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

Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

640
James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
640
Line, Surface, and Volume Integrals01:15

Line, Surface, and Volume Integrals

2.8K
A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a prescribed path. If the prescribed path is closed, the integrals reduce to a closed-line integral. The closed-contour integral of the vector field is referred to in terms of the circulation of the vector field around the closed path. A vector with zero circulation around every closed path is called a conservative field, while one with non-zero...
2.8K
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

1.7K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.7K
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

403
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
403
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

3.4K
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.
3.4K
Continuity Equation01:20

Continuity Equation

1.0K
The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area can be written as the surface integral of the current density.
1.0K

You might also read

Related Articles

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

Sort by
Same author

Adenine-DNA adducts derived from the highly tumorigenic Dibenzo[a,l]pyrene are resistant to nucleotide excision repair while guanine adducts are not.

Chemical research in toxicology·2013
Same author

Application of acoustic radiation force impulse imaging for the evaluation of focal liver lesion elasticity.

Hepatobiliary & pancreatic diseases international : HBPD INT·2013
Same author

KLF4 promoted odontoblastic differentiation of mouse dental papilla cells via regulation of DMP1.

Journal of cellular physiology·2013
Same author

Tertiary origin and pleistocene diversification of dragon blood tree (Dracaena cambodiana-Asparagaceae) populations in the Asian tropical forests.

PloS one·2013
Same author

Restoration of miR-1228* expression suppresses epithelial-mesenchymal transition in gastric cancer.

PloS one·2013
Same author

Myeloid differentiation factor 88 promotes growth and metastasis of human hepatocellular carcinoma.

Clinical cancer research : an official journal of the American Association for Cancer Research·2013
Same journal

Correction to: 'Stokes settling and particle-laden plumes: implications for deep-sea mining and volcanic eruption plumes' (2020), by Mingotti et al.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

A stable hothouse triggered by a tipping mechanism.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Beyond distance: quantifying point cloud dynamics with persistent homology and dynamic optimal transport.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Global stability of the Atlantic overturning circulation: edge state, long transients and boundary crisis under CO2 forcing.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Morse index classification and landscape of Kuramoto system for Hebbian-based binary pattern recognition.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Interpretable and equation-free response theory for complex systems.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
See all related articles

Related Experiment Video

Updated: Sep 11, 2025

Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

10.4K

Efficient integral equation solvers for layered-medium scattering problems.

Tao Yin1, Lu Zhang2

  • 1State Key Laboratory of Mathematical Sciences and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|August 14, 2025
PubMed
Summary
This summary is machine-generated.

This study presents accurate boundary integral equation (BIE) solvers for layered-medium scattering problems, using the windowed Green's function (WGF) and perfectly matched layer (PML) methods. These novel approaches avoid computationally expensive Sommerfeld integrals for enhanced efficiency in acoustic, elastic, and electromagnetic simulations.

Keywords:
acousticelasticelectromagneticintegral equationlayered media

More Related Videos

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

541
In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
06:49

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

Published on: March 2, 2021

6.3K

Related Experiment Videos

Last Updated: Sep 11, 2025

Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

10.4K
Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics
10:23

Author Spotlight: Computing the Effects of a Local Radiofrequency Hyperthermia Intervention on Tumor Biomechanics

Published on: December 1, 2023

541
In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation
06:49

In situ Grazing Incidence Small Angle X-ray Scattering on Roll-To-Roll Coating of Organic Solar Cells with Laboratory X-ray Instrumentation

Published on: March 2, 2021

6.3K

Area of Science:

  • Computational electromagnetics
  • Wave scattering theory
  • Numerical analysis

Background:

  • Layered-medium scattering problems are crucial in various physics and engineering domains.
  • Traditional boundary integral equation (BIE) methods often rely on computationally intensive Green's functions.
  • Efficient solvers are needed to overcome the limitations of existing numerical techniques.

Purpose of the Study:

  • To present and validate accurate BIE solvers for acoustic, elastic, and electromagnetic layered-medium scattering.
  • To introduce and detail the windowed Green's function (WGF) method and the perfectly matched layer (PML)-based BIE method.
  • To demonstrate that these methods circumvent the need for expensive Sommerfeld integrals.

Main Methods:

  • The windowed Green's function (WGF) method utilizes the free-space Green's function (FGF) with operator windowing and a correction strategy.
  • The perfectly matched layer (PML)-based BIE method employs PML to truncate the domain, transforming the FGF for BIEs on local defects.
  • Both methods are formulated to avoid the use of layer Green's functions with Sommerfeld integrals.

Main Results:

  • Numerical examples validate the accuracy and effectiveness of both the WGF and PML-BIE methods.
  • The presented solvers demonstrate high accuracy in solving complex layered-medium scattering problems.
  • The methods offer a computationally efficient alternative to standard approaches.

Conclusions:

  • The WGF and PML-BIE methods provide accurate and efficient solutions for layered-medium scattering problems.
  • These techniques successfully avoid the computational burden associated with Sommerfeld integrals.
  • The study opens avenues for further research in advanced computational electromagnetics.