Related Experiment Video
Updated: Jul 20, 2026
10:16
Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects
Published on: February 8, 2014
Krylov subspace iterative methods for boundary element method based near-field acoustic holography
Nicolas Valdivia1, Earl G Williams
1Code 7130, Naval Research Laboratory, Washington, DC 20375, USA. valdivia@pa.nrl.navy.mil
The Journal of the Acoustical Society of America
|March 12, 2005
Summary
This study reconstructs acoustic fields using iterative regularization methods, avoiding computationally expensive singular value decomposition. It examines Krylov subspace methods for accurate acoustic field reconstruction from noisy measurements.
Area of Science:
- Acoustics
- Numerical Analysis
- Computational Mechanics
Background:
- Acoustic field reconstruction is crucial for applications like noise control and structural health monitoring.
- Boundary integral equations and boundary element methods are standard for acoustic problems.
- Noise in measurements can significantly corrupt solutions, necessitating robust reconstruction techniques.
Purpose of the Study:
- To investigate iterative regularization methods for acoustic field reconstruction from noisy data.
- To analyze the regularizing properties of Krylov subspace methods, including conjugate gradients, least squares QR, and a Hybrid method.
- To compare different stopping rules for iterative methods in the context of acoustic field reconstruction.
Main Methods:
- Discretization of boundary integral equations using the boundary element method.
- Application of iterative regularization techniques to solve the resulting large-scale matrix systems.
- Analysis of Krylov subspace methods (conjugate gradients, least squares QR, Hybrid method) and their semi-convergence properties.
- Evaluation of various stopping rules for iterative solvers.
Main Results:
- Iterative regularization methods effectively counteract measurement noise without requiring singular value decomposition.
- Krylov subspace methods exhibit semi-convergence, where early iterations yield optimal regularization.
- The number of iterations in Krylov methods functions as the regularization parameter, crucial for avoiding corrupted solutions.
- A vibrating plate example validates the proposed methods and stopping rule comparisons.
Conclusions:
- Iterative regularization, particularly Krylov subspace methods, offers an efficient and robust approach for acoustic field reconstruction.
- Careful selection of stopping rules is essential to leverage the semi-convergence property and obtain accurate solutions.
- The study provides a framework for improved acoustic field reconstruction in the presence of noisy measurements.
Related Concept Videos
01:16Electrostatic 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...
The surface integral of an electric field is given by Gauss's law in integral form and is related to...
01:27Electrostatic 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.
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.
01:25Boundary Conditions for Current Density
Current density becomes discontinuous across an interface of materials with different electrical conductivities. The normal component of the current density is continuous across the boundary.
01:28Magnetostatic 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...
01:28Standing 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:
01:21Boundary Conditions: Lossless Lines
Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...