Palace Learning Guide

Concepts build in stages — from physical intuition to advanced Palace workflows.

This document assumes no prior background in computational electromagnetics. It first builds physical intuition, then explains the five Palace problem types, then introduces the numerical ideas needed to obtain trustworthy results. The final sections cover advanced RF, microwave, superconducting-circuit and high-performance-computing concepts.

Learning Outcomes

• Explain what Palace solves and identify when it is the right tool.
• Choose the correct Palace problem type for an engineering question.
• Understand the roles of geometry, materials, mesh attributes, boundary conditions, ports and excitations.
• Read common outputs such as capacitance matrices, inductance matrices, eigenfrequencies, quality factors and S-parameters.
• Recognize mesh, solver and modeling errors before trusting a result.
• Progress toward RF devices, antennas, resonators, transmission lines and superconducting quantum circuits.

1. What Palace Is

Palace stands for Parallel Large-scale Computational Electromagnetics. It is an open-source, parallel finite-element solver for full-wave three-dimensional electromagnetic analysis. In practical terms, you describe an electromagnetic device using a mesh and a JSON configuration file; Palace then computes electric and magnetic fields and converts them into engineering quantities such as capacitance, inductance, resonant frequency, quality factor, voltage, current and scattering parameters.

1.1 What Palace Is Designed to Simulate

1.2 What Palace Does Not Directly Solve

Palace is not a general-purpose solver for every branch of physics. It does not directly solve structural stress, fluid flow, heat transfer, chemical reactions or rigid-body motion. Electromagnetic losses computed in Palace can be exported and used as inputs to thermal or structural tools, but that becomes a multiphysics workflow.

2. Palace v0.14.0 Problem Types

A beginner’s decision tree for selecting the Palace problem type.

A beginner’s decision tree for selecting the Palace problem type.

3. A Complete Simulation in One Picture

Every credible simulation follows an iterative engineering workflow.

Every credible simulation is an iterative loop, from engineering question to validation.

A simulation is not merely a mesh plus a command. It begins with a precise engineering question and ends with validation. The most common beginner error is to focus on solver settings before defining the physical question, material assumptions and boundaries.

4. The Basic Electromagnetic Quantities

4.1 Four Equations Worth Remembering

5. Static, Frequency-Domain and Time-Domain Thinking

6. Frequency, Period, Wavelength and Phase

Frequency (f): Number of cycles per second. 1 GHz means one billion cycles per second.

Period (T): Time for one cycle. T = 1/f.

Wavelength (λ): Distance traveled during one cycle. In vacuum, λ ≈ 0.3/fGHz metres.

Phase: Position within the wave cycle. Two signals may have equal amplitude but different phase.

Propagation velocity: Speed of the wave in a material. It is slower in most dielectrics than in vacuum.

Wavelength is central to meshing. A device that is electrically small may be modeled with relatively few elements, while a structure many wavelengths long needs many more elements. Small gaps, thin layers and sharp corners can impose even stricter mesh requirements than wavelength.

7. Materials

7.1 Permittivity, Permeability and Conductivity

Permittivity (ε): Controls how strongly a material stores electric-field energy. Relative permittivity εr is measured against vacuum.

Permeability (μ): Controls magnetic-field storage. Relative permeability μr is measured against vacuum.

Conductivity (σ): Controls how easily electric current flows and how strongly conductive loss occurs.

Loss tangent (tan δ): A convenient measure of dielectric loss under sinusoidal excitation.

8. Geometry, Domains, Surfaces and Attributes

A Palace mesh contains volume elements for material regions and surface elements for boundaries. Each region or surface is assigned an integer attribute (also called a physical tag in Gmsh workflows). The JSON file refers to these integers. The geometry name may help humans, but Palace ultimately uses the numerical attributes.

9. Boundary Conditions

10. Terminals, Lumped Ports, Wave Ports and Current Sources

11. Finite Element Method — An Intuitive View

The finite element method (FEM) breaks a complicated electromagnetic domain into many small elements. Palace represents the unknown field inside each element using polynomial basis functions and then assembles the local contributions into a large system of equations. Solving that system gives an approximation to the field throughout the model.

