- Lee , D. , Saad , Y. , Schultz , M. H. , Lee , D. , Sternberg , R. L. and Schultz , M. H. 1988 . “ An Efficient Method for Solving the Three-dimensional Wide Angle Wave Equation ” . In Computatonal Acoustics-Wave Propogation Edited by: Schultz , M. H. 75 – 90 . Amsternam, North-Holland
- Lee , D. 1988 . “ Ocean Acoustic Propagation by Finite Difference Methods ” . In Peragamon Press , Oxford .
- Nagem R. J. Lee D. A Formulation of the Parabolic fluid-Elastic Interface Conditions in preparation
- Nagem , R. J. , Lee , D. and Chen , T. 1995 . Modeling Elastic Wave Propagation in the Ocean Bottom . J. Math. Modelling and Scientific Computing , 2 ( 4 ) : 1 – 10 .
- Lee , D. , Nagem , R. J. , Li , G. , Teng , Y. , Lee , D. , Pao , Y. , Schultz , M. H. and Teng , Y. 1996 . “ A Numerical Solution of Parabolic Elastic Wave Equation ” . In in Proc. 2nd Int'l Conf. Theo. and comp. Acoust. , Edited by: Teng , Y. Singapore : World Scientific Pub. Co. .
- Lee , D. and Nagem , R. J. 1996 . “ An Onterface Model for Coupled Fluid-Elastic Parabolic Equation ” . In Proc. 3rd European Conf. Underwater Acoust , Edited by: Papadakis , J.S. Vol. 1 , 159 – 164 . Heraklion : Forth-Iacm .
- Achebach , J. D. 1987 . “ Wave Propagation in Elastic Solids ” . North-Holland
- Lee , D. and Papadakis , J. S. 1980 . Numerical Solutions of the Parabolic Wave Equation: An Ordinary-differential-equation Approach . J. Acoust. Soc. Am. , 68 ( 5 ) : 1482 – 1488 .
- Papadakis , J. S. 1994 . Exact, Nonreflecting Bouondary Conditions for the Parabolic-type Approximations in Underwater Acoustics . J. Comp. Acoust. , 2 ( 2 ) : 83 – 98 .
- McCoy , J. J. 1977 . A Parabolic Theory of Stress Wave Propagation Through Inhomogeneous Linearly Elastic Solids . J. Applied Mechanics , 44 ( 2 ) : 462 – 468 .
- Shang , C. and Lee , D. 1989 . A Numerical Treatment of the Fluid/Elastic Interface Under Range-dependent environments . J. Acoust. Soc. Am. , 85 ( 2 ) : 654 – 660 .
- Tappert , F. D. , Keller , J. B. and Papadakis , J. S. 1977 . “ The Parabolic Equation Approximation Method ” . In in Wave propagation and Underwater Acoustics , Edited by: Papadakis , J. S. Vol. 70 , 224 – 284 . Heidlberg : Spring-Verlag .
- Mathews , J. H. 1992 . “ Numerical Methods for Mathematics, Science, and Engineering ” . 2 Englewood Cliffs, Jersey : Prentice Hall .
- Lee , D. and Schultz , M. H. 1995 . “ Numerical Ocean acoustic Propagation in Three Dimensions ” . In World Sci. Pub. Co. Singapore
- Botseas , G. , Lee , D. and King , D. “ FORD3D: A Computer Model for Solving the LSS Three-dimensional Wide Angle Wave Equation ” . In U.S. Naval Underwater Systems Center TR 7943, 1987
- Schmidt , H. 1990 . “ SAFARI, Seismo-Acoustic Fast Field Algorithm for Range Independent Environments, User's Guide ” . In Saclant SR-113 Saclantcen La Spezia, , Italy
- Greene , R. R. 1985 . A High-Angle One-way Wave equation for Siesmic Wave Propagation Along Rough and Sloping Interfaces . J. Acous. Soc. Am. , 77 : 1991 – 1998 .
- Thomson , D. J. and Mayfield , M. E. 1994 . An Exact Radiation Condition for Use with a Posterior PE method . J. Comp. Acoust , 2 ( 2 ) : 113 – 133 .
- Collins , M. D. , Lee , D. , Cakmak , A. and Vichnevetsky , R. 1990 . “ Higher-order and Elastic Parabolic Equations for Wave Propagation in the Ocean ” . In Computational Acoustics: Seismo-Ocean Acoustics and Modeling Edited by: Vichnevetsky , R. 167 – 184 . North-Holland, Amsterdam
- Colloins , M. D. , Chin-Bing , S. A. , King , D. B. , Davis , J. A. and Evans , R. B. “ Higher-order, Energy-Conserving, Two-way, and Elastic Parabolic Equation ” . In PE Workshoop II - Proc. nd Parabolic Equation Workshop Edited by: Evans , R. B.
- Hudson , J. A. 1980 . A Parabolic Approximation for Elastic Waves . Wave Motion , 2 : 207 – 214 .
- Wales , S. C. and McCoy , J. J. 1983 . A Comparison of Parabolic Wave Theories for Linearly Elastic Solids . Wave Motion , 5 : 99 – 113 .
- Wetton , B. T. R. , Brooke , G. , Lee , D. , Cakmak , A. and Vichnevetsky , R. 1990 . “ One-way Seismos-Acoustic Propagation in Elastic Waveguides with Range-dependent Material Parameters ” . In Computational Acoustics: Seismo-Acoustics and Modeling Edited by: Vichnevetsky , R. 275 – 288 . North-Holland, Amsterdam
- Wetton , B. T. R. and Brooke , G. 1990 . One-way Wave Equations for Seismoacoustic Propagation in ElasticWaveguides . J. Acoust. Soc. Am. , 87 : 624 – 632 .
- Lee , D. , Nagem , R. J. and Resasco , D. C. 1997 . Numerical Computation of Elastic Wave Equations . Journal of Computational Acoustics , 5 ( 2 ) : 157 – 176 .
- Lee , D. , Schultz , M. H. , Siegmann , W. L. and Mary , D. F. 1992 . A Numerical Marching Scheme to Compute Scattering in the Ocean . J. Math. Comput. Simulations , 34 ( 2 ) : 525 – 540 .
- Lee , D. 1974 . “ Nonlinear Multistep Methods for Solving Initial Value Problems in Ordinary Differential Equations ” . In Ph.D. dissertation Polytechnic Institute of New York
- Lee , D. and Preiser , S. 1978 . A Class of Nonlinear Multistep Multistep A-stable Numerical Methods for Solving Stiff Differential Equations . Comput. Math. Appl. , 4 ( 1 ) : 43 – 51 .
- Henrici , H. 1962 . “ Discrete Variable Methods in Ordinary Differential Equations ” . Wiley, New York
- Keller , H. B. 1968 . “ Numerical Methods for Two-Point Boundary Problems ” . Blaisdell, Waltham MA
A coupled 3D fluid-elastic wave propagation model: mathematical formulation and analysis
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