A fast level set method for propagating interfaces
Journal of Computational Physics
The sharpness of Kuznetsov's ODx L1 -error estimate for monotone difference schemes
Mathematics of Computation
Multi-phase computations in geometrical optics
Journal of Computational and Applied Mathematics - Special issue on TICAM symposium
Semi-Lagrangian methods for level set equations
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Motion of curves in three spatial dimensions using a level set approach
Journal of Computational Physics
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
Journal of Computational Physics
Journal of Computational Physics
A Wigner-Measure Analysis of the Dufort--Frankel Scheme for the Schrödinger Equation
SIAM Journal on Numerical Analysis
Using K-branch entropy solutions for multivalued geometric optics computations
Journal of Computational Physics
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
Local level set method in high dimension and codimension
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
Discretization of Dirac delta functions in level set methods
Journal of Computational Physics
The numerical approximation of a delta function with application to level set methods
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A Level Set Framework for Capturing Multi-Valued Solutions of Nonlinear First-Order Equations
Journal of Scientific Computing
Journal of Computational Physics
Two methods for discretizing a delta function supported on a level set
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Geometric integration over irregular domains with application to level-set methods
Journal of Computational Physics
A semiclassical transport model for two-dimensional thin quantum barriers
Journal of Computational Physics
High order numerical methods to a type of delta function integrals
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
High Order Numerical Quadratures to One Dimensional Delta Function Integrals
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Eulerian Gaussian beams for Schrödinger equations in the semi-classical regime
Journal of Computational Physics
High order numerical methods to two dimensional delta function integrals in level set methods
Journal of Computational Physics
A Hybrid Phase-Flow Method for Hamiltonian Systems with Discontinuous Hamiltonians
SIAM Journal on Scientific Computing
Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation
Journal of Computational Physics
Journal of Computational Physics
High Order Numerical Methods to Three Dimensional Delta Function Integrals in Level Set Methods
SIAM Journal on Scientific Computing
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We develop a fourth order numerical method for the computation of multivalued physical observables (density, momentum, etc.) in the semiclassical limit of the one-dimensional linear Schrödinger equation in the case of discontinuous potentials. We adopt the level set framework developed in (Jin et al. in J. Comput. Phys. 210:497---518, 2005) which allows one to compute the multivalued physical observables via solving the classical Liouville equation with bounded initial data and approximating delta function integrals. We achieve high order accuracy for our method by studying two issues. The first is to highly accurately compute the solution and its derivatives of the Liouville equation with bounded initial data and discontinuous potentials. The second is to design high order numerical methods to evaluate one-dimensional delta function integrals with discontinuous kernel functions. Numerical examples are presented to verify that our method achieves the fourth order L 1-norm accuracy for computing multivalued physical observables of the one-dimensional linear Schrödinger equation with general discontinuous potentials.