Efficient fictitious eigenfrequency issue-free full-wave simulation of 3D ultrasonic NDE using CFIE-based Nyström...

Area of Science:

• Engineering
• Computational Mechanics
• Materials Science

Background:

• Conventional boundary integral equations (CBIE) in ultrasonic non-destructive evaluation (UNDE) suffer from fictitious eigenfrequency issues, leading to numerical instability and unsolvable matrix equations.
• These issues arise at specific frequencies, preventing accurate simulation of UNDE models using methods like the Nyström method (NM).

Purpose of the Study:

• To develop a robust and efficient numerical method for 3D UNDE that avoids fictitious eigenfrequencies.
• To enhance the computational speed and accuracy of solving the combined field integral equation (CFIE) for complex geometries and multiple excitations.

Main Methods:

• A combined field integral equation (CFIE) formulation is proposed, linearly combining CBIE with hyper-singular boundary integral equations (HBIE) to suppress fictitious eigenfrequencies.
• A high-order Nyström method (NM) is employed for discretization, accelerated by a kernel-independent algorithm and adaptive cross approximation (ACA) for reduced computational complexity (O(N log N)).
• The fast excitation sweep (FES) algorithm is introduced to accelerate iterative solutions for multiple excitations, and Kriging interpolation is used to reduce frequency domain simulations.

Main Results:

• The proposed CFIE framework effectively eliminates fictitious eigenfrequencies and enhances numerical stability in 3D UNDE simulations.
• The integration of high-order NM, ACA, and FES algorithms leads to significant improvements in computational efficiency for complex models and multiple scanning positions.
• Experimental validation on benchmark cases shows excellent agreement between numerical predictions and measured data, confirming the model's accuracy and robustness.

Conclusions:

• The developed high-order NM solver, accelerated by ACA and FES within a CFIE framework, provides an efficient and accurate solution for 3D UNDE problems.
• The method demonstrates robustness and superior performance compared to existing techniques, particularly for complex geometries and multi-excitation scenarios.
• This approach offers a reliable tool for locating and reconstructing geometric or material information of defects in materials using UNDE.