Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Electrostatic Boundary Conditions in Dielectrics

Electrostatic Boundary Conditions in Dielectrics

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.

Electrostatic Boundary Conditions

Electrostatic Boundary Conditions

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...

Partial Differential Equations

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...

Standing Waves in a Cavity

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:

Mesh Analysis for AC Circuits

Mesh Analysis for AC Circuits

In the domain of radio communication, the significance of impedance matching must be considered. It is crucial to ensure the efficient transmission of signals between radio transmitters and receivers. Achieving this balance involves using impedance-matching circuits, with one fundamental configuration comprising a resistor, capacitor, and inductor.
The process of harmonizing these impedances begins with a clear understanding of the input and output signals. Once these signals are known, the...

Magnetostatic Boundary Conditions

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...

You might also read

Related Articles

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

Sort by

Same author

Delayed Cardiovascular Response to Acute Hypotension in Heart Failure Patients Compared to Healthy Adults.

International journal of vascular medicine·2026

Same author

Integrating new fruit and vegetable growth parameters in SWAT models for improved simulations.

Frontiers in plant science·2026

Same author

Reconfigurable metasurface polarization rotator utilizing a phase-shifter-loaded truncated patch.

Optics express·2025

Same author

Black South Africans Who Migrate Away From Their Rural Homes and Their Chances of Having Abdominal Obesity.

American journal of human biology : the official journal of the Human Biology Council·2025

Same author

The nexus of the risk of depression and residential mobility for urban poor mothers: New longitudinal evidence from Nairobi.

SSM. Mental health·2025

Same author

Correction: Evaluation of flood metrics across the Mississippi-Atchafalaya River Basin and their relation to flood damages.

PloS one·2025

Search research articles

Related Experiment Video

Updated: Jul 4, 2026

Tracking Infiltration Front Depth Using Time-lapse Multi-offset Gathers Collected with Array Antenna Ground Penetrating Radar

Tracking Infiltration Front Depth Using Time-lapse Multi-offset Gathers Collected with Array Antenna Ground Penetrating Radar

Published on: May 1, 2018

Multilevel fast multipole algorithm for acoustic wave scattering by truncated ground with trenches.

Mei Song Tong¹, Weng Cho Chew, Michael J White

¹Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. meisongt@uiuc.edu

The Journal of the Acoustical Society of America

|June 6, 2008

Summary

The multilevel fast multipole algorithm (MLFMA) efficiently analyzes acoustic wave scattering from large, complex shapes. This enhanced method, using the Nystrom method, tackles problems with millions of unknowns for noise mitigation applications.

More Related Videos

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Published on: August 21, 2018

Related Experiment Videos

Last Updated: Jul 4, 2026

Tracking Infiltration Front Depth Using Time-lapse Multi-offset Gathers Collected with Array Antenna Ground Penetrating Radar

Tracking Infiltration Front Depth Using Time-lapse Multi-offset Gathers Collected with Array Antenna Ground Penetrating Radar

Published on: May 1, 2018

Scattering And Absorption of Light in Planetary Regoliths

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Microparticle Manipulation by Standing Surface Acoustic Waves with Dual-frequency Excitations

Published on: August 21, 2018

Area of Science:

Computational physics
Acoustics
Numerical analysis

Background:

The fast multipole method (FMM) is a precursor to MLFMA.
Acoustic wave scattering problems often involve millions of unknowns.
Existing methods like BEM and method of moments struggle with large-scale acoustic problems.

Purpose of the Study:

Extend the MLFMA to solve acoustic wave scattering for very large, arbitrary 3D objects.
Analyze acoustic behavior of large truncated ground with trenches for gun blast noise mitigation.
Investigate the efficiency and capability of MLFMA for large-scale acoustic simulations.

Main Methods:

Implementation of MLFMA based on the Nystrom method for acoustic boundary integral equations.
Utilizing a robust technique for evaluating singular or near-singular integrals in near-interaction terms.
Comparing the efficiency of the Nystrom-based MLFMA with traditional methods like BEM and method of moments.

Main Results:

The MLFMA, implemented with the Nystrom method, demonstrates enhanced efficiency for acoustic problems.
The approach successfully handles acoustic wave scattering problems with over two million unknowns on standard workstations.
Numerical examples validate the MLFMA's performance, reporting CPU time and memory usage.

Conclusions:

The extended MLFMA provides an efficient and robust solution for large-scale 3D acoustic wave scattering problems.
This method is suitable for analyzing complex acoustic environments, such as proving grounds, for noise reduction.
MLFMA offers a significant advancement in computational acoustics, enabling simulations previously intractable due to scale.