Suppressing the onset of instabilities in the time-domain equivalent source method using a multistep approach

Area of Science:

• Acoustics
• Numerical Analysis
• Computational Physics

Background:

• Numerical instability is a critical challenge in the time-domain equivalent source method (TESM).
• Accurate optimization of equivalent source strengths using measured acoustic pressure data is essential for TESM applications.

Purpose of the Study:

• To propose and validate a novel multistep method for stabilizing TESM.
• To enhance the reliability and accuracy of TESM by mitigating numerical instability.

Main Methods:

• A multistep approach is introduced, solving multiple time steps simultaneously instead of sequentially.
• The method modifies the matrix inversion process within the time-marching algorithm, incorporating truncated singular value decomposition or Tikhonov regularization.
• Numerical simulations are conducted using three distinct examples to evaluate the method's performance.

Main Results:

• The multistep method significantly improves solution stability compared to the conventional single-step TESM.
• Error accumulation rates are reduced, and filtering effects are enhanced due to the modified matrix structure.
• The study analyzes the impact of the number of merged time steps on solution quality.

Conclusions:

• The proposed multistep method effectively stabilizes TESM, offering a more robust solution for acoustic analysis.
• The findings provide guidance on selecting optimal parameters, such as the number of merged time steps.
• The method demonstrates consistent performance across various numerical parameter configurations.