openEMS Electromagnetic Field Solver Documentation

openEMS is a free and open-source electromagnetic field solver that utilizes the Finite-Difference Time-Domain (FDTD) method. It is designed for high-performance simulations and provides flexible scripting interfaces via Octave, Matlab, and Python.

Key features include:

• Mesh Support: Fully 3D Cartesian and cylindrical coordinates with graded mesh capabilities.
• Performance: High-speed FDTD via multi-threading, SIMD (SSE), and MPI support.
• Material Modeling: Support for dispersive materials using Drude, Lorentz, and Debye models.
• Data Export: Field dumps available in both time and frequency domains using .vtk or .hdf5 file formats.
• Post-processing: Flexible routines available through Octave, Matlab, and Python interfaces.

openEMS is an open-source electromagnetic field solver that uses the Equivalent-Circuit Finite-Difference Time Domain (EC-FDTD) method. It solves Maxwell's equations in a 3D full-wave manner to simulate electromagnetic wave propagation.

Key components include:

• The Engine: Written in C++ for high performance.
• Interfaces: Extensive Matlab/Octave and Python interfaces for defining simulations.
• CSXCAD: A separate library used for handling the geometry of FDTD simulations.
• AppCSXCAD: A graphical user interface for inspecting 3D models created in CSXCAD.

The Lorentz model extends the Drude model by adding Lorentz pole frequencies. It can be used for both dielectric and magnetic materials.

Key Parameters:

• $f_{\mathrm{Lor}\epsilon}(n)$: $n$-th electric Lorentz pole frequency.
• $f_{\mathrm{Lor}\mu}(n)$: $n$-th magnetic Lorentz pole frequency.
• $\tau_{\epsilon}(n)$ / $\tau_{\mu}(n)$: Relaxation times (inverse of damping factor).
• $\omega_{p\epsilon}(n)$ / $\omega_{p\mu}(n)$: Plasma frequencies.

Note: If the Lorentz pole frequency terms are zeroed, the Lorentz model reduces to the Drude model.

In openEMS, you can customize simulations using user-defined symbolic mathematical expressions passed as strings. These strings are evaluated by the C++ engine using the fparser library.

Custom expressions are used for three primary purposes:

1. Varying material properties in space: Using a weighting function via SetMaterialWeight.
2. Constructing custom excitation signals: Creating a custom input waveform $e[t]$ via SetCustomExcite.
3. Varying excitation field values in space: Using a weighting function via SetExcitationWeight to construct custom field patterns or polarizations (e.g., for hollow waveguides or coaxial cables).

Important: fparser uses its own Domain-Specific Language (DSL). Its syntax is independent of the outer interface (C++, Matlab/Octave, or Python).

In openEMS, a property defines the material or simulation behavior (e.g., metal, dielectric, magnetic material, or lumped elements like resistors). A primitive is a geometrical shape (e.g., a Box or Cylinder).

To create a physical or non-physical object in the CSXCAD model, you must assign one or more primitives to a property. Simulation entities like excitation sources, probes, and field dump boxes are also treated as properties assigned to geometrical shapes.

# Example: Creating a property and assigning a primitive (conceptual)
# In Python:
metal = csx.AddMetal('plate')
metal.AddBox([x1, y1, z1], [x2, y2, z2])

Magnetic Conductivity ($\sigma$) is a hypothetical property used to model magnetic conduction currents. While magnetic monopoles do not exist physically, this parameter is used in openEMS to:

1. Implement the Perfect Magnetic Conductor (PMC) boundary condition (where $\sigma \to \infty$).
2. Implement Perfectly Matched Layers (PML) for EM wave absorption.
3. Create custom localized EM wave absorbers by combining electric and magnetic conductivity with weighting functions.

A mesh partitions a 3D volume into discrete rectangular cuboids called Yee cells, which are the fundamental units for electromagnetic field computation.

Coordinate Systems

• Cartesian: The default system using a standard FDTD algorithm. It supports non-uniform meshes, allowing fine mesh sizes around small features to save computational resources while using coarse meshes elsewhere.
• Cylindrical: An extension for simulating round structures without "staircasing" errors. It can be uniform or non-uniform. Because the origin is a coordinate singularity (cells become progressively smaller near the origin), openEMS provides a subgridding feature to reduce angular resolution by dropping half of the azimuthal mesh lines within specific radii.

In openEMS, signals are defined by specific waveforms used to excite the simulation. Common waveform types include Sinusoids, Dirac Impulses, Heaviside Steps, and Gaussian Pulses.

Important Simulation Constraints:

• Bandwidth Limitation: Note that bandwidth limitation is currently not implemented and is ignored by the simulation engine.
• Simulation Termination: To prevent simulations from running indefinitely, it is recommended to limit the maximum simulation to 10,000 timesteps.