Implementation of a parallel conjugate gradient method for simulation of elastic light scattering

We simulate elastic light scattering with the coupled dipole method. The kernel of this method is a large set of linear equations. The n×n system matrix is complex, symmetric, full, and diagonally dominant. This application is a typical example of problems arising in computational electromagnetics. The matrix equations are usually solved with (preconditioned) conjugate gradient methods. For realistic problems the size of the matrix is very large (n ~ 104 to 106). In that case sustained calculation speeds in the Gflop/s range are required to keep execution times acceptable. We introduce a methodology to parallelize the conjugate gradient method for this type of problems, with emphasis on coarse grain distributed memory implementations. We present results for an implementation on a transputer network.