{
 "challenge_id": "plate-strike-v1",
 "title": "Struck free aluminum plate: radiated pressure",
 "generated": "2026-09-17T18:04:09+00:00",
 "metrics": [
  "waveform_l2",
  "spectrogram_l2"
 ],
 "primary_metric": "waveform_l2",
 "reference": "plate-solutions/kirchhoff-bfs/bfs-n48",
 "reference_selection": {
  "reference": "plate-solutions/kirchhoff-bfs/bfs-n48",
  "rule": "partial-order-agreement",
  "candidates": [
   {
    "candidate": "plate-solutions/kirchhoff-bfs/bfs-n48",
    "pairs_total": 0,
    "pairs_preserved": 0,
    "score": null,
    "convergence_gap": 0.040946219169599264,
    "mean_error_to_other_candidates": 0.0,
    "violated_pairs": []
   }
  ]
 },
 "order_violations_vs_reference": [],
 "solutions": [
  {
   "key": "plate-solutions/kirchhoff-bfs/bfs-n48",
   "source": "plate-solutions",
   "source_url": "https://vault1.magland.org/challenges/plate-solutions",
   "submission_id": "kirchhoff-bfs",
   "submission_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solutions/plate-strike-v1/kirchhoff-bfs.json",
   "solution_id": "bfs-n48",
   "submitter": "Jeremy Magland",
   "date": "2026-09-17",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
    "elements_per_side": 48,
    "element_size_m": 0.00635,
    "n_dof": 9604,
    "n_modes": 5041,
    "rigid_modes": 3,
    "mode_cutoff_hz": 200000.0
   },
   "timing_seconds": 491.104,
   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "code_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solvers/kirchhoff-bfs/kl_bfs_plate.py",
   "viz_url": "https://vault1.magland.org/challenges/plate-solutions/site/",
   "fields_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solutions/plate-strike-v1/kirchhoff-bfs/bfs-n48.h5",
   "more_accurate_than": [
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   ],
   "notes": "lowest nonrigid mode frequencies (Hz): 36.32, 53.005, 67.183, 94.365, 94.365, 167.748",
   "audio": "audio/plate-solutions/kirchhoff-bfs/bfs-n48.wav",
   "peak": 0.49692749977111816,
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    "waveform_l2": 0.0,
    "spectrogram_l2": 0.0
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   "is_reference": true
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   "source": "plate-solutions",
   "source_url": "https://vault1.magland.org/challenges/plate-solutions",
   "submission_id": "kirchhoff-bfs",
   "submission_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solutions/plate-strike-v1/kirchhoff-bfs.json",
   "solution_id": "bfs-n32",
   "submitter": "Jeremy Magland",
   "date": "2026-09-17",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
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    "element_size_m": 0.009525,
    "n_dof": 4356,
    "n_modes": 4078,
    "rigid_modes": 3,
    "mode_cutoff_hz": 200000.0
   },
   "timing_seconds": 154.684,
   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "code_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solvers/kirchhoff-bfs/kl_bfs_plate.py",
   "viz_url": "https://vault1.magland.org/challenges/plate-solutions/site/",
   "fields_url": null,
   "more_accurate_than": [
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   "notes": "lowest nonrigid mode frequencies (Hz): 36.32, 53.005, 67.183, 94.365, 94.365, 167.748",
   "audio": "audio/plate-solutions/kirchhoff-bfs/bfs-n32.wav",
   "peak": 0.49696794152259827,
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   "source_url": "https://vault1.magland.org/challenges/plate-solutions",
   "submission_id": "kirchhoff-bfs",
   "submission_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solutions/plate-strike-v1/kirchhoff-bfs.json",
   "solution_id": "bfs-n24",
   "submitter": "Jeremy Magland",
   "date": "2026-09-17",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
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    "element_size_m": 0.0127,
    "n_dof": 2500,
    "n_modes": 2496,
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    "mode_cutoff_hz": 200000.0
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   "timing_seconds": 63.718,
   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "code_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solvers/kirchhoff-bfs/kl_bfs_plate.py",
   "viz_url": "https://vault1.magland.org/challenges/plate-solutions/site/",
   "fields_url": null,
   "more_accurate_than": [
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   "notes": "lowest nonrigid mode frequencies (Hz): 36.32, 53.005, 67.183, 94.365, 94.365, 167.749",
   "audio": "audio/plate-solutions/kirchhoff-bfs/bfs-n24.wav",
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   "submission_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solutions/plate-strike-v1/kirchhoff-bfs.json",