12. Mesh Fundamentals

The mesh is one of the strongest determinants of simulation accuracy, runtime and memory. A coarse mesh may run quickly but miss important field variation. An excessively fine mesh may consume all available memory without improving the result meaningfully.

12.1 Mesh Attributes

Domain attributes identify material volumes; boundary attributes identify surfaces. In Palace 0.14.0, attribute integers should be positive and do not have to be contiguous. The JSON keyword "Attributes" selects the tagged regions to which a material, boundary condition, port or postprocessing request applies.

Example concept only:
"Domains": {
  "Materials": [
    {"Attributes": [1], "Permeability": 1.0, "Permittivity": 11.45},
    {"Attributes": [2], "Permeability": 1.0, "Permittivity": 1.0}
  ]
},
"Boundaries": {
  "PEC": {"Attributes": [10, 11]},
  "Absorbing": {"Attributes": [20], "Order": 1}
}

13. Units and the Model Length Scale L0

Palace nondimensionalizes the problem internally. The configuration parameter Model.L0 tells Palace what one mesh coordinate unit means in metres. For example, if the mesh coordinates are in micrometres, L0 = 1e-6. If coordinates are in millimetres, L0 = 1e-3. Incorrect L0 can shift resonant frequencies and all dimensional outputs by orders of magnitude.

14. Palace JSON Configuration

A Palace configuration is a structured JSON file. The exact sections vary by problem type, but the following mental map is useful.

{
  "Problem": {
    "Type": "Eigenmode",
    "Output": "postpro"
  },
  "Model": {
    "Mesh": "model.msh",
    "L0": 1.0e-3
  },
  "Domains": {
    "Materials": [...]
  },
  "Boundaries": {
    "PEC": {...}
  },
  "Solver": {
    "Order": 1,
    "Eigenmode": {...}
  }
}

15. Running Palace 0.14.0

The standard wrapper command is:

palace -np <NUM_PROCS> config.json

To keep the console output and save it for later diagnosis:

palace -np 4 config.json 2>&1 | tee palace.log

The -np value controls MPI processes. In a GPU run, the correct number of MPI processes depends on the number of GPUs, the build, memory limits and the model. More processes are not automatically faster.

16. Core Problem Type 1 — Electrostatic

Electrostatic simulation assumes the electric field is constant in time. Palace applies a unit voltage to each terminal in turn while the others and the ground are held at zero, then constructs capacitance matrices.

16.1 How to Read a Capacitance Matrix

Diagonal entries primarily represent self-capacitance relative to the reference, while off-diagonal entries represent coupling between terminals. Sign conventions depend on the matrix form. Always verify units and the precise matrix definition before comparing against another tool.

16.2 Common Electrostatic Mistakes

• No ground or reference boundary, leaving the potential undefined.
• A conductor surface split into multiple attributes but only one attribute is assigned as the terminal.
• Incorrect dielectric permittivity.
• Mesh too coarse in narrow gaps where the electric field is concentrated.
• Confusing Maxwell capacitance, mutual capacitance and two-terminal capacitance.

17. Core Problem Type 2 — Magnetostatic

Magnetostatic simulation assumes steady current. Palace excites current-source surfaces and computes magnetic fields and inductance matrices.

17.1 Common Magnetostatic Mistakes

• An open or incomplete current path.
• Incorrect source direction or surface orientation.
• Using unsuitable boundary conditions around the current-carrying region.
• Ignoring magnetic material permeability.
• Mesh too coarse near conductors or in small magnetic gaps.

18. Core Problem Type 3 — Eigenmode

An eigenmode simulation finds the structure’s natural electromagnetic resonances. No external drive is required. Each mode has an eigenfrequency, a field pattern and, when loss is included, a quality factor.

A resonant response has a centre frequency and a bandwidth; their ratio gives an intuitive Q.

Resonance, bandwidth and quality factor: Q ≈ f₀ / Δf.

18.1 Mode Identification

A mode number is not a permanent physical label. Mesh changes, target frequency and solver settings can reorder computed modes. Identify modes using field patterns, symmetry, energy distribution and continuity across parameter sweeps—not only by row number.

18.2 Common Eigenmode Mistakes

• Searching around the wrong frequency because geometry units or L0 are wrong.
• Requesting too few modes and missing the mode of interest.
• Mistaking a spurious, port-localized or box mode for the intended device mode.
• Comparing mode 1 in two designs without checking field-pattern similarity.
• Reporting Q without stating which loss mechanisms were included.

