Elsevier

Parallel Computing

Volume 22, Issue 14, March 1997, Pages 1997-2005
Parallel Computing

Parallel implementation of the Kronecker product technique for numerical solution of parabolic partial differential equations

https://doi.org/10.1016/S0167-8191(96)00089-0Get rights and content

Abstract

Using the alternating directional Galerkin technique we show that the approximate solution of the initial boundary value problem of parabolic partial differential equations is equivalent to the least squares solution of the linear system A ⊗ B = b. In the full rank case, 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 deficient case using the RRQR factorization of matrices A and B together with the commutatively property of the Kronecker product. Solution algorithm and parallel implementation are discussed. Timing results are presented and compared with previous work.

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On leave from Mathematics and Physics Department, Faculty of Engineering, Mansoura University, Al-Mansoura, Egypt.

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