On the use of complex stretching coordinates in generalized finite difference method with applications in inhomogeneous visco-elasto dynamics

Abstract

In the study, in conjunction with perfectly matched layer (PML) analysis, an approach is proposed for the evaluation of complex derivatives directly in terms of complex stretching coordinates of points in PML. For doing this within the framework of generalized finite difference method (GFDM), a difference equation is formulated and presented, where both the function values and coordinates of data points might be complex. The use of the proposed approach is considered in the analysis of inhomogeneous visco-elasto-dynamic system and assessed through three example problems analyzed in Fourier space: the composite and inhomogeneous tube, layer and impedance problems. The GFDM results obtained for the tube and layer problems compare very closely and coincide almost exactly with the exact solution. In the impedance problems, rigid surface or embedded footings resting on a composite inhomogeneous half-space are considered. The influences of various types of inhomogeneities, as well as, of various geometric shapes of PML-(physical region) interfaces on impedance curves are examined.