1{
2 "schema_version": 1,
3 "submission_id": "vonkarman-modal",
4 "challenge_id": "cymbal-tapered-v1",
5 "submitter": {
6 "name": "Jeremy Magland",
7 "email": "jmagland@flatironinstitute.org"
8 },
9 "date": "2026-09-17",
10 "description": "Marguerre shallow-shell reduction of the challenge model on a Cartesian grid at 8 mm and 4 mm spacing, as for the hammered cymbal, with the thickness taper entering the mass, the bending stiffness and the membrane compliance 1/(E h) as Gauss-point coefficients of the assembled operators; 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).",
11 "code_url": "https://vault1.magland.org/challenges/cymbal-solutions/blob/main/solvers/vonkarman-modal-disk/vk_modal_disk.py",
12 "viz_url": "https://vault1.magland.org/challenges/cymbal-solutions/site/",
13 "solutions": [
14 {
15 "solution_id": "vk-g8-w200-a200-m2",
16 "output": "vonkarman-modal/vk-g8-w200-a200-m2.wav",
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",
18 "parameters": {
19 "grid_spacing_m": 0.008,
20 "cells": 2024,
21 "n_dof": 8500,
22 "transverse_modes": 200,
23 "basis_even_in_y": false,
24 "airy_modes": 200,
25 "oversampling": 2,
26 "dt_s": 1.0416666666666666e-05,
27 "highest_transverse_mode_hz": 10644.3
28 },
29 "timing_seconds": 72.53,
30 "more_accurate_than": [],
31 "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)"
32 },
33 {
34 "solution_id": "vk-g8-w400-a400-m2",
35 "output": "vonkarman-modal/vk-g8-w400-a400-m2.wav",
36 "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",
37 "parameters": {
38 "grid_spacing_m": 0.008,
39 "cells": 2024,
40 "n_dof": 8500,
41 "transverse_modes": 400,
42 "basis_even_in_y": false,
43 "airy_modes": 400,
44 "oversampling": 2,
45 "dt_s": 1.0416666666666666e-05,
46 "highest_transverse_mode_hz": 16678.6
47 },
48 "timing_seconds": 399.021,
49 "more_accurate_than": [
50 "vk-g8-w200-a200-m2"
51 ],
52 "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)"
53 },
54 {
55 "solution_id": "vk-g4-w400-a400-m2",
56 "output": "vonkarman-modal/vk-g4-w400-a400-m2.wav",
57 "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",
58 "parameters": {
59 "grid_spacing_m": 0.004,
60 "cells": 8112,
61 "n_dof": 33268,
62 "transverse_modes": 400,
63 "basis_even_in_y": false,
64 "airy_modes": 400,
65 "oversampling": 2,
66 "dt_s": 1.0416666666666666e-05,
67 "highest_transverse_mode_hz": 12904.8
68 },
69 "timing_seconds": 478.696,
70 "more_accurate_than": [
71 "vk-g8-w400-a400-m2"
72 ],
73 "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)"
74 },
75 {
76 "solution_id": "vk-g4-w600-a600-m2",
77 "output": "vonkarman-modal/vk-g4-w600-a600-m2.wav",
78 "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",
79 "parameters": {
80 "grid_spacing_m": 0.004,
81 "cells": 8112,
82 "n_dof": 33268,
83 "transverse_modes": 600,
84 "basis_even_in_y": false,
85 "airy_modes": 600,
86 "oversampling": 2,
87 "dt_s": 1.0416666666666666e-05,
88 "highest_transverse_mode_hz": 14584.7
89 },
90 "timing_seconds": 1364.02,
91 "more_accurate_than": [
92 "vk-g4-w400-a400-m2"
93 ],
94 "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)",
95 "fields": {
96 "path": "vonkarman-modal/vk-g4-w600-a600-m2.h5",
97 "format": "hdf5"
98 }
99 }
100 ]
101}