These are working notes, not marketing. Each one is a piece of Nabla's own development written up: the method, why that method and not another, what it measured out at, and where it stops working. Where a result is unflattering it is published with the rest — a solver you can only see the good runs of is not one you can trust.
Open-boundary FEA without a giant air box
A Dirichlet box twenty times the device radius is mostly wasted mesh. A
far-field (balloon) boundary matches it at three — 0.09 %
against 12.5 % for Dirichlet at the same radius. The maths, the
measured error table, the axisymmetric 1/r subtlety, and the
two settings you have to get right.
Second-order (P2) elements: a coarse mesh that beats a fine one
In a P1 triangle B is constant, and everything an engineer
wants is computed from B. On a PMSM air gap, coarse P2 lands
an order of magnitude closer to the converged answer than P1 on a
4×-finer mesh — plus the three implementation details that
decide whether you actually get that accuracy.
Two rotors in one model
Most 2D tools move exactly one part. Several simultaneous sliding-band motion zones — counter-rotating rotors, magnetic gears, a rotor plus a linear mover — come down to one line of relative-displacement geometry. Verified by two rotors reporting equal and opposite torque from independent contour integrals.
Second-order time integration, and the trap underneath it
Backward Euler is first order and damps what it cannot resolve. Crank–Nicolson measures 100 to 500 times more accurate at the same time step — but only once the algebraic (air) rows of the FEM system are handled as the differential-algebraic system they are.
Force on a part that touches another part
Maxwell stress needs air around the body. For two iron parts in contact the total force is well defined and the split between them is not — it depends on the stress model. What the coenergy (Korteweg–Helmholtz) tensor gives you, and the invariant that tells you whether the answer is sound.
Giving an LLM a FEM solver
Nabla ships an MCP server, so a language model can draw, mesh, solve and read results directly. Wiring it up is a weekend; making it trustworthy is the project — read-back verification, an explicit model state machine, long-running jobs, and peak-preserving decimation that does not delete the answer.
Everything here is testable on your own machine. Nabla Free is permanent, needs no licence key, and opens every example model on the site.