19. Core Problem Type 4 — Driven Frequency Domain

A driven simulation applies a sinusoidal source at selected frequencies and solves the steady-state response. This is the main Palace workflow for S-parameters, filters, transmission lines, crosstalk and input matching.

19.1 A Frequency Sweep

A frequency sweep solves the same physical model at multiple frequencies. A coarse sweep is useful for finding broad behavior. A fine sweep is needed near narrow resonances. Palace 0.14.0 supports uniform and flexible sample definitions, plus an adaptive fast frequency sweep using a reduced-order model.

19.2 Common Driven-Simulation Mistakes

• Exciting the wrong port or more ports than intended.
• Incorrect reference impedance or port geometry.
• Frequency range does not include the resonance or cutoff region.
• Absorbing boundary placed too close to a radiating structure.
• Interpreting S21 without checking whether both ports support the intended mode.

20. Core Problem Type 5 — Transient

A transient simulation starts from rest and follows the electromagnetic response to a time-dependent excitation. It is useful for pulses, propagation delay, ringing and broadband effects viewed in time.

20.1 Time Step and Duration

The time step must be small enough to resolve the highest important frequency and numerical dynamics. The total duration must be long enough for the pulse to reach the observation point and for ringing to decay. Palace 0.14.0 also supports adaptive time stepping through CVODE and ARKODE integrators.

20.2 Common Transient Mistakes

• Simulation time ends before the signal reaches the output.
• The excitation pulse has bandwidth far beyond what the mesh can resolve.
• Output is saved too infrequently, hiding the waveform shape.
• A reflected pulse is mistaken for numerical noise.
• Using dielectric loss tangent assumptions where the transient formulation requires conductivity-based loss treatment.

21. Impedance and Matching

Impedance describes how voltage and current relate under alternating excitation. A source transfers power efficiently when the device and transmission system are appropriately matched. A discontinuity in impedance produces reflections.

Resistance: Dissipates energy as heat.

Reactance: Stores and returns energy through electric or magnetic fields.

Characteristic impedance: The voltage-to-current relation of a propagating transmission-line mode.

Reference impedance: The impedance against which S-parameters are normalized, often 50 Ω in RF systems.

22. S-Parameters

S-parameters are complex numbers. Magnitude shows how much; phase shows timing or phase shift. In dB, magnitude is commonly reported as 20 log10|Sij|. A value of −20 dB corresponds to a magnitude of 0.1, not a power fraction of 20%.

23. Resonance and Quality Factor Q

A resonator stores energy and exchanges it between electric and magnetic forms. The quality factor Q measures how slowly stored energy decays relative to the oscillation rate. High Q means a narrow resonance and low loss; low Q means a broad resonance and faster decay.

24. Loss Mechanisms

A Q value is meaningful only when the included losses are stated. An ideal PEC cavity with lossless dielectric may have an effectively infinite physical Q, while the numerical eigensolver still reports finite error estimates that must not be confused with physical loss.

25. Field Visualization and Postprocessing

Palace can write field data for ParaView. Common quantities include electric field E, magnetic flux density B, potential V, magnetic vector potential A, electric and magnetic energy density, Poynting vector, surface charge and surface current. Palace 0.14.0 also writes problem-specific CSV measurements such as eigenfrequencies, port voltage/current and matrix data.

26. Mesh Convergence

A result is mesh-converged when further sensible mesh refinement changes the quantity of interest by less than an agreed tolerance. Convergence should be tested on the engineering quantity you plan to report—not merely on the solver residual.

26.1 A Basic Convergence Procedure

1. Run a coarse model that is small enough to debug quickly.
2. Refine the mesh globally or locally in physically important regions.
3. Repeat the simulation without changing the physical model.
4. Compare the key quantity of interest.
5. Continue until the change is below your tolerance and the field pattern remains physically consistent.
6. Record element count, degrees of freedom, order, runtime and memory for every level.

27. Polynomial Order: h-Refinement and p-Refinement

Reducing element size is called h-refinement. Increasing the finite-element polynomial order is p-refinement. Both can increase accuracy, but their cost and effectiveness differ. Smooth fields in well-shaped elements often benefit from higher order; singular corners, thin gaps and abrupt material changes often still require local h-refinement.

