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A Stable Phantom Material for Optical and Acoustic Imaging

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Fast volumetric integral-equation solver for high-contrast acoustics.

E Bleszynski¹, M Bleszynski, T Jaroszewicz

¹Monopole Research, Thousand Oaks, California 91360, USA. elizabeth@monopoleresearch.com

The Journal of the Acoustical Society of America

|February 12, 2009

Summary

A new method improves solving acoustic volumetric integral equations, especially for large density contrasts. This approach enhances numerical stability and computational efficiency for complex acoustic problems.

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Area of Science:

Acoustics
Computational Physics
Numerical Analysis

Background:

Conventional Lippmann-Schwinger integral equations can be ill-conditioned for problems with large density contrasts.
Efficient numerical methods are crucial for solving complex acoustic scattering and propagation problems.

Purpose of the Study:

To present a novel approach for solving volumetric integral equations in acoustics that overcomes limitations with large density contrasts.
To enhance a fast solver by incorporating a reformulated integral equation system for improved stability and efficiency.

Main Methods:

Reformulation of Lippmann-Schwinger integral equations into an equivalent system of well-conditioned surface and volume integral equations.
Enhancement of a fast solver utilizing stiffness matrix compression based on fast Fourier transforms (FFTs).
Application of the method to numerically large-scale problems in acoustics.

Main Results:

The proposed approach yields a well-conditioned system of integral equations, improving numerical stability for large density contrasts.
The enhanced fast solver maintains O(N log N) solution complexity and storage requirements, where N is the number of unknowns.
Demonstration of the method's effectiveness on representative large-scale acoustic problems.

Conclusions:

The reformulated integral equation system provides a robust and efficient solution for acoustic problems with significant density variations.
The enhanced fast solver offers a computationally advantageous tool for tackling complex acoustic simulations.
This work advances numerical techniques for solving challenging problems in computational acoustics.