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    This study introduces a fast numerical method for analyzing acoustic scattering from complex objects. The technique efficiently handles large, inhomogeneous scatterers, crucial for biomedical and oceanographic applications.

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    Area of Science:

    • Computational physics
    • Acoustics
    • Numerical methods

    Background:

    • Analyzing acoustic scattering from highly inhomogeneous objects is computationally challenging.
    • Existing methods struggle with acoustically large scatterers of complex topologies.
    • Efficient numerical techniques are needed for practical applications in diverse fields.

    Purpose of the Study:

    • To develop and validate an accelerated method-of-moment solver for acoustic scattering problems.
    • To enable the efficient analysis of acoustically large and complex inhomogeneous scatterers.
    • To provide a robust numerical tool for biomedical and oceanographic applications.

    Main Methods:

    • Utilized a method-of-moment solver for the volume integral equation.
    • Implemented a kernel-independent algebraic compression scheme using butterfly forms for matrix acceleration.
    • Applied hierarchical partitioning of the moment stiffness matrix for efficient scaling.

    Main Results:

    • The developed butterfly-based compression scheme offers favorable scaling for volume problems compared to low-rank approximations.
    • Validated the numerical formulation, parameter tuning, and performance of the fast method.
    • Demonstrated the method's effectiveness on various examples relevant to biomedical and oceanographic applications.

    Conclusions:

    • The proposed fast numerical method significantly accelerates the analysis of acoustic scattering from large, inhomogeneous objects.
    • The technique provides a scalable and efficient solution for complex scattering problems.
    • This advancement has direct implications for enhancing simulations in fields like medical ultrasound and underwater acoustics.