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

  • Authors:

  • M. A. Amer;B. A. Abdel-Hamida;D. Fausett

  • Affiliations:

  • Mathematics and Computer Science Department, Faculty of Science, United Arab Emirates University, Al-Ain, United Arab Emirates;Mathematics and Computer Science Department, Faculty of Science, United Arab Emirates University, Al-Ain, United Arab Emirates;Applied Mathematics Department, Florida Institute of Technology, USA

  • Venue:
  • Parallel Computing
  • Year:
  • 1997

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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.