  A spectral formulation of the boundary integral equation method for antiplane
problems is presented. The boundary integral equation method relates the slip
and the shear stress at an interface between two half-planes. It involves
evaluating a space-time convolution of the shear stress or the slip at the
interface. In the spectral formulation, the convolution with respect to the
spatial coordinate is performed in the spectral domain. This leads to greater
numerical efficiency. Prior work on the spectral formulation of the boundary
integral equation method has performed the elastodynamic convolution of the
slip at the interface. In the present work, the convolution is performed of the
shear stress at the interface. The spectral formulation is developed both for
an interface between identical solids and for a bi-material interface. It is
validated by numerically calculating the response of the interface to harmonic
and to impulsive disturbances and comparing with known analytical solutions. To
illustrate use of the method, dynamic slip rupture propagation with a
slip-weakening friction law is simulated.