   "solution_id": "bfs-n16",
   "submitter": "Jeremy Magland",
   "date": "2026-09-17",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
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   "code_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solvers/kirchhoff-bfs/kl_bfs_plate.py",
   "viz_url": "https://vault1.magland.org/challenges/plate-solutions/site/",
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   "more_accurate_than": [
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   "notes": "lowest nonrigid mode frequencies (Hz): 36.32, 53.005, 67.183, 94.366, 94.366, 167.755",
   "audio": "audio/plate-solutions/kirchhoff-bfs/bfs-n16.wav",
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   "source": "plate-solutions",
   "source_url": "https://vault1.magland.org/challenges/plate-solutions",
   "submission_id": "kirchhoff-bfs",
   "submission_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solutions/plate-strike-v1/kirchhoff-bfs.json",
   "solution_id": "bfs-n12",
   "submitter": "Jeremy Magland",
   "date": "2026-09-17",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
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   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "code_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solvers/kirchhoff-bfs/kl_bfs_plate.py",
   "viz_url": "https://vault1.magland.org/challenges/plate-solutions/site/",
   "fields_url": null,
   "more_accurate_than": [
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   "notes": "lowest nonrigid mode frequencies (Hz): 36.32, 53.006, 67.184, 94.368, 94.368, 167.77",
   "audio": "audio/plate-solutions/kirchhoff-bfs/bfs-n12.wav",
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   "source": "plate-solutions",
   "source_url": "https://vault1.magland.org/challenges/plate-solutions",
   "submission_id": "kirchhoff-bfs",
   "submission_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solutions/plate-strike-v1/kirchhoff-bfs.json",
   "solution_id": "bfs-n8",
   "submitter": "Jeremy Magland",
   "date": "2026-09-17",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
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   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "code_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solvers/kirchhoff-bfs/kl_bfs_plate.py",
   "viz_url": "https://vault1.magland.org/challenges/plate-solutions/site/",
   "fields_url": null,
   "more_accurate_than": [
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   "notes": "lowest nonrigid mode frequencies (Hz): 36.322, 53.008, 67.19, 94.383, 94.383, 167.852",
   "audio": "audio/plate-solutions/kirchhoff-bfs/bfs-n8.wav",
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   "submission_id": "kirchhoff-bfs",
   "submission_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solutions/plate-strike-v1/kirchhoff-bfs.json",
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   "viz_url": "https://vault1.magland.org/challenges/plate-solutions/site/",
   "fields_url": null,
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   "notes": "lowest nonrigid mode frequencies (Hz): 36.345, 53.051, 67.284, 94.598, 94.598, 168.854",
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   "plate-solutions/kirchhoff-bfs/bfs-n48": {
    "plate-solutions/kirchhoff-bfs/bfs-n4": 1.084271626155645,
    "plate-solutions/kirchhoff-bfs/bfs-n8": 0.6875193596883752,
    "plate-solutions/kirchhoff-bfs/bfs-n12": 0.38824241661402376,
    "plate-solutions/kirchhoff-bfs/bfs-n16": 0.1902090668255135,
    "plate-solutions/kirchhoff-bfs/bfs-n24": 0.059970556088690063,
    "plate-solutions/kirchhoff-bfs/bfs-n32": 0.02022473549295553,
    "plate-solutions/kirchhoff-bfs/bfs-n48": 0.0
   }
  }
 },
 "submissions": [
  {
   "schema_version": 1,
   "submission_id": "kirchhoff-bfs",
   "challenge_id": "plate-strike-v1",
   "submitter": {
    "name": "Jeremy Magland",
    "email": "jmagland@flatironinstitute.org"
   },
   "date": "2026-09-17",
   "description": "Kirchhoff-Love thin-plate reduction of the challenge model, solved with Bogner-Fox-Schmit C1 finite elements on uniform meshes, a closed-form modal time response, and an exact evaluation of the retarded Rayleigh integral. This is a thin-plate approximation, so its converged limit differs from the three-dimensional model that defines the challenge. Ordered by mesh refinement.",
   "code_url": "https://vault1.magland.org/challenges/plate-solutions/blob/main/solvers/kirchhoff-bfs/kl_bfs_plate.py",
   "viz_url": "https://vault1.magland.org/challenges/plate-solutions/site/",
   "key": "plate-solutions/kirchhoff-bfs",
   "source": "plate-solutions",
   "source_url": "https://vault1.magland.org/challenges/plate-solutions"
  }
 ]
}