Oscillating sphere
A 30,000-element dual-BIE FMM model is compared with angular and frequency-domain analytical solutions from 20–1000 Hz.
Verification and accuracy
Acoustic BEM results checked against analytical solutions
The cases cover exterior and interior domains, radiation and scattering, pressure, velocity and impedance boundary conditions, and low-to-high frequency behavior.
Primary benchmark
Radiation from a vibrating sphere
A monopole at (R/2, 0, 0) produces a nonuniform velocity boundary condition on a unit sphere. Benchmark models range from 588 to 14,520,000 DOF at ka=2 and 20.
Boundary pressure
Computed pressure on the sphere at ka=20.
Exterior field
Boundary and field-surface pressure for the same radiation case.
V9 performance
Millions of unknowns on a laptop
Using four of twenty threads on an Intel Core i7-13800H laptop, the 14.52-million-DOF FMM case required 580.97 seconds at ka=2 and 1,102.88 seconds at ka=20 in the current V9 benchmark workbook.
These values supersede the older 15- and 20-minute wording previously shown on this page.
Radiation and interior fields
Frequency response and resonant behavior
Interior vibrating sphere
FMM center-pressure results from 20–2000 Hz track the analytical response and its resonant peaks.
Scattering
Rigid and pressure-release surfaces
Rigid sphere, ka=20
10,800-element FMM model with a reported maximum polar-pressure error of 0.18%.
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Rigid sphere, ka=100
187,500-element ACA model with a reported maximum polar-pressure error of 3.21%.
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Soft sphere, ka=20
Pressure-release boundary case with a reported maximum polar-pressure error of 0.45%.
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Exterior field surface
Pressure contours show the incident and scattered-field interaction around the sphere.
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Sources and boundaries
Interior source and impedance checks
Monopole and dipole in a cube
A 10,800-element rigid cube compares frequency responses at a field point with analytical monopole and dipole solutions from 20–500 Hz.
View pressure contour
Vibrating box channel
A 51,600-element ACA model at ka=100 reports less than 2% maximum pressure error along the channel axis.
Watch animationImpedance tube
An 8,400-element FMM model at ka=30 reports 1.85% maximum pressure error against the analytical solution.
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High-frequency radiating box
The HFBEM predicts far-field SPL from 20–2000 Hz using less than 1% of the reported conventional-BEM CPU time for this case.
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Reproduce the verification workflow
Use the Verification Manual and included sample models to examine inputs, analytical references, and expected results.