AirInduct Sim computes coupling and inductance from closed-form expressions rather than from a discretised field. Where a closed form exists, the solver evaluates it directly — so there is no discretisation error to quote. What follows is the method, and an honest account of where it stops.
AirInduct Sim is exact wherever a closed-form expression exists, because the solver evaluates that expression directly instead of approximating it on a mesh. For two coaxial circular loops, for example, it computes mutual inductance from the Maxwell–Neumann elliptic-integral formula tabulated by Grover (1946) and Babic & Akyel (2008), so there is no discretisation error to quote. The real limit is the model, not the numerics: the solver assumes air-core coils, filamentary conductors and a magnetostatic field, which suits inductive wireless power transfer from kilohertz to low megahertz. Ferrite, shielding plates, nearby metal, self-resonance and radiation are not modelled, and a FEM or full-wave tool is the right instrument when they dominate. AirInduct Sim does not publish a head-to-head percentage against commercial FEM packages, because any such figure depends on the mesh and settings chosen. Where the solver integrates on a grid, as for square coils and self-inductance, its built-in check against Grover's formulas measures errors of up to about 4 %.
We integrate Biot–Savart directly and evaluate mutual inductance through the Neumann double integral in its closed elliptic-integral form. There is no FEM mesh to refine, no relaxation parameter, no element order to sweep. The same input always returns the same output.
For the geometries above, the solver is not approximating the reference result — it evaluates the same analytic expression the reference derives. The accuracy question becomes whether the magnetostatic model fits your problem, not whether the numerics converged.
There are no surrogate models, neural nets or curve fits between your geometry and the reported coupling. Every output traces back to a closed-form integral or its standard numerical reduction.
Because the path is analytic, a result you publish today reproduces exactly on any later version, on any platform — the browser and mobile apps run the same kernels.
Mutual inductance, coaxial circular loops
M = μ₀√(R₁R₂)·[(2/k − k)K(k) − (2/k)E(k)]
Maxwell / Neumann; tabulated in Grover (1946) and Babic & Akyel (2008)
Self-inductance, circular loop
L = μ₀R·[ln(8R/a) − 2]
Grover (1946), Table 4. The solver uses a near-field flux integral with no wire-radius input; compared at an assumed 0.5 mm wire radius
On-axis field, circular loop
H₂(0,0,z) = I·R² / [2(R² + z²)^{3/2}]
Biot–Savart, closed form
Skin-effect resistance factor
Exact Bessel-function solution for a cylindrical conductor
Stratton (1941)
Being exact against a closed form is not the same as being right about your hardware. The magnetostatic model assumes the coil is small relative to a wavelength and ignores radiative behaviour, so it is appropriate for inductive WPT in the kilohertz-to-low- megahertz range and not for antenna or radiative problems.
It also treats conductors as filamentary or lightly discretised paths. Strong proximity effects in tightly-packed litz bundles, nearby ferrite and shielding, and lossy or permeable materials in the field volume are approximated or, in some cases, not modelled at all. If those dominate your design, a full-wave or FEM tool is the right instrument and we will say so.
We do not currently publish a head-to-head percentage against commercial FEM packages. Any such figure depends on the geometry, the mesh and the solver settings chosen for the comparison, and a single number quoted out of that context would be marketing rather than evidence.
The closed forms above are standard and independently checkable — you do not have to take our word for any of them. Evaluate the Maxwell–Neumann expression for a pair of coaxial loops in whatever tool you trust, run the same geometry in AirInduct, and compare.
If you find a case where the simulator disagrees with the analytic result, that is a bug and we want it: email info@airinductsim.com with the geometry and we will publish the correction.
