vonkarman-modal chain for the 1000 N strike
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solutions/cymbal-flat-disk-v1/vonkarman-modal.jsonadded+101−0View file
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1+{
2+ "schema_version": 1,
3+ "submission_id": "vonkarman-modal",
4+ "challenge_id": "cymbal-flat-disk-v1",
5+ "submitter": {
6+ "name": "Jeremy Magland",
7+ "email": "jmagland@flatironinstitute.org"
8+ },
9+ "date": "2026-09-17",
10+ "description": "Von Karman thin-plate reduction (Airy stress function, in-plane inertia neglected, damping on bending only) of the challenge model on a Cartesian grid: the disk is approximated by the square cells whose centers lie inside it (a staircase boundary) at 8 mm and 4 mm spacing. Linear free-plate modes and clamped Airy modes come from Bogner-Fox-Schmit finite elements on the cells and a sparse shift-invert eigensolver; the bases are restricted to functions even in y, which is exact because the strike is centered on the x axis. The cubic coupling tensor is integrated on the cells, the time stepping is a two-step scheme exact in the linear part, and the retarded Rayleigh integral uses cubic fractional delays. The chain is ordered by grid spacing, number of modes, and time step; the mode truncation caps the frequency the cascade can reach. Caution on the staircase: the free disk's low modes radiate as a near-cancelling sum, and the staircase edge breaks that cancellation. In the linear closed-form solution on the same meshes the ring level after a strike falls from 8 mm to 6, 4 and 3 mm roughly as 4 : 1.7 : 1.25 : 1, while the mode frequencies agree to within a percent, so the 8 mm members ring several times too loud and the 4 mm members are probably still 20 to 30 percent too loud; the large errors between the two grids reflect this, not the number of modes. A boundary-conforming discretization is needed for the radiated pressure to converge.",
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-w100-a100-m2",
16+ "output": "vonkarman-modal/vk-g8-w100-a100-m2.wav",
17+ "method": "von Karman plate (Airy form) on a Cartesian grid masked to the disk, modal method on Bogner-Fox-Schmit modes, Gautschi-type integrator exact in the linear part, retarded Rayleigh integral with cubic fractional delays",
18+ "parameters": {
19+ "grid_spacing_m": 0.008,
20+ "cells": 2024,
21+ "n_dof": 8500,
22+ "transverse_modes": 100,
23+ "basis_even_in_y": true,
24+ "airy_modes": 100,
25+ "oversampling": 2,
26+ "dt_s": 1.0416666666666666e-05,
27+ "highest_transverse_mode_hz": 2776.3
28+ },
29+ "timing_seconds": 56.155,
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-w200-a200-m2",
35+ "output": "vonkarman-modal/vk-g8-w200-a200-m2.wav",
36+ "method": "von Karman plate (Airy form) on a Cartesian grid masked to the disk, modal method on Bogner-Fox-Schmit modes, Gautschi-type integrator exact in the linear part, retarded Rayleigh integral with cubic fractional delays",
37+ "parameters": {
38+ "grid_spacing_m": 0.008,
39+ "cells": 2024,
40+ "n_dof": 8500,
41+ "transverse_modes": 200,
42+ "basis_even_in_y": true,
43+ "airy_modes": 200,
44+ "oversampling": 2,
45+ "dt_s": 1.0416666666666666e-05,
46+ "highest_transverse_mode_hz": 5832.6
47+ },
48+ "timing_seconds": 48.943,
49+ "more_accurate_than": [
50+ "vk-g8-w100-a100-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-w200-a200-m2",
56+ "output": "vonkarman-modal/vk-g4-w200-a200-m2.wav",
57+ "method": "von Karman plate (Airy form) on a Cartesian grid masked to the disk, modal method on Bogner-Fox-Schmit modes, Gautschi-type integrator exact in the linear part, retarded Rayleigh integral with cubic fractional delays",
58+ "parameters": {
59+ "grid_spacing_m": 0.004,
60+ "cells": 8112,
61+ "n_dof": 33268,
62+ "transverse_modes": 200,
63+ "basis_even_in_y": true,
64+ "airy_modes": 200,
65+ "oversampling": 2,
66+ "dt_s": 1.0416666666666666e-05,
67+ "highest_transverse_mode_hz": 5890.6
68+ },
69+ "timing_seconds": 64.792,
70+ "more_accurate_than": [
71+ "vk-g8-w200-a200-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-w300-a300-m2",
77+ "output": "vonkarman-modal/vk-g4-w300-a300-m2.wav",
78+ "method": "von Karman plate (Airy form) on a Cartesian grid masked to the disk, modal method on Bogner-Fox-Schmit modes, Gautschi-type integrator exact in the linear part, retarded Rayleigh integral with cubic fractional delays",
79+ "parameters": {
80+ "grid_spacing_m": 0.004,
81+ "cells": 8112,
82+ "n_dof": 33268,
83+ "transverse_modes": 300,
84+ "basis_even_in_y": true,
85+ "airy_modes": 300,
86+ "oversampling": 2,
87+ "dt_s": 1.0416666666666666e-05,
88+ "highest_transverse_mode_hz": 9000.3
89+ },
90+ "timing_seconds": 203.828,
91+ "more_accurate_than": [
92+ "vk-g4-w200-a200-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-w300-a300-m2.h5",
97+ "format": "hdf5"
98+ }
99+ }
100+ ]
101+}
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