Download Non-Iterative Schemes for the Simulation of Nonlinear Audio Circuits In this work, a number of numerical schemes are presented in the
context of virtual-analog simulation. The schemes are linearlyimplicit in character, and hence directly solvable without iterative
methods. Schemes of increasing order of accuracy are constructed,
and convergence and stability conditions are proven formally. The
schemes are able to handle stiff problems very efficiently, because
of their fast update, and can be run at higher sample rates to reduce
aliasing. The cases of the diode clipper and ring modulator are
investigated in detail, including several numerical examples.
Download Real-Time Modal Synthesis of Nonlinearly Interconnected Networks Modal methods are a long-established approach to physical modeling sound synthesis. Projecting the equation of motion of a linear, time-invariant system onto a basis of eigenfunctions yields a set of independent forced, lossy oscillators, which may be simulated efficiently and accurately by means of standard time-stepping methods. Extensions of modal techniques to nonlinear problems are possible, though often requiring the solution of densely coupled nonlinear time-dependent equations. Here, an application of recent results in numerical simulation design is employed, in which the nonlinear energy is first quadratised via a convenient auxiliary variable. The resulting equations may be updated in time explicitly, thus avoiding the need for expensive iterative solvers, dense linear system solutions, or matrix inversions. The case of a network of interconnected distributed elements is detailed, along with a real-time implementation as an audio plugin.