{
 "schema_version": 1,
 "submission_id": "vonkarman-modal",
 "challenge_id": "cymbal-bell-v1",
 "submitter": {
  "name": "Jeremy Magland",
  "email": "jmagland@flatironinstitute.org"
 },
 "date": "2026-09-17",
 "description": "Marguerre shallow-shell reduction of the challenge model (Airy stress function with the initial shape, in-plane inertia neglected, damping proportional to the full linearized stiffness) on a Cartesian grid at 8 mm and 4 mm spacing, as for the bow, with the bell included in the initial shape. The mounting hole is not represented: the solver closes it, neglecting the mass and stiffness of a 12 mm disk at the apex. The bell flank has a slope of 0.46, beyond the comfort zone of shallow-shell theory, so these solutions carry a modeling error in the bell region in addition to the discretization error. Shell modes are built from the Bogner-Fox-Schmit plate modes of the staircase domain by diagonalizing the membrane stiffening once (the lowest mode is sensitive to the Airy count because of the bell's tight curvature); bases even in y; two-step integrator exact in the linear part; retarded integral of the normal acceleration with distances to the curved top face. Cautions as for the flat disk and the bow: first-order convergence of the radiated ring on staircase grids, and a chaotic response beyond about 0.15 s that puts a floor of roughly 0.6 (waveform) and 0.5 (spectrogram) under the errors between any two solutions.",
 "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/",
 "solutions": [
  {
   "solution_id": "vk-g8-w100-a100-m2",
   "output": "vonkarman-modal/vk-g8-w100-a100-m2.wav",
   "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, Gautschi-type integrator exact in the linear part, retarded Rayleigh-type integral with cubic fractional delays",
   "parameters": {
    "grid_spacing_m": 0.008,
    "cells": 2024,
    "n_dof": 8500,
    "transverse_modes": 100,
    "basis_even_in_y": true,
    "airy_modes": 100,
    "oversampling": 2,
    "dt_s": 1.0416666666666666e-05,
    "highest_transverse_mode_hz": 11990.4
   },
   "timing_seconds": 91.638,
   "more_accurate_than": [],
   "hardware": "Intel(R) Xeon(R) w5-3435X (32 threads), numpy/scipy for the setup; coupling tensor and time stepping on NVIDIA RTX 6000 Ada Generation (PyTorch 2.14.0+cu130)"
  },
  {
   "solution_id": "vk-g8-w200-a200-m2",
   "output": "vonkarman-modal/vk-g8-w200-a200-m2.wav",
   "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, Gautschi-type integrator exact in the linear part, retarded Rayleigh-type integral with cubic fractional delays",
   "parameters": {
    "grid_spacing_m": 0.008,
    "cells": 2024,
    "n_dof": 8500,
    "transverse_modes": 200,
    "basis_even_in_y": true,
    "airy_modes": 200,
    "oversampling": 2,
    "dt_s": 1.0416666666666666e-05,
    "highest_transverse_mode_hz": 13247.1
   },
   "timing_seconds": 63.168,
   "more_accurate_than": [
    "vk-g8-w100-a100-m2"
   ],
   "hardware": "Intel(R) Xeon(R) w5-3435X (32 threads), numpy/scipy for the setup; coupling tensor and time stepping on NVIDIA RTX 6000 Ada Generation (PyTorch 2.14.0+cu130)"
  },
  {
   "solution_id": "vk-g4-w200-a200-m2",
   "output": "vonkarman-modal/vk-g4-w200-a200-m2.wav",
   "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, 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": 200,
    "basis_even_in_y": true,
    "airy_modes": 200,
    "oversampling": 2,
    "dt_s": 1.0416666666666666e-05,
    "highest_transverse_mode_hz": 13149.7
   },
   "timing_seconds": 78.71,
   "more_accurate_than": [
    "vk-g8-w200-a200-m2"
   ],
   "hardware": "Intel(R) Xeon(R) w5-3435X (32 threads), numpy/scipy for the setup; coupling tensor and time stepping on NVIDIA RTX 6000 Ada Generation (PyTorch 2.14.0+cu130)"
  },
  {
   "solution_id": "vk-g4-w300-a300-m2",
   "output": "vonkarman-modal/vk-g4-w300-a300-m2.wav",
   "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, 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": 300,
    "basis_even_in_y": true,
    "airy_modes": 300,
    "oversampling": 2,
    "dt_s": 1.0416666666666666e-05,
    "highest_transverse_mode_hz": 14038.5
   },
   "timing_seconds": 212.295,
   "more_accurate_than": [
    "vk-g4-w200-a200-m2"
   ],
   "hardware": "Intel(R) Xeon(R) w5-3435X (32 threads), numpy/scipy for the setup; coupling tensor and time stepping on NVIDIA RTX 6000 Ada Generation (PyTorch 2.14.0+cu130)",
   "fields": {
    "path": "vonkarman-modal/vk-g4-w300-a300-m2.h5",
    "format": "hdf5"
   }
  }
 ]
}