Efficient Nyström Method for Solving Ultrasonic Scattering Problems

Elasticodynamic scattering plays an important role in ultrasonic scattering problems, especially in evaluating the far-field scattering amplitude of defects. To address the elasticodynamic scattering problem, we employ the high-order Nyström method (NM). This approach utilizes high-order surface triangles for meshing and employs high-order interpolation to define the basis functions on each surface triangle unit. Within the impedance matrix generated by the high-order NM model based on the conventional boundary integral equation (CBIE), the diagonal and near blocks are stored in a full matrix, while the far blocks are compressed and stored using adaptive cross approximation (ACA) technique. The results predicted by the ACA based solver are compared with those predicted by pure NM to verify the accuracy and effectiveness of this method.