vonkarman-modal chain for cymbal-tapered-v1
6 changed files+104−0
solutions/cymbal-tapered-v1/vonkarman-modal.jsonadded+101−0View file
@@ -0,0 +1,101 @@
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+}
solutions/cymbal-tapered-v1/vonkarman-modal/vk-g4-w400-a400-m2.wavadded+0−0View file
Binary file not shown.
solutions/cymbal-tapered-v1/vonkarman-modal/vk-g4-w600-a600-m2.h5added+3−0View file
@@ -0,0 +1,3 @@
1+version https://git-lfs.github.com/spec/v1
2+oid sha256:90da49eea24e5b95dd649a953b1f19bea3073efdef402dcbe38e36a0d6fdf91d
3+size 31570290
solutions/cymbal-tapered-v1/vonkarman-modal/vk-g4-w600-a600-m2.wavadded+0−0View file
Binary file not shown.
solutions/cymbal-tapered-v1/vonkarman-modal/vk-g8-w200-a200-m2.wavadded+0−0View file
Binary file not shown.
solutions/cymbal-tapered-v1/vonkarman-modal/vk-g8-w400-a400-m2.wavadded+0−0View file
Binary file not shown.