vonkarman-modal chain for cymbal-bell-v1
6 changed files+104−0
solutions/cymbal-bell-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-bell-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 at 8 mm and 4 mm spacing, as for the bow, with the bell included in the initial shape. The mounting hole is not represented: the solver closes it, neglecting the mass and stiffness of a 12 mm disk at the apex. The bell flank has a slope of 0.46, beyond the comfort zone of shallow-shell theory, so these solutions carry a modeling error in the bell region in addition to the discretization error. Shell modes are built from the Bogner-Fox-Schmit plate modes of the staircase domain by diagonalizing the membrane stiffening once (the lowest mode is sensitive to the Airy count because of the bell's tight curvature); bases even in y; two-step integrator exact in the linear part; retarded integral of the normal acceleration with distances to the curved top face. Cautions as for the flat disk and the bow: first-order convergence of the radiated ring on staircase grids, and a chaotic response beyond about 0.15 s that puts a floor of roughly 0.6 (waveform) and 0.5 (spectrogram) under the errors between any two solutions.",
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": 11990.4
28+ },
29+ "timing_seconds": 91.638,
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": 13247.1
47+ },
48+ "timing_seconds": 63.168,
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": 13149.7
68+ },
69+ "timing_seconds": 78.71,
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": 14038.5
89+ },
90+ "timing_seconds": 212.295,
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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