Numerical solution of the high frequency asymptotic expansion for the scalar wave equation
Journal of Computational Physics
One-dimensional transport equations with discontinuous coefficients
Nonlinear Analysis: Theory, Methods & Applications
Sticky Particles and Scalar Conservation Laws
SIAM Journal on Numerical Analysis
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
Journal of Computational Physics
High-frequency wave propagation by the segment projection method
Journal of Computational Physics
Using K-branch entropy solutions for multivalued geometric optics computations
Journal of Computational Physics
Numerical Approximations of Pressureless and Isothermal Gas Dynamics
SIAM Journal on Numerical Analysis
A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations
Journal of Scientific Computing
Computing multi-valued velocity and electric fields for 1D Euler--Poisson equations
Applied Numerical Mathematics
Journal of Computational Physics
A Bloch band based level set method for computing the semiclassical limit of Schrödinger equations
Journal of Computational Physics
Bloch decomposition-based Gaussian beam method for the Schrödinger equation with periodic potentials
Journal of Computational Physics
Hi-index | 31.47 |
We present a computational approach for the WKB approximation of the wave function of an electron moving in a periodic one-dimensional crystal lattice. We derive a nonstrictly hyperbolic system for the phase and the intensity where the flux functions originate from the Bloch spectrum of the Schrödinger operator. Relying on the framework of the multibranch entropy solutions introduced by Brenier and Corrias, we compute efficiently multiphase solutions using well adapted and simple numerical schemes. In this first part we present computational results for vanishing exterior potentials which demonstrate the effectiveness of the proposed method.