(untitled) (Advances in Applied Mathematics and Mechanics, 2020)
We mainly research the reduced-order of the classical natural boundary element (CNBE) method for the two-dimensional (2D) viscoelastic wave equation by means of proper orthogonal decomposition (POD) technique. For this purpose, we firstly establish the CNBE model and analyze the existence, stability, and errors for the CNBE solutions. We then build a highly efficient reduced-order extrapolating natural boundary element (HEROENBE) mode including few degrees of freedom but possessing sufficiently high accuracy for the 2D viscoelastic wave equation by the POD method and analyze the existence, stability, and errors of the HEROENBE solutions by the CNBE method. We finally employ some numerical experiments to verify that the numerical results are accorded with the theoretical ones so that the validity for the HEROENBE model is further verified.