Babich’s Expansion and High-Order Eulerian Asymptotics for Point-Source Helmholtz Equations

[1]  Jianliang Qian,et al.  Fast Huygens sweeping methods for Helmholtz equations in inhomogeneous media in the high frequency regime , 2014, J. Comput. Phys..

[2]  Jianliang Qian,et al.  High-Order Factorization Based High-Order Hybrid Fast Sweeping Methods for Point-Source Eikonal Equations , 2014, SIAM J. Numer. Anal..

[3]  Jianliang Qian,et al.  Fast Sweeping Methods for Factored Anisotropic Eikonal Equations: Multiplicative and Additive Factors , 2012, J. Sci. Comput..

[4]  Jianliang Qian,et al.  Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes , 2011, J. Comput. Phys..

[5]  Chi-Wang Shu,et al.  Fast Sweeping Fifth Order WENO Scheme for Static Hamilton-Jacobi Equations with Accurate Boundary Treatment , 2010, J. Sci. Comput..

[6]  Jianliang Qian,et al.  A stopping criterion for higher-order sweeping schemes for static Hamilton-Jacobi equations , 2010 .

[7]  Hongkai Zhao,et al.  Fast sweeping method for the factored eikonal equation , 2009, J. Comput. Phys..

[8]  Randall J. LeVeque,et al.  Finite difference methods for ordinary and partial differential equations - steady-state and time-dependent problems , 2007 .

[9]  Hongkai Zhao,et al.  High Order Fast Sweeping Methods for Static Hamilton–Jacobi Equations , 2006, J. Sci. Comput..

[10]  Linbin Zhang,et al.  Eikonal solver in the celerity domain , 2005 .

[11]  S. Osher,et al.  Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations , 2004 .

[12]  Jianliang Qian,et al.  A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations , 2003, J. Sci. Comput..

[13]  Jean-David Benamou,et al.  An Introduction to Eulerian Geometrical Optics (1992–2002) , 2003, J. Sci. Comput..

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

[15]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[16]  John E. Vidale,et al.  Rapid calculation of seismic amplitudes , 1990 .

[17]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[18]  Joseph B. Keller,et al.  The high‐frequency asymptotic field of a point source in an inhomogeneous medium , 1963 .

[19]  Kristian Kirsch,et al.  Theory Of Ordinary Differential Equations , 2016 .

[20]  Jesse Freeman,et al.  in Morse theory, , 1999 .

[21]  Jianliang Qian,et al.  Adaptive Finite Difference Method For Traveltime And Amplitude , 1999 .

[22]  A. Pica.  Fast And Accurate Finite-difference Solutions of the 3D Eikonal Equation Parametrized In Celerity , 1997 .

[23]  J. Ortega.  Matrix Theory: A Second Course , 1987 .

[24]  V. M. Babich.  The short wave asymptotic form of the solution for the problem of a point source in an inhomogeneous medium , 1965 .