Numerics — FEM formulation, solvers, and quantities of interest

• Numerics — FEM formulation, solvers, and quantities of interest (overview) - The finite-element formulation, solvers and quantities of interest, with the measurements behind each choice.
• 1. Discretisation - The discretisation: elements, spaces and assembly.
• 2. Axisymmetric weak forms - The axisymmetric weak forms, the axis and the quadrature order that avoids NaN.
• 3. Nondimensionalisation - The nondimensionalisation and the scales that keep every field of order one.
• 4. Stabilisation - Stabilisation: the mode as built and what each term does.
• 5. Nonlinear solution - The nonlinear solution: damped Newton, convergence tests and the continuation ladder.
• 6. Linear solvers - Linear solvers, with UMFPACK and SuperLU measured at production size.
• 7. Quantities of interest — and the flux trap - The quantities of interest, the flux trap and the routes that extract them.
• 8. Mesh resolution and adaptivity - Mesh resolution and adaptivity, measured against the reference mesh.
• 8.1 NGSolve traps found by implementing this — all silent - NGSolve traps found by implementing the model, all of them silent.
• 9. Unverified / to measure - Items still unverified or to be measured.
• Tier-1 test evidence: norms and the attribution identity (WP45 item 20) - What the Tier-1 tests of norms and the attribution identity establish, recorded at WP45 item 20.
• Tier-1 test evidence: the Langevin cutoff (WP45 item 21) - What the Tier-1 tests of the Langevin cutoff establish, recorded at WP45 item 21.
• Tier-1 test evidence: the domain indicator and the quality measures (WP45 item 22) - What the Tier-1 tests of the domain indicator and the quality measures establish, recorded at WP45 item 22.
• Tier-1 test evidence: Newton's counterexamples, the band and the vector indicator (WP45 item 23) - What the Tier-1 tests of Newton's counterexamples, the band and the vector indicator establish, recorded at WP45 item 23.
• Tier-1 test evidence: scaling, the wall-distance clamp and the warm-start rationale (WP45 item 24) - What the Tier-1 tests of scaling, the wall-distance clamp and the warm-start rationale establish, recorded at WP45 item 24.
• Tier-2 test evidence: ladder walks, block systems and extraction routes (WP45 item 25) - What the Tier-2 tests of ladder walks, block systems and extraction routes establish, recorded at WP45 item 25.
• Tier-3 test evidence: the mesh geometry digest (WP45 item 27) - What the Tier-3 tests of the mesh geometry digest establish, recorded at WP45 item 27.