1{
2 "schema_version": 1,
3 "submission_id": "vonkarman-modal",
4 "challenge_id": "cymbal-bow-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 (Airy stress function with the initial shape, in-plane inertia neglected, damping proportional to the full linearized stiffness) on a Cartesian grid: the disk is approximated by the square cells whose centers lie inside it at 8 mm and 4 mm spacing. Shell modes are built from the Bogner-Fox-Schmit plate modes of the staircase domain by diagonalizing the membrane stiffening once; the bases are even in y (exact for this strike). The cubic and quadratic coupling tensors are integrated on the cells, the time stepping is a two-step scheme exact in the linear part, and the retarded integral of the normal acceleration uses the distances to the curved top face with cubic fractional delays. The chain is ordered by grid spacing, number of modes, and time step. Two cautions: the staircase boundary makes the radiated ring converge only at first order in the spacing (see the flat-disk submission), and at this strike the response is chaotic beyond about 0.15 s, so two identical runs differ by about 0.66 in the waveform error and 0.5 in the spectrogram error; differences below that level between solutions are not meaningful.",
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": "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",
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": 2849.5
28 },
29 "timing_seconds": 147.298,
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": "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",
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": 5866.3
47 },
48 "timing_seconds": 62.814,
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": "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",
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": 5928.5
68 },
69 "timing_seconds": 79.08,
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": "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",
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": 9023.3
89 },
90 "timing_seconds": 212.743,
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}