Fast simulation of the Kirchhoff-Carrier string with an energy-storing boundary condition using a Scalar Auxiliary Variable approach

Various string vibration models exist; linear models are common in musical acoustics but lack accuracy for complex phenomena. Nonlinear terms are necessary for pitch glides and modal couplings at higher amplitudes. Realistic boundary conditions are vital, often overlooked for simplicity. This study proposes an efficient time-stepping routine for nonlinear strings with energy-storing boundaries, derived from the Scalar Auxiliary Variable method, allowing fast inversion using the Sherman-Morisson formula.