtd[cad]"). scale is required: STL, OBJ and PLY have no units, so pass 1e-3 for a file drawn in millimetres. STEP files are converted to metres on load, so pass 1.0. The mesh is rasterized on the host, so a CAD shape cannot carry a gradient.

Simulation.add_thin_conductor(shape, *, sigma_bulk=5.8e7, thickness=35e-6,
                              eps_r=1.0, surface_impedance_f0=None)
    -> Simulation

Declares copper foil (ground plane, patch, trace) as a sheet: one grid plane, zero thickness, no cell of its own. Give the shape zero thickness along its normal.

sim.add_thin_conductor(Box((0.005, 0.005, 0.004), (0.035, 0.025, 0.004)))
sim.add_thin_conductor(Box((0.012, 0.010, 0.0056), (0.028, 0.020, 0.0056)),
                       surface_impedance_f0=3e9)

• With the default sigma_bulk (copper) the sheet is lossless PEC, and rfx warns once to say so. thickness and eps_r are then not used.
• surface_impedance_f0=f0 adds conductor loss as a surface resistance matched at f0. The sheet keeps exactly the same footprint, so f0 changes the loss and never the geometry. Combinations the loss model does not support raise.
• sigma_bulk < 1e6 makes a resistive sheet whose sheet conductance is sigma_bulk * thickness.

A metal plate or wall that really is thick is a volume: add(Box(...), material="pec"). A PEC volume has walls at both drawn faces at any thickness.

The removed two_plane=True keyword of add() raises TypeError. Delete it: a PEC volume already gets both faces.

• Metal with sigma >= 1e6 S/m is lossless. For ohmic loss, use a sheet with surface_impedance_f0 or a below-threshold sigma.
• A shape face between two grid planes snaps to the nearest plane. For thin layers, choose dx or a graded profile so the faces fall on grid planes, and check with fidelity_report().
• A sheet declared through add_thin_conductor must be one grid plane thick. A PEC shape that is thinner than a cell but not zero is ambiguous; see How conductors land on the lattice.
• MeshShape geometry is not differentiable.