Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Parseval's Theorem for Fourier transform01:15

Parseval's Theorem for Fourier transform

884
Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a...
884
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

66
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
66
Convergence of Fourier Series01:21

Convergence of Fourier Series

130
The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...
130
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

2.6K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
2.6K
Navier–Stokes Equations01:28

Navier–Stokes Equations

430
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
430
Trigonometric Fourier series01:17

Trigonometric Fourier series

244
Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
244

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Dynamically orthogonal narrow-angle parabolic equations for stochastic underwater sound propagation. Part I: Theory and schemes.

The Journal of the Acoustical Society of America·2024
Same author

Dynamically orthogonal narrow-angle parabolic equations for stochastic underwater sound propagation. Part II: Applications.

The Journal of the Acoustical Society of America·2024
Same author

Generalized neural closure models with interpretability.

Scientific reports·2023
Same author

Single-shot link discovery for terahertz wireless networks.

Nature communications·2020

Related Experiment Video

Updated: Jun 9, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.6K

Range-dynamical low-rank split-step Fourier method for the parabolic wave equation.

Aaron Charous1, Pierre F J Lermusiaux1

  • 1Department of Mechanical Engineering, Center for Computational Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

The Journal of the Acoustical Society of America
|October 30, 2024
PubMed
Summary

A new low-rank split-step Fourier method significantly accelerates numerical solutions for the parabolic wave equation. This efficient approach enables high-frequency acoustic simulations on larger domains, even on laptops.

More Related Videos

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

8.6K
Quantitative Locomotion Study of Freely Swimming Micro-organisms Using Laser Diffraction
10:03

Quantitative Locomotion Study of Freely Swimming Micro-organisms Using Laser Diffraction

Published on: October 25, 2012

11.5K

Related Experiment Videos

Last Updated: Jun 9, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.6K
Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

8.6K
Quantitative Locomotion Study of Freely Swimming Micro-organisms Using Laser Diffraction
10:03

Quantitative Locomotion Study of Freely Swimming Micro-organisms Using Laser Diffraction

Published on: October 25, 2012

11.5K

Area of Science:

  • Computational physics
  • Acoustics
  • Numerical analysis

Background:

  • Numerical solutions to the parabolic wave equation face challenges with dimensionality and the Nyquist criterion.
  • Existing methods are computationally expensive and require significant storage.

Purpose of the Study:

  • To develop a novel range-dynamical low-rank split-step Fourier method.
  • To overcome the limitations of traditional methods for solving the parabolic wave equation.
  • To enable efficient, high-frequency acoustic simulations on larger scales.

Main Methods:

  • A new range-dynamical low-rank split-step Fourier method is introduced.
  • The integration scheme exhibits sub-linear scaling with transverse degrees of freedom.
  • A rank-adaptive scheme optimizes low-rank equations for accuracy and efficiency.

Main Results:

  • The new method is orders of magnitude faster and requires less storage than the full-rank algorithm.
  • Simulations can be performed on laptops, enabling higher frequencies and larger domains.
  • Analysis of acoustic pressure, transmission loss, and phase in realistic ocean environments demonstrates the method's effectiveness.

Conclusions:

  • The developed method offers a significant improvement for solving the parabolic wave equation.
  • It facilitates more accessible and efficient acoustic simulations.
  • The rank-adaptive approach ensures accurate and efficient approximations.