28. Adaptive Mesh Refinement (AMR)

AMR uses an error indicator from the computed solution to refine selected elements. Palace 0.14.0 supports solution-based AMR for all problem types except Transient. AMR is powerful, but it does not replace physical judgment: the error estimator may refine a mathematically difficult region that is irrelevant to your design objective, or it may need help through initial local refinement.

29. Solver Convergence vs Physical Accuracy

30. Verification and Validation

Verification: Did we solve the mathematical model correctly? Examples: mesh convergence, solver tolerance and code benchmark.

Validation: Does the mathematical model represent the real device? Examples: comparison with measurement or a trusted experiment.

For an engineering report, include both. A highly converged result can still be invalid if the material permittivity, conductor thickness, connector geometry or environmental boundary is wrong.

31. Lumped Ports vs Numeric Wave Ports

A wave port is usually more physically descriptive for a true propagating cross-section, but it has stricter geometric and meshing requirements. The port must lie on an outer boundary and the cross-section must be large and clean enough to support the intended mode.

32. Adaptive Fast Frequency Sweeps

A conventional driven sweep solves the large full-order system at every requested frequency. An adaptive sweep solves selected frequencies, constructs a reduced-order model and uses it to approximate the response over the band. Palace activates this behavior through a nonzero AdaptiveTol.

33. Multiple Excitations

Palace 0.14.0 can represent multiple excitation indices in one driven configuration and simulate them consecutively. This is useful for generating multiple columns of a multiport response, but output-column naming and S-parameter behavior must be interpreted carefully. Automated workflows should explicitly map excitation index, source port and output columns.

34. Periodic and Floquet-Periodic Boundaries

Periodic boundaries model a repeated unit cell by matching fields on a donor and receiver surface. Floquet-periodic boundaries introduce a phase shift between repeated cells. Palace 0.14.0 added exact periodic and Floquet phase-delay constraints. This feature is a boundary condition within supported problem types; it is not the later standalone FloquetPort feature.

• Donor and receiver surface meshes must match exactly for configuration-specified periodic matching in v0.14.0.
• The translation or rotation relationship must be correct.
• The Floquet wave vector controls the phase progression between cells.
• A sign or coordinate-system mistake can reverse the intended propagation phase.

35. Energy Participation Ratio (EPR)

EPR describes how much of a mode’s energy is stored in a particular element or material region. In superconducting-circuit analysis, Palace can use lumped inductive ports representing linearized Josephson junctions and compute inductive participation data for circuit quantization.

36. Superconducting Electromagnetics

Superconductors are not always equivalent to ideal PEC surfaces. Depending on frequency, temperature, film thickness and the desired accuracy, one may need finite penetration depth, kinetic inductance or a London-equation model. Palace includes superconducting modeling capabilities, but the correct parameters must come from the physical fabrication stack and operating conditions.

37. Surface Impedance, Skin Depth and Thin Conductors

At high frequency, current concentrates near a conductor surface. The skin depth becomes small, making full volumetric meshing of a thick conductor wasteful. A finite-conductivity or impedance boundary can approximate the surface behavior when its assumptions are valid. Very thin films, superconductors and multilayers may require more specialized treatment.

38. Symmetry

Symmetry can reduce a model to a fraction of the full geometry, saving memory and runtime. PEC and PMC-like symmetry planes select different field parities. A symmetry plane is valid only if geometry, materials, boundaries, excitation and the desired mode all share that symmetry.

39. High-Order Elements and Curved Geometry

High-order finite elements can represent smooth fields accurately with fewer elements than first-order methods, especially in wave problems. Curved high-order geometry also reduces staircase error on cylindrical and smoothly curved surfaces. The trade-off is more degrees of freedom per element and greater implementation complexity.

40. GPU, MPI and HPC Concepts

Palace 0.14.0 supports NVIDIA and AMD GPU acceleration and multi-GPU parallelism when built with the required dependencies. Performance depends on problem type, finite-element order, partial assembly, solver/preconditioner, mesh partitioning and the ratio of computation to communication.

