Helmholtz Scattering — frequency-domain EM scattering L1-233

ElectromagneticsFrequency-domain vector Helmholtz scatteringδ=5 · challengingL_DAG = 3.2📋 Stub — not mineable

📋

Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

Read the contribution guide →Open a claim issue →

Forward model E

c u r l c u r l E - k^{2} E = J_{s} r c; E_{s} c a t = (e x p (- j \cdot k \cdot r) /4 p i / r) f (t h e t a, p hi) a t f a r - f i e l d

Helmholtz Scattering — frequency-domain EM scattering forward model.

L-DAG

L.incident_wave -> L.scatter_boundary -> L.green_function -> int.frequency

L.incident_waveL.scatter_boundaryL.green_functionint.frequency

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 800

Conditional stability; mismatch parameters dominate at Omega bounds.

Solvability C

Solver class:: MoM-EFIE, MLFMA, FEM-Helmholtz
Convergence rate q:: 2
Complexity:: O(N log N) per iteration

Specs (0)

No L2 specs registered yet for this principle.