Simulation of the geometrically exact nonlinear string via energy quadratisation

String vibration represents an active field of research in acoustics. Small-amplitude is often assumed, leading to simplified physical models that can be simulated efficiently. However, the inclusion nonlinear phenomena due larger string stretchings necessary capture important features, and efficient numerical algorithms are currently lacking this context. Of available techniques, many lead schemes which may only solved iteratively, resulting high computational cost, additional concerns existence uniqueness solutions. Slow fast waves present concurrently transverse longitudinal directions motion, adding further complications concerning dispersion. This work presents a linearly-implicit scheme for simulation geometrically exact model. The conserves energy, expressed as sum quadratic terms only, including auxiliary state variable yielding effects. allows treat separately, using mixed finite difference/modal two motion. A matrix decomposition algorithm presented, so sparse full parts update separately. Numerical experiments presented throughout. • linearly implicit space–time discretisation case wave equation. one single linear system. energy conserved machine accuracy. Use appropriate free parameters increases wideband resolution