A new method to generate an almost-diagonal matrix in the boundary integral equation formulation

Area of Science:

• Computational physics
• Numerical analysis
• Acoustic scattering

Background:

• Traditional boundary integral equation methods for acoustic scattering problems often result in dense matrices.
• Dense matrices require significant computational resources, limiting the scale of solvable problems.

Purpose of the Study:

• To develop a new numerical procedure for solving acoustic scattering problems more efficiently.
• To overcome the computational limitations of traditional methods by generating an almost-diagonal matrix.

Main Methods:

• A new numerical procedure is developed for boundary integral equation formulation.
• Basis functions are grouped into clusters, and geometry is modeled using planar triangles with node-based basis functions.
• This clustering approach generates an almost-diagonal matrix.

Main Results:

• The new procedure eliminates the dense system matrix drawback of traditional methods.
• An almost-diagonal matrix is generated, leading to a smaller initial matrix size.
• The method significantly reduces the required computer resources.

Conclusions:

• The developed solution procedure is efficient for very large acoustic scattering problems.
• The method's validity is confirmed by comparing results for simple shapes with known solutions.