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.