Computing multivalued physical observables for the semiclassical limit of the Schrödinger equation

[1]  Hailiang Liu,et al.  A Level Set Framework for Capturing Multi-Valued Solutions of Nonlinear First-Order Equations , 2006, J. Sci. Comput..

[2]  S. Osher,et al.  Reflection in a Level Set Framework for Geometric Optics , 2004 .

[3]  John H Booske,et al.  Eulerian method for computing multivalued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  B. Engquist,et al.  Regularization Techniques for Numerical Approximation of PDEs with Singularities , 2003, J. Sci. Comput..

[5]  Laurent Gosse,et al.  TWO MOMENT SYSTEMS FOR COMPUTING MULTIPHASE SEMICLASSICAL LIMITS OF THE SCHRÖDINGER EQUATION , 2003 .

[6]  S. Osher,et al.  COMPUTATIONAL HIGH-FREQUENCY WAVE PROPAGATION USING THE LEVEL SET METHOD, WITH APPLICATIONS TO THE SEMI-CLASSICAL LIMIT OF SCHRÖDINGER EQUATIONS∗ , 2003 .

[7]  Chohong Min,et al.  Simplicial isosurfacing in arbitrary dimension and codimension , 2003 .

[8]  Stanley Osher,et al.  A level set method for the computation of multi-valued solutions to quasi-linear hyperbolic PDE's and Hamilton-Jacobi equations , 2003 .

[9]  Shi Jin,et al.  Multi-phase computations of the semiclassical limit of the Schrödinger equation and related problems: Whitham vs Wigner , 2003 .

[10]  B. Engquist,et al.  Computational high frequency wave propagation , 2003, Acta Numerica.

[11]  S. Osher,et al.  A level set-based Eulerian approach for anisotropic wave propagation , 2003 .

[12]  Yoshikazu Giga,et al.  A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations , 2003, Math. Comput..

[13]  L. Gosse Using K-Branch Entropy Solutions for Multivalued Geometric Optics Computations , 2002 .

[14]  Stanley Osher,et al.  Geometric Optics in a Phase-Space-Based Level Set and Eulerian Framework , 2002 .

[15]  Steven J. Ruuth,et al.  A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods , 2002, SIAM J. Numer. Anal..

[16]  P. Markowich,et al.  On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime , 2002 .

[17]  P. Markowich,et al.  Wigner functions versus WKB‐methods in multivalued geometrical optics , 2001, math-ph/0109029.

[18]  Danping Peng,et al.  Weighted ENO Schemes for Hamilton-Jacobi Equations , 1999, SIAM J. Sci. Comput..

[19]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[20]  J. Strain Fast Tree-Based Redistancing for Level Set Computations , 1999 .

[21]  J. Strain Semi-Lagrangian Methods for Level Set Equations , 1999 .

[22]  Peter A. Markowich,et al.  Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit , 1999, Numerische Mathematik.

[23]  Y. Brenier,et al.  Sticky Particles and Scalar Conservation Laws , 1998 .

[24]  Y. Brenier,et al.  A kinetic formulation for multi-branch entropy solutions of scalar conservation laws , 1998 .

[25]  S. Osher,et al.  Regular Article: A PDE-Based Fast Local Level Set Method , 1999 .

[26]  P. Markowich,et al.  Homogenization limits and Wigner transforms , 1997 .

[27]  P. Markowich,et al.  Quantum hydrodynamics, Wigner transforms, the classical limit , 1997 .

[28]  B. Engquist,et al.  Multi-phase computations in geometrical optics , 1996 .

[29]  Y. Egorov,et al.  Fourier Integral Operators , 1994 .

[30]  T. Paul,et al.  Sur les mesures de Wigner , 1993 .

[31]  ShuChi-Wang,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes, II , 1989 .

[32]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[33]  E. Kluk,et al.  A semiclasical justification for the use of non-spreading wavepackets in dynamics calculations , 1984 .

[34]  Johannes J. Duistermaat,et al.  Oscillatory integrals, lagrange immersions and unfolding of singularities , 1974 .

[35]  L. Hörmander Fourier integral operators. I , 1995 .

[36]  Y. Zel’dovich Gravitational instability: An Approximate theory for large density perturbations , 1969 .

[37]  Donald Ludwig,et al.  Uniform asymptotic expansions at a caustic , 1966 .

[38]  Joseph B. Keller,et al.  Corrected bohr-sommerfeld quantum conditions for nonseparable systems , 1958 .

[39]  J. Mayer,et al.  On the Quantum Correction for Thermodynamic Equilibrium , 1947 .

[40]  Eric F Darve,et al.  Author ' s personal copy A hybrid method for the parallel computation of Green ’ s functions , 2009 .