Mesh and materials

The Mesh stage turns the drawing into a physical problem: MagFEM detects the closed regions, you say what each one is made of, where current flows and what the boundary conditions are, and then the triangle mesh is generated.

Regions

Every area closed by curves becomes a region, detected automatically and numbered (“Region 1”, “Region 2”…). Construction lines do not form regions. A region keeps what was assigned to it even when the drawing changes: it is identified by an interior point, like FEMM block labels.

  • Click a region in the drawing to select it; double-click its name (in the tree) to rename it.

  • The region label can be dragged in the drawing.

  • A region without a material is left out of the mesh (as in FEMM).

Overlapping curves

Two lines lying on top of each other along the same stretch do not close regions properly. Split the lines where they meet (the trim tool helps) instead of overlapping them.

Materials

Under Mesh › Materials, each region has a searchable material list. The library lives in the right drawer (Problem and libraries › Materials):

  • Groups: air, conductors, steels (with B-H curves), magnets and your own.

  • Properties: relative permeability μr, conductivity σ (MS/m), remanence Br (T) for magnets, color, and the Steinmetz coefficients for iron losses (k_h, α, k_e; used in AC analysis).

  • B-H curve: materials with a curve are nonlinear. The curve opens in its own tab, with linear or log scales.

  • FEMM 4.2 library: 245 ready materials in the search. Import from FEMM… also reads the matlib.dat of your installation.

  • For magnets, the magnetization direction (angle) is set on the region.

  • Laminated sheets (Construction › Laminated sheets): stacking factor \(f\) and sheet thickness \(d\). The field uses the equivalent material \(B = f\,B_{steel}(H) + (1-f)\,\mu_0 H\) (induced voltage and force come out right with the full depth); there are no bulk eddy currents; iron losses are in the steel volume (\(f\,V\)) with \(B_{steel} = B/f\). Without \(k_e\), it is computed from the thickness: \(k_e = \pi^2 \sigma d^2/6\) (enter the sheet’s \(\sigma\)).

Circuits and currents

Under Mesh › Circuits, + creates a circuit. In the region properties, connect it to a circuit with a number of turns; negative turns reverse the direction (the go and return sides of a coil).

The current is a source of the analysis, so it lives under Solver › (physics) › Currents: in A, it accepts variables and, in transient analysis, functions of t such as 2*sin(2*pi*60*t). Each physics has its own currents: changing the static current does not change the transient or AC one. Without a value of its own, a physics uses the circuit’s default current.

  • Every region of a circuit carries the same current (a series circuit). The “parallel” type of FEMM files is kept, but splitting the current among parallel regions is not implemented yet.

  • A region can also have its own current, without a circuit.

The current density is J = N·I / region area.

Coil wire (in the region properties): round by AWG or by diameter, or rectangular (width × height), with parallel strands. The DC R becomes \(R = |N|\,\ell/(\sigma A_{turn})\), with \(\ell = 2\pi r\) in axisymmetric problems or the depth in planar ones (no end turns), and the circuit table shows the fill factor \(|N|\,A_{turn}/A_{region}\) (above 100 %, the turns do not fit). Without a wire, the whole region counts as copper. In harmonic analysis, the wire also gives the skin and proximity losses and the AC R (see Results).

Boundaries

The outer border of the domain automatically belongs to Dirichlet (A = 0): flux does not cross it. For other boundaries, click the edges in the drawing (Shift for several) and choose the boundary; the types live in the right drawer, with the same names as in FEMM:

Type

Condition

Use

Prescribed A (Dirichlet)

A = A0 + A1·x + A2·y (x, y in m)

A = 0 at the border; a uniform field imposed with A1/A2

Neumann

∂A/∂n = 0

magnetic symmetry: flux crosses the curve at right angles

Mixed (Robin)

ν ∂A/∂n + c0·A + c1 = 0

asymptotic open boundary: c0 = 1/(μ0·R), c1 = 0, with R the domain radius in m

Periodic

equal A on the curve pair

repeats the domain (one pole of a machine)

Antiperiodic

A with opposite sign on the pair

half a period

Periodic and antiperiodic link pairs of curves: select both. The mesh is generated with matching nodes on the two curves. The “small skin depth”, “strategic dual image” and “periodic air gap” types exist so FEMM files can be read, but they are not solved yet.

In axisymmetric problems the r = 0 axis always has A = 0 (ψ = r·A vanishes on the axis).

Generating the mesh

The mesh uses Tangle, the FEMM mesh generator (by David Meeker, MIT license), compiled to WebAssembly.

  • Elements: default element size (empty = automatic) and minimum angle (quality: no triangle will have a smaller interior angle; 30° is a good default, 34° is the maximum accepted). ▶ generates the mesh.

  • Regions: element size per region, to refine where the field changes most (air gap, corners, core).

  • Per curve: size along chosen curves (m.curve_size in the console).

  • The Elements properties show nodes, triangles, the smallest angle and the time, with a quality map.

Solving without a mesh generates it first, automatically.