PARALLEL IMPLEMENTATION OF THE KRONECKER PRODUCT TECHNIQUE FOR NUMERICAL-SOLUTION OF PARABOLIC PARTIAL-DIFFERENTIAL EQUATIONS

Using the alternating directional Galerkin technique we show that the approximate solution of the initial boundary value problem of paraboli c partial differential equations is equivalent to the least squares so lution of the linear system A circle times B = b. In the full rank cas e, an efficient method for obtaining the solution of the least squares problem suitable for distributive memory computers was presented in ( Fausett et al., 1994). This method is extended to solve the rank defic ient case using the RRQR factorization of matrices A and B together wi th the commutatively property of the Kronecker product. Solution algor ithm and parallel implementation are discussed. Timing results are pre sented and compared with previous work.