Related Experiment Video
Updated: Jun 1, 2026
09:04
Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
Published on: February 23, 2018
Perfectly matched layers for frequency-domain integral equation acoustic scattering problems.
Erwin J Alles1, Koen W A van Dongen
1Department of Imaging Science and Technology, Delft University of Technology, Delft, The Netherlands. E.J.Alles@tudelft.nl
Summary
A new perfectly matched layer (PML) formulation effectively suppresses non-physical reflections in 3D acoustic scattering simulations using integral equations. This method significantly attenuates scattered pressure fields within thin boundary layers, ensuring accurate simulations.
Area of Science:
- Computational physics
- Acoustics
- Numerical methods
Background:
- Simulations of acoustic wavefields require finite numerical domains.
- Reflections from domain boundaries introduce non-physical artifacts.
- Perfectly matched layers (PMLs) absorb boundary reflections but haven't been applied to integral equation methods.
Purpose of the Study:
- To derive and test a PML formulation for 3D frequency-domain integral-equation-based acoustic scattering.
- To evaluate the effectiveness of PMLs in suppressing boundary reflections.
- To validate the accuracy of the integral equation method with PMLs.
Main Methods:
- Derivation of a PML formulation for the 3D frequency-domain integral equation.
- Testing the formulation using 3D acoustic scattering configurations.
- Comparison of simulation results with analytical solutions.
Main Results:
- Strong attenuation (200x amplitude) of scattered pressure fields achieved.
- PMLs demonstrated to be virtually reflectionless.
- Thin PML layers (less than a wavelength) were effective.
- Integral equation method accurately reproduced pressure fields with and without PMLs.
Conclusions:
- The derived PML formulation is effective for 3D acoustic scattering problems.
- PMLs significantly improve the accuracy of integral equation simulations by eliminating boundary reflections.
- This work extends the application of PMLs to integral equation methods in acoustics.
Related Concept Videos
01:12Mesh 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...
The process of harmonizing these impedances begins with a clear understanding of the input and output signals. Once these signals are known, the...
01:29Integration by Parts: Problem Solving
Smart speakers process voice commands by modeling audio inputs as piecewise functions and analyzing them through integration against trigonometric functions, such as cosine. This mathematical approach is fundamental in signal processing, where complex sound waves are decomposed into simpler frequency components.Consider a definite integral involving a piecewise function multiplied by a cosine function. Because the function is defined differently over separate intervals, the integral is split...
02:18Interference and Diffraction
Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
00:53Sound Waves: Interference
Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure waves. When two identical waves from the same source superimpose on each other, the combination of two crests or two troughs results in amplitude reinforcement known as constructive interference. If two identical waves, that are initially in phase, become out of phase because of different path lengths, the combination of crests with troughs...
01:10Interference: Path Lengths
Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
01:26Linear Approximation in Frequency Domain
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.