{ "challenge_id": "cymbal-tapered-v1", "title": "Bowed, belled and hammered bronze disk lathed to a tapered thickness, struck with a drum stick, geometrically nonlinear: radiated pressure", "generated": "2026-09-17T20:36:16+00:00", "metrics": [ "waveform_l2", "spectrogram_l2" ], "primary_metric": "waveform_l2", "reference": "cymbal-solutions/vonkarman-modal/vk-g4-w600-a600-m2", "reference_selection": { "reference": "cymbal-solutions/vonkarman-modal/vk-g4-w600-a600-m2", "rule": "partial-order-agreement", "candidates": [ { "candidate": "cymbal-solutions/vonkarman-modal/vk-g4-w600-a600-m2", "pairs_total": 0, "pairs_preserved": 0, "score": null, "convergence_gap": 1.5986096057719428, "mean_error_to_other_candidates": 0.0, "violated_pairs": [] } ] }, "order_violations_vs_reference": [], "solutions": [ { "key": "cymbal-solutions/vonkarman-modal/vk-g4-w600-a600-m2", "source": "cymbal-solutions", "source_url": "https://vault1.magland.org/challenges/cymbal-solutions", "submission_id": "vonkarman-modal", "submission_url": "https://vault1.magland.org/challenges/cymbal-solutions/blob/main/solutions/cymbal-tapered-v1/vonkarman-modal.json", "solution_id": "vk-g4-w600-a600-m2", "submitter": "Jeremy Magland", "date": "2026-09-17", "method": "Marguerre shallow shell (Airy form) on a Cartesian grid masked to the disk, modal method on shell modes built from Bogner-Fox-Schmit plate modes with variable thickness, Gautschi-type integrator exact in the linear part, retarded Rayleigh-type integral with cubic fractional delays", "parameters": { "grid_spacing_m": 0.004, "cells": 8112, "n_dof": 33268, "transverse_modes": 600, "basis_even_in_y": false, "airy_modes": 600, "oversampling": 2, "dt_s": 1.0416666666666666e-05, "highest_transverse_mode_hz": 14584.7 }, "timing_seconds": 1364.02, "hardware": "Intel(R) Xeon(R) w5-3435X (32 threads), numpy/scipy for the setup; 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the Airy modes are the eigenfunctions of the variable-coefficient compatibility operator. Full modal basis (the dents break the symmetry): 200 and 400 modes at 8 mm, 400 and 600 at 4 mm. The dents are a millimeter deep in a rim that is 0.7 mm thick, and the 8 mm cells barely resolve them, so the 8 mm members are coarse. The hole is closed (a stated approximation); the bell flank exceeds the shallow-shell range; the staircase boundary makes the radiated ring converge only at first order; and the response is chaotic beyond about 0.15 s, so errors between any two solutions have a floor of roughly 0.6 (waveform) and 0.5 (spectrogram).", "code_url": "https://vault1.magland.org/challenges/cymbal-solutions/blob/main/solvers/vonkarman-modal-disk/vk_modal_disk.py", "viz_url": "https://vault1.magland.org/challenges/cymbal-solutions/site/", "key": "cymbal-solutions/vonkarman-modal", "source": "cymbal-solutions", "source_url": "https://vault1.magland.org/challenges/cymbal-solutions" } ] }