soniumElectromagnetics · 29
H(curl) Maxwell, eddy currents, and magnetostatics on affine and curved meshes. Method shown on hover; tolerance is the pass gate. back to QA
| Case | Tier | Reference | Gate |
|---|---|---|---|
fem.hcurl-order2-curved-p2-transfer.v1 | physics-gate | curved same-mesh global-state identity, finite affine-to-curved transfer, typed rejection coverage | curved self-transfer error <= 2e-9; affine-to-curved finite; four typed rejections |
fem.hcurl-cross-space-assembly.v1 | physics-gate | finite/nonzero vector mass, swapped-order transpose parity, malformed-topology rejection | transpose error <= 2e-12; nonzero vector block; at least one typed rejection |
fem.hcurl-curved-cross-space-assembly.v1 | physics-gate | finite/nonzero curved vector mass, swapped-order transpose parity, malformed-topology rejection | curved transpose error <= 2e-10; nonzero vector block; at least one typed rejection |
fem.hcurl-curl-cross-space-assembly.v1 | physics-gate | finite/nonzero physical curl-curl block, swapped-order transpose parity, malformed-topology rejection | transpose error <= 1e-12; nonzero physical block; at least one typed rejection |
fem.hcurl-curved-curl-cross-space-assembly.v1 | physics-gate | independent published Piola reference, finite/nonzero curved blocks, swapped-order transpose parity, malformed-topology rejection | transpose error <= 2e-10 in both dimensions; nonzero physical blocks; typed rejection in both dimensions |
fem.h1-hcurl-commuting-reference.v1 | physics-gate | independent analytical edge line integrals of the affine scalar gradient | checks_passed == 3 |
fem.h1-hcurl-p2-commuting-reference.v1 | physics-gate | independent analytical P2 gradient edge moments and production order-2 H(curl) oriented patch | one independent P2 commuting-reference check passes |
fem.maxwell-coefficient-reference.v1 | physics-gate | independent H(curl) edge-basis quadrature | relative complex mass-matrix error <= 5e-12 |
fem.hcurl-curved-p2-reference.v1 | physics-gate | independent P2 isoparametric physical-coordinate and Jacobian reconstruction | four independent curved H(curl) reference checks pass |
fem.h1-hcurl-curved-p2-commuting-reference.v1 | physics-gate | independent reference-triangle scalar gradient and P2 map Jacobian | field and curl residuals <= 3e-11 |
fem.hcurl-tensor-curved-p2-reference.v1 | physics-gate | independent Q2 isoparametric map and tensor-product Nedelec reference | all coordinate, value, and curl checks pass at the focused numerical thresholds |
fem.hcurl-order1-hanging-edge-contract.v1 | physics-gate | independent geometric edge fractions, MPC recovery, order/tolerance rejection | geometric admission tolerance 1e-10; signed-fraction error <= 1e-12 |
fem.hcurl-order2-hanging-edge-contract.v1 | physics-gate | independent trace matrix, signed orientation, MPC recovery, rejection checks | geometric admission tolerance 1e-10; coefficient/recovery error <= 1e-12 |
fem.hcurl-order2-3d-hanging-face-interior-contract.v1 | physics-gate | pointwise tangential trace identity, complex two-mode face MPC recovery, conforming no-op, and typed rejection | geometric admission tolerance 1e-10; tangential/recovery errors <= 1e-8 |
fem.hcurl-order2-3d-hanging-face-contract.v1 | physics-gate | independent order-2 edge moments, complex multi-master MPC recovery, conforming no-op, and typed rejection | geometric admission tolerance 1e-10; coefficient and recovery errors <= 1e-10 |
fem.hcurl-order1-3d-hanging-face-contract.v1 | physics-gate | independent signed tangential line moments, complex multi-master MPC recovery, conforming no-op, and typed rejection | geometric admission tolerance 1e-10; line-moment and recovery errors <= 1e-11 |
fem.hcurl-order1-3d-hanging-edge-contract.v1 | physics-gate | independent signed line moments, complex MPC recovery, conforming no-op and unsupported-input rejection | geometric admission tolerance 1e-10; signed-fraction and recovery errors <= 1e-12 |
fem.hcurl-order2-periodic-edge-contract.v1 | physics-gate | independent odd/even orientation parity, complex MPC recovery, typed rejection | phase/recovery residual <= 1e-12 |
fem.hcurl-order2-periodic-face-contract.v1 | physics-gate | identity/cyclic/reversed face maps, complex MPC recovery, typed rejection | phase/recovery residual <= 1e-12 |
fem.hcurl-order1-refinement-transfer.v1 | physics-gate | independent affine Nedelec field edge integrals, source-state/order/geometry rejection | edge-moment absolute error <= 1e-10 |
fem.hcurl-order1-curved-transfer.v1 | physics-gate | curved self-recovery, analytic Nedelec edge moments, malformed/order/non-finite rejection | edge-moment absolute error <= 3e-9 |
fem.maxwell-validation.v1 | physics-gate | closed-form cutoff wavenumber, sin(pi x/a) mode shape, and cavity spectrum | waveguide kc error <= 5e-3; cavity k error <= 2e-2; residuals <= 1e-6 |
fem.magnetostatics-validation.v1 | physics-gate | dipole/Biot-Savart closed forms, unshielded baseline, and quadrature-of-analytic energy | dipole/wire field error <= 4e-2; shielding >= 50x with contraction <= 10%; energy <= 2%; inductance <= 8% |
fem.eddy-current-1d-skin-effect.v1 | physics-gate | independent exponential/cosh complex diffusion solution and integrated sheet-current impedance | field <= 4e-2; impedance <= 1.5e-3; phase/depth <= 1e-3; refinement rate >= 0.8; residual <= 1e-10 |
fem.eddy-current-thin-sheet.v1 | physics-gate | independent exponential/cosh complex diffusion solution and integrated sheet-current impedance | field <= 6e-3; impedance <= 3e-5; refinement rate >= 0.8; residual <= 1e-10 |
fem.maxwell-plane-wave.v1 | physics-gate | complex exp(i k x) field and curl, incident-helper differential identities, weak Gauss law | field/curl <= 2e-2; first-order rates >= 0.8; residual/Gauss <= 1e-10; identities <= 1e-6 |
fem.magnetostatics-solenoid.v1 | physics-gate | independent Ampere-law Bz(r), enclosed bore flux and magnetic energy for infinite thick winding | potential/flux/energy <= 2e-3; field <= 2e-2; rates >= 1.5 and 0.8; residual <= 1e-10 |
fem.magnetostatics-dipole.v1 | physics-gate | phi=m.r/(4pi r^3), B=mu*(3r(m.r)/r^5-m/r^3)/(4pi); source moment equals integrated remanence mu*m | fine potential <= 1%, field <= 10%; both errors contract with potential/field rates >= 1.8/0.8; residual <= 1e-9; source moments <= 1e-12 |
fem.magnetostatics-air-gap.v1 | physics-gate | series reluctance R=g/mu0+(1-g)/(mu0*mur), flux=drive/R, total energy=drive^2/(2R), gap energy=B^2*g/(2mu0) | all field/flux/energy comparisons <= 1e-7; residual <= 1e-8; boundary <= 1e-9; 36 actually solved cases |