This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely used iterative Bregman projections algorithm (or Sinkhorn–Knopp algorithm). We first proposed to rely on regularized nonlinear acceleration schemes. In practice, such approaches lead to fast algorithms, but their global convergence is not ensured. Hence, we next proposed a new algorithm with convergence guarantees. The idea is to overrelax the Bregman projection operators, allowing for faster convergence. We proposed a simple method for establishing global convergence by ensuring the decrease of a Lyapunov function at each step. An adaptive choice of the overrelaxation parameter based on the Lyapunov function was constructed. We also suggested a heuristic to choose a suitable asymptotic overrelaxation parameter, based on a local convergence analysis. Our numerical experiments showed a gain in convergence speed by an order of magnitude in certain regimes.

Accurate modeling of the acoustic propagation in tubes of varying cross section in musical acoustics must include the effects of the viscous and thermal boundary layers. Models of viscothermal losses are classically written in the frequency domain. An approximate time-domain model is proposed in which all of the physical parameters of the instrument, the bore shape or the wave celerity, are explicit coefficients. The model depends on absolute tabulated constants, which only reflect that the pipe is axisymmetric. It can be understood as a telegrapher's equations augmented by an adjustable number of auxiliary unknowns. A global energy is dissipated. A time discretization based on variational approximation is proposed along with numerical experiments and comparisons with other models.

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