Discrete Wave Model Research Articles

Indoor Sound Source Localization via Inverse Element-Free Simulation Based on Joint Sparse Recovery

Indoor sound source localization is a key technique in many engineering applications, and an inverse element-free method based on joint sparse recovery in a Bayesian framework is proposed for reverberant environments. In this method, a discrete wave model is constructed to represent the relationships between the sampled sound pressure and the source intensity distribution, and localization in the reverberant environment is realized via inversion from the wave model. By constructing a compact supporting domain, the source intensity can be sparsely represented in subdomains, and the sparse Bayesian framework is used to recover the source intensity. In particular, joint sparse recovery in the frequency domain is exploited to improve the recovery performance. Numerical and experimental verifications show that, compared with another state-of-the-art method, the proposed method achieves high source-localization accuracy and low sidelobes with low computational complexity in highly reverberant environments.

Multi-symplectic spectral discretizations for the Zakharov–Kuznetsov and shallow water equations

The time evolution of multi-symplectic PDEs with periodic boundary conditions in one and two space dimensions is considered. We introduce the idea of a multi-symplectic Fourier transformfor systems on periodic domains leading to a semi-discretization on Fourier space, and to the concept of multi-symplecticity on Fourier space. The spatial discretization leads to a discrete lattice model with certain discrete conservation laws imposed on it — a discrete wave model. A by-product of the semi-discretization is that it leads automatically to a system of Hamiltonian ODEs in time when truncated. We show that the one-dimensional shallow water equations and the two-dimensional Zakharov–Kuznetsov equation are multi-symplectic and derive spectral discretizations for these systems and present numerical experiments.

On Stability of Discrete Wave Models with a Not Self-Adjoint Operator

On Stability of Discrete Wave Models with a Not Self-Adjoint Operator