  A parallel algorithm for computing the finite difference solution to the
elliptic equations with non-separable variables is presented. The resultant
matrix is symmetric positive definite, thus the preconditioning conjugate
gradient or the chebyshev method can be applied. A differential analog to the
Laplace operator is used as preconditioner. For inversion of the Laplace
operator we implement a parallel version of the separation variable method,
which includes the sequential FFT algorithm and the parallel solver for
tridiagonal matrix equations (dichotomy algorithm). On an example of solving
acoustic equations by the integral Laguerre transformation method, we show that
the algorithm proposed is highly efficient for a large number of processors.
