{
 "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/",
 "solutions": [
  {
   "solution_id": "bfs-n4",
   "output": "kirchhoff-bfs/bfs-n4.wav",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
    "elements_per_side": 4,
    "element_size_m": 0.0762,
    "n_dof": 100,
    "n_modes": 100,
    "rigid_modes": 3,
    "mode_cutoff_hz": 200000.0
   },
   "timing_seconds": 0.861,
   "more_accurate_than": [],
   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "notes": "lowest nonrigid mode frequencies (Hz): 36.345, 53.051, 67.284, 94.598, 94.598, 168.854"
  },
  {
   "solution_id": "bfs-n8",
   "output": "kirchhoff-bfs/bfs-n8.wav",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
    "elements_per_side": 8,
    "element_size_m": 0.0381,
    "n_dof": 324,
    "n_modes": 324,
    "rigid_modes": 3,
    "mode_cutoff_hz": 200000.0
   },
   "timing_seconds": 3.321,
   "more_accurate_than": [
    "bfs-n4"
   ],
   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "notes": "lowest nonrigid mode frequencies (Hz): 36.322, 53.008, 67.19, 94.383, 94.383, 167.852"
  },
  {
   "solution_id": "bfs-n12",
   "output": "kirchhoff-bfs/bfs-n12.wav",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
    "elements_per_side": 12,
    "element_size_m": 0.0254,
    "n_dof": 676,
    "n_modes": 676,
    "rigid_modes": 3,
    "mode_cutoff_hz": 200000.0
   },
   "timing_seconds": 8.639,
   "more_accurate_than": [
    "bfs-n8"
   ],
   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "notes": "lowest nonrigid mode frequencies (Hz): 36.32, 53.006, 67.184, 94.368, 94.368, 167.77"
  },
  {
   "solution_id": "bfs-n16",
   "output": "kirchhoff-bfs/bfs-n16.wav",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
    "elements_per_side": 16,
    "element_size_m": 0.01905,
    "n_dof": 1156,
    "n_modes": 1156,
    "rigid_modes": 3,
    "mode_cutoff_hz": 200000.0
   },
   "timing_seconds": 17.946,
   "more_accurate_than": [
    "bfs-n12"
   ],
   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "notes": "lowest nonrigid mode frequencies (Hz): 36.32, 53.005, 67.183, 94.366, 94.366, 167.755"
  },
  {
   "solution_id": "bfs-n24",
   "output": "kirchhoff-bfs/bfs-n24.wav",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
    "elements_per_side": 24,
    "element_size_m": 0.0127,
    "n_dof": 2500,
    "n_modes": 2496,
    "rigid_modes": 3,
    "mode_cutoff_hz": 200000.0
   },
   "timing_seconds": 63.718,
   "more_accurate_than": [
    "bfs-n16"
   ],
   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "notes": "lowest nonrigid mode frequencies (Hz): 36.32, 53.005, 67.183, 94.365, 94.365, 167.749"
  },
  {
   "solution_id": "bfs-n32",
   "output": "kirchhoff-bfs/bfs-n32.wav",
   "method": "Kirchhoff-Love plate, Bogner-Fox-Schmit C1 finite elements, closed-form modal time response, exact retarded Rayleigh integral",
   "parameters": {
    "elements_per_side": 32,
    "element_size_m": 0.009525,
    "n_dof": 4356,
    "n_modes": 4078,
    "rigid_modes": 3,
    "mode_cutoff_hz": 200000.0
   },
   "timing_seconds": 154.684,
   "more_accurate_than": [
    "bfs-n24"
   ],
   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "notes": "lowest nonrigid mode frequencies (Hz): 36.32, 53.005, 67.183, 94.365, 94.365, 167.748"
  },
  {
   "solution_id": "bfs-n48",
   "output": "kirchhoff-bfs/bfs-n48.wav",
   "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,
   "fields": {
    "path": "kirchhoff-bfs/bfs-n48.h5",
    "format": "hdf5"
   },
   "more_accurate_than": [
    "bfs-n32"
   ],
   "hardware": "Intel Xeon workstation, single process, numpy/scipy (LAPACK eigh)",
   "notes": "lowest nonrigid mode frequencies (Hz): 36.32, 53.005, 67.183, 94.365, 94.365, 167.748"
  }
 ]
}