  We develop an efficient numerical method for calculating the image stress
field induced by spherical voids in materials. The method is applied to
dislocation-void interactions in dislocation dynamics simulations. We obtain a
complete set of basis functions for the solution of the image stress problem,
as well as their corresponding displacement, stress, and traction fields in
terms of the linear combination of spherical harmonics. Using the fast
transformation between the real and spherical-harmonics spaces provided by the
SHTOOLS package, the method is more efficient than other image stress solvers
such as the finite-element method. This method can readily be extended for
solving elasticity problems involving inclusions and inhomogeneities, contact
between spheres, as well as other differential equations with spherical
boundaries beyond elasticity.
