2020/12/20 by Armand Wirgin, Wirgin, Armand
Engineering · #FOS: Physical sciences #Geophysics (physics.geo-ph) #Geotechnical Engineering and Analysis #Geotechnical Engineering and Soil Stabilization #Geotechnical Engineering and Underground Structures
paper · pdf · doi:10.48550/arxiv.2012.10989
openalex publication_date 2020/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Three types of boundary integral equation (BIE) methods are employed to obtain closed-form solutions of a wave-scattering problem which are compared to the exact, closed-form (reference), solution deriving from the separation-of-variables technique. The problem involves either Dirichlet (D) or Neumann (N) boundary conditions (BC) for a scatterer that is a circular cylinder submitted to one or two incident waves. The three BIE methods lead to different expressions for the traction (for D-BC) or boundary displacement (for N-BC) by which numerous resonances are predicted whose frequency of occurrence differs from one method to another. This is interpreted as being the sign that the three methods are generally-defective and the resonances are 'spurious'. This 'disease' is cured by combining two BIE into one in such a way that the resulting BIE gives rise to a closed-form solution identical to the exact reference solution devoid of spurious resonances.