The adiabatic mode parabolic equation

A method is developed for increasing the efficiency of broadband parabolic equation modeling. For broadband adiabatic mode calculations, the smoothness of the wavenumbers and mode functions in frequency permits interpolation across frequency. In order to permit frequency interpolation, the pressure field computed by the PE is transformed to mode space and the complex mode amplitudes are interpolated across frequency. For mildly range dependent environments a speed increase of a factor of ten can be achieved. A convergence test of propagation through internal waves indicates that a frequency interpolation across four frequencies is possible.

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Three-dimensional adiabatic mode parabolic equation method and its applications

Acta Physica Sinica ◽

10.7498/aps.65.034301 ◽

2016 ◽

Vol 65 (3) ◽

pp. 034301

Author(s):

Qin Ji-Xing ◽

Katsnelson Boris ◽

Peng Zhao-Hui ◽

Li Zheng-Lin ◽

Zhang Ren-He ◽

...

Keyword(s):

Parabolic Equation ◽

Three Dimensional ◽

Equation Method ◽

Parabolic Equation Method ◽

Adiabatic Mode

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Numerical solution of the three-dimensional parabolic equation with non-standard boundary conditions

Applied Mathematics and Computation ◽

10.1016/s0096-3003(02)00083-8 ◽

2002 ◽

Author(s):

M Dehghan

Keyword(s):

Parabolic Equation ◽

Boundary Conditions ◽

Numerical Solution ◽

Three Dimensional

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Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2002.7.1.15204 ◽

2002 ◽

Vol 7 (1) ◽

pp. 93-104 ◽

Cited By ~ 10

Author(s):

Mifodijus Sapagovas

Keyword(s):

Parabolic Equation ◽

Parabolic Equations ◽

Existence And Uniqueness ◽

Nonlocal Condition ◽

Nonlocal Conditions ◽

Numerical Algorithms ◽

Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

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