On numerical methods for acoustic problems

Numerical Methods for High Frequency Acoustic Scattering Problems

Acoustic wave scattering problems arise in application areas as diverse as the modelling of sonar, acoustic noise barriers, and ultrasound. In many practical applications the characteristic length scale L of the domain is large compared to the wavelength  . In such cases the small dimensionless wavelength L /  leads to oscillatory solutions. In order to resolve these solutions, standard numer...

Numerical Methods for Multiscale Problems

[2] J. Bourgain, Fourier Transform Restriction Phenomena for Certain Lattice Subsets and Applications to Nonlinear Evolution Equations, Geometric and Functional Analysis 3 (1993), 107–156. [3] M. Christ, J. Colliander and T. Tao, Instability of the periodic nonlinear Schrödinger equation, Preprint, 2003. [4] M. Hochbruck, A. Ostermann, Explicit exponential Runge-Kutta methods for semilinear par...

2. Numerical methods for nonlinear acoustic resonators

For the study of pressure waves in an oscillating acoustic resonator, one has to solve the compressible NavierStokes equations. The geometry of the resonator strongly influences its resonance frequencies and the nonlinear standing pressure waveform generated within the cavity. Studying the acoustic wave by real physical experiments would be expensive due to the cost of constructing different re...

Numerical Methods for Power-Law Diffusion Problems

Numerical Methods for Scalar Convection-Dominated Problems