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Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization
Zai You Yan1, Kin Chew Hung, Hui Zheng
1Institute of High Performance Computing, 1 Science Park Road #01-01 The Capricorn, Singapore Science Park II, Singapore 117528.
The Journal of the Acoustical Society of America
|May 27, 2003
Summary
This study introduces a novel regularization method for hypersingular integrals in acoustic problems. The new approach significantly enhances computational efficiency and accuracy for Helmholtz integral equations.
Area of Science:
- Computational acoustics
- Numerical methods for integral equations
Background:
- The conventional Helmholtz integral equation presents challenges with hypersingular integrals.
- Efficient numerical solutions are crucial for acoustic radiation and scattering problems.
Purpose of the Study:
- To develop and validate a new regularization method for hypersingular integrals in the Helmholtz equation.
- To improve computational efficiency and accuracy in acoustic simulations.
Main Methods:
- Introduction of a discretized operator matrix to simplify double surface integral evaluation.
- Application of the method to acoustic radiation and scattering problems using curvilinear quadrilateral isoparametric elements.
Main Results:
- The proposed method reduces double surface integral evaluation to matrix multiplication, enhancing computational efficiency.
- Computational cost becomes comparable to conventional methods as the number of frequencies increases.
- Numerical results demonstrate rapid convergence to analytical solutions with finer meshes.
Conclusions:
- The new regularization technique offers a computationally efficient and accurate solution for acoustic radiation and scattering.
- The method is effective for problems involving pulsating, oscillating, and insonified spheres.