Supplemental Document forComputational Design of Metallophone Contact Sounds

Accurate simulation is critical for sound design problems. Even a frequency error of a few percent can impact the perceived quality of the results. No matter how robust our optimization scheme, it can be doomed to failure if simulation results do not match real-world outcomes. Many fabrication algorithms in computer graphics rely on linear (referring to the shape function order) tetrahedral finite elements to predict the physical behavior of design instances (e.g., in Bickel et al. [2010]). However, such finite elements are well-known to be extremely inaccurate; worse yet, they do not approach the correct solution value even as the simulation discretization is refined [Hughes 2012]. In this paper we rely on 3rd and 4th order finite elements via COMSOL [2005]. COMSOL also performs online remeshing in order to guarantee solution quality. However, even in the presence of this remeshing scheme experimental evidence (Figure 1) shows that the results produced by our algorithm would not be possible without higherorder finite elements.