Applications of a higher order operator splitting scheme on parabolic-equation methods for modeling underwater sound propagation

2012 ◽  
Vol 132 (3) ◽  
pp. 1973-1973
Author(s):  
Ying-Tsong Lin ◽  
Timothy F. Duda ◽  
Jon M. Collis ◽  
Arthur E. Newhall
Keyword(s):  
Parabolic Equation ◽  
Sound Propagation ◽  
Operator Splitting ◽  
Higher Order ◽  
Splitting Scheme ◽  
Underwater Sound ◽  
Order Operator

scholarly journals Operator splitting around Euler-Maruyama scheme and high order discretization of heat kernels

2020 ◽  
Author(s):  
Toshihiro Yamada ◽  
Yuga Iguchi
Keyword(s):  
Commutative Algebra ◽  
Computational Algorithm ◽  
Diffusion Processes ◽  
Operator Splitting ◽  
Heat Kernels ◽  
Heat Equations ◽  
Discretization Method ◽  
Splitting Scheme ◽  
Order Operator ◽  
Numerical Examples

This paper proposes a general higher order operator splitting scheme for diffusion semigroups using the Baker-Campbell-Hausdorff type commutator expansion of non-commutative algebra and the Malliavin calculus. An accurate discretization method for the fundamental solution of heat equations or the heat kernel is introduced with a new computational algorithm which will be useful for the inference for diffusion processes. The approximation is regarded as the splitting around the Euler-Maruyama scheme for the density. Numerical examples for diffusion processes are shown to validate the proposed scheme.

OS2IFD: A microcomputer implementation of the parabolic equation for predicting underwater sound propagation

1991 ◽  
Vol 17 (6) ◽  
pp. 731-757 ◽  
Author(s):  
J.S. Robertson ◽  
W.L. Siegmann ◽  
M.J. Jacobson
Keyword(s):  
Parabolic Equation ◽  
Sound Propagation ◽  
Underwater Sound

scholarly journals THREE-DIMENSIONAL SOUND PROPAGATION MODELS USING THE PARABOLIC-EQUATION APPROXIMATION AND THE SPLIT-STEP FOURIER METHOD

2013 ◽  
Vol 21 (01) ◽  
pp. 1250018 ◽  
Author(s):  
YING-TSONG LIN ◽  
TIMOTHY F. DUDA ◽  
ARTHUR E. NEWHALL
Keyword(s):  
Parabolic Equation ◽  
Sound Propagation ◽  
Azimuthal Angle ◽  
Three Dimensional ◽  
Fourier Method ◽  
Radial Coordinate ◽  
Underwater Sound ◽  
Propagation Models ◽  
Cylindrical Grid ◽  
Grid Points

The split-step Fourier method is used in three-dimensional parabolic-equation (PE) models to compute underwater sound propagation in one direction (i.e. forward). The method is implemented in both Cartesian (x, y, z) and cylindrical (r, θ, z) coordinate systems, with forward defined as along x and radial coordinate r, respectively. The Cartesian model has uniform resolution throughout the domain, and has errors that increase with azimuthal angle from the x axis. The cylindrical model has consistent validity in each azimuthal direction, but a fixed cylindrical grid of radials cannot produce uniform resolution. Two different methods to achieve more uniform resolution in the cylindrical PE model are presented. One of the methods is to increase the grid points in azimuth, as a function of r, according to nonaliased sampling theory. The other is to make use of a fixed arc-length grid. In addition, a point-source starter is derived for the three-dimensional Cartesian PE model. Results from idealized seamount and slope calculations are shown to compare and verify the performance of the three methods.

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