Hypersingular meshless method using double-layer potentials for three-dimensional exterior acoustic problems.

Area of Science:

• Computational Mathematics
• Acoustics Engineering
• Numerical Analysis

Background:

• Exterior acoustic problems in 3D with irregular domains present significant computational challenges.
• The standard Method of Fundamental Solutions (MFS) faces difficulties with boundary singularities, preventing source point placement on the real boundary.
• This limits the MFS's applicability in certain complex acoustic scattering scenarios.

Purpose of the Study:

• To develop and analyze an efficient hypersingular meshless method for solving 3D exterior acoustic problems.
• To extend previous 2D research to address the complexities of 3D irregular domains.
• To overcome the singularity issues inherent in the standard MFS when applied to boundary problems.

Main Methods:

• The study employs a hypersingular meshless method, building upon the framework of the Method of Fundamental Solutions (MFS).
• The formulation utilizes a double-layer potential representation on the physical boundary.
• Numerical comparisons are made against the standard MFS and the Boundary Element Method (BEM).

Main Results:

• The proposed hypersingular meshless method effectively handles 3D exterior acoustic problems with irregular domains.
• The method successfully circumvents the singularity issues encountered when source points are placed on the boundary in MFS.
• Numerical examples demonstrate good performance and accuracy compared to established methods.

Conclusions:

• The developed hypersingular meshless method offers an efficient and robust solution for 3D exterior acoustic problems.
• This approach provides a viable alternative to traditional methods, particularly for complex geometries where MFS struggles.
• The findings contribute to advancing numerical techniques in computational acoustics.