A Weak Form of the Conjugate Gradient FFT Method for Two-Dimensional Elastodynamics

The problem of two-dimensional scattering of elastic waves by an elastic inclusion can be formulated in terms of a domain integral equation, in which the grad-div operator acts on a vector potential. The vector potential is the spatial convolution of a Greenʹs function with the product of the density and the displacement over the domain of interest. A weak form of the integral equation for the unknown displacement is obtained by testing it with rooftop functions. This method shows excellent numerical performance.