40.1 Memory Planning

• Record total elements, degrees of freedom and polynomial order.
• Leave memory headroom for mesh refinement, coarse matrices, eigensolver subspaces and output fields.
• Do a small run before launching a production model.
• Avoid saving every field at every frequency or time step unless necessary.
• Treat GPU memory and host memory as separate constraints.

41. Design Sweeps, Sensitivity and Uncertainty

A single simulation answers one model. Engineering design requires understanding how results change with geometry and material uncertainty. Examples include substrate permittivity tolerance, conductor width, gap size, junction inductance and package dimensions.

42. Multiphysics Coupling

Palace results can feed other solvers. For example, conductor and dielectric loss can become heat sources in a thermal solver; thermal expansion can then update geometry; stress and temperature can change material properties. Such workflows require explicit data transfer, unit consistency and validation at every interface.

43. Version-Specific Feature Awareness

44. Recommended 12-Week Sequence

45. Ordered Hands-On Exercises

Exercise 1 — Capacitance of Two Conductors

Problem type: Electrostatic

Objective: Learn terminals, ground, dielectric permittivity, electric field and capacitance.

• Run the official spheres example or construct two parallel plates.
• Visualize potential and electric-field magnitude.
• Change separation and predict whether capacitance rises or falls.
• Refine the mesh in the gap and make a convergence table.

Deliverable: A one-page report with geometry, assumptions, C value, field plot and convergence result.

Exercise 2 — Inductance of Current Loops

Problem type: Magnetostatic

Objective: Learn current sources, magnetic flux, self-inductance and mutual inductance.

• Run the official rings example.
• Reverse one current direction and observe the sign/coupling change.
• Change ring spacing and predict mutual inductance.
• Check mesh convergence around conductors.

Deliverable: Inductance matrix plus a magnetic-field visualization and interpretation.

Exercise 3 — Resonant Modes of a Cavity

Problem type: Eigenmode

Objective: Learn target frequency, mode shape, frequency convergence and Q interpretation.

• Run the official cylinder example.
• Request multiple modes and classify them by field pattern.
• Change a cavity dimension and predict frequency change.
• Compare first-order and higher-order or refined-mesh results.

Deliverable: A mode table containing frequency, mode description, mesh size and numerical error.

Exercise 4 — Coaxial Transmission

Problem type: Driven and Transient

Objective: Learn wave/lumped ports, S11/S21, propagation delay and reflections.

• Run the official coaxial example in driven mode.
• Plot S11 and S21 over frequency.
• Introduce an impedance discontinuity and observe reflection.
• Run a pulse and measure arrival/reflection time.

Deliverable: Frequency and time-domain plots with a physical explanation.

Exercise 5 — Coplanar Waveguide / Quantum-Device Preparation

Problem type: Driven and Eigenmode

Objective: Learn field concentration, ports, substrate effects, resonators and participation concepts.

• Run the official CPW example.
• Change substrate permittivity and observe propagation/resonance changes.
• Refine gaps and conductor edges.
• Add a simple lumped inductive element only after the baseline model is validated.

Deliverable: A reproducible CPW report and a list of assumptions needed before an EPR model.

46. Suggested Capstone Projects

47. What a Good Simulation Report Contains

• Engineering question and acceptance criteria
• Palace version, build/backend and command used
• Geometry source and dimensional units
• Mesh file format, element count, attributes and refinement strategy
• Material properties with sources and operating conditions
• Boundary conditions, ports, directions and excitations
• Solver order, frequency/time settings and convergence tolerances
• Hardware, MPI ranks, GPU device, runtime and memory
• Results with units and field/S-parameter plots
• Mesh-convergence and validation evidence
• Known limitations and recommended next step

48. Pre-Run Checklist

49. Post-Run Credibility Checklist

50. Beginner Troubleshooting Map

51. Essential Glossary

52. Official Source Basis

This learning guide summarizes concepts from the Palace v0.14.0 source documentation and release history. The following official sources should be treated as the primary references when implementing or validating configurations:

53. Final Learning Advice

Progress in simulation comes from repeatedly connecting three views: physical intuition, mathematical formulation and numerical evidence. Use the five Palace problem types as tools for answering specific questions, and require every important result to pass unit checks, field-pattern checks, mesh convergence and independent validation.