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A mesh-free approach to acoustic scattering from multiple spheres nested inside a large sphere by using diagonal
Andrew J Hesford1, Jeffrey P Astheimer, Leslie F Greengard
1Department of Electrical and Computer Engineering, University of Rochester, Rochester, New York 14627, USA. hestford@ece.rochester.edu
The Journal of the Acoustical Society of America
|February 9, 2010
Summary
This study presents a multiple-scattering method for solving the Helmholtz equation with nested spheres. The approach offers accurate and efficient acoustic wave scattering solutions for complex interior geometries.
Area of Science:
- Acoustics
- Computational Physics
- Wave Scattering
Background:
- Solving the Helmholtz equation is crucial for wave propagation problems.
- Modeling acoustic scattering from multiple objects presents computational challenges.
- Existing methods may struggle with complex geometries or arbitrary surfaces.
Purpose of the Study:
- To develop a high-order accurate method for acoustic scattering from nested spheres.
- To provide an efficient computational approach for the Helmholtz equation.
- To address limitations of traditional integral equation methods.
Main Methods:
- A multiple-scattering approach using partial-wave expansions.
- Derivation of a linear system to enforce continuity conditions.
- Utilization of diagonal translation operators for computational acceleration.
Main Results:
- The method achieves high-order accuracy in solving the Helmholtz equation.
- It effectively handles nested spherical scatterers within an enclosing sphere.
- Numerical results validate the accuracy and computational efficiency.
Conclusions:
- The presented multiple-scattering method is accurate and efficient for acoustic wave problems.
- It offers an advantage over integral equation methods for specific geometries.
- The technique is suitable for modeling complex scattering scenarios.
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