Boundary integral equations and boundary elements methods in elastodynamics

We review the application of boundary integral equation (BIE) methods to elastic wave propagation problems. BIE methods express the wavefield as an integral equation defined over the boundary of the domain studied. They can be grouped into two "Direct" BIE relate the wavefield (generally the displacements and trac tions) to the values of the wavefield at the boundary of the domain, while "Indirect" BIE rely on an intermediate unknown, which is usually a distribution of fictitious sources along the boundary. We present the mathematical bases of the methods and discuss and review their various numerical implementations. We illustrate some of the applications for seismic wave propagation.