Reword the opening of the background section
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1212 ## Background
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14-Realistic instrument sound generated from physical models is something we would like to have at our fingertips, and producing it is not trivial: it requires coupled elastodynamics and acoustics, stiff time integration, and trade-offs between accuracy and cost that the ear judges harshly, since it detects errors in pitch, decay, and timbre that are easy to miss in a convergence plot. The primary contribution we are after is numerical methods and benchmarks of their accuracy against cost, with instrument sound as the application. The same physics arises in vibroacoustics and acoustic scattering, so the methods should be relevant beyond music.
14+The motivating application for this project is realistic instrument sound generated from physical models. Producing it is not trivial. It requires coupled elastodynamics and acoustics, stiff time integration, and careful trade-offs between accuracy and cost, and the ear judges the result harshly: it detects errors in pitch, decay, and timbre that are easy to miss in a convergence plot. The primary contribution we are after is the numerical methods themselves and benchmarks of their accuracy against cost. The same physics arises in vibroacoustics and acoustic scattering, so the methods should be relevant beyond music.
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1616 Simulation methods are hard to compare fairly unless they are applied to the same problem with the same reference and the same error measures. A challenge here is therefore a fully specified continuum model together with a precisely defined output signal and error measures. The specification states the governing equations, boundary and initial conditions, every parameter in SI units, and exactly how the output is sampled into a file. The intent is that the true solution is a well-defined function that does not depend on any discretization, so that methods of very different kinds, modal, finite difference, finite element, integral equation, can be compared on equal terms. Tiers add realism: toy problems first, then thin plates, then geometric nonlinearity, then radiation into air, up to complete instruments.
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