The discrete one-sided Lipschitz condition for convex scalar conservation laws
SIAM Journal on Numerical Analysis
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Numerical solution of the high frequency asymptotic expansion for the scalar wave equation
Journal of Computational Physics
Journal of Computational Physics
Multi-phase computations in geometrical optics
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
One-dimensional transport equations with discontinuous coefficients
Nonlinear Analysis: Theory, Methods & Applications
Mathematics of Computation
A fixed grid method for capturing the motion of self-intersecting wavefronts and related PDEs
Journal of Computational Physics
High-frequency wave propagation by the segment projection method
Journal of Computational Physics
Kinetic Semidiscretization of Scalar Conservation Laws and Convergence by Using Averaging Lemmas
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A level set based Eulerian method for paraxial multivalued traveltimes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Computing multi-valued velocity and electric fields for 1D Euler--Poisson equations
Applied Numerical Mathematics
Journal of Computational Physics
A quadrature-based third-order moment method for dilute gas-particle flows
Journal of Computational Physics
Superposition of Multi-Valued Solutions in High Frequency Wave Dynamics
Journal of Scientific Computing
Journal of Scientific Computing
Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation
Journal of Computational Physics
Bloch decomposition-based Gaussian beam method for the Schrödinger equation with periodic potentials
Journal of Computational Physics
Realizable high-order finite-volume schemes for quadrature-based moment methods
Journal of Computational Physics
Conditional quadrature method of moments for kinetic equations
Journal of Computational Physics
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This paper is devoted to a numerical simulation of the classical WKB system arising in geometric optics expansions. It contains the nonlinear eikonal equation and a linear conservation law whose coefficient can be discontinuous. We address the problem of treating it in such a way that superimposed signals can be reproduced by means of the kinetic formulation of "multibranch solutions," originally due to Brenier and Corrias. Some existence and uniqueness results are given, together with computational test cases of increasing difficulty displaying up to five multivaluations.