Efficient parallel algorithm for the two-dimensional diffusion equation subject to specification of mass

An efficient L 0 -stable parallel algorithm is developed for the two-dimensional diffusion equation with non-local time-dependent boundary conditions. The algorithm is based on subdiagonal Padé approximation to the matrix exponentials arising from the use of the method of lines and may be implemente...

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Bibliographic Details
Published inInternational journal of computer mathematics Vol. 64; no. 1-2; pp. 153 - 163
Main Authors Gumel, A. B., Ang, W. T., Twizell, E. H.
Format Journal Article
LanguageEnglish
Published Abingdon Gordon and Breach Science Publishers 01.01.1997
Taylor and Francis
Subjects
Exact sciences and technology
G.1.8
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Padé approximant
parallel algorithm
Partial differential equations, boundary value problems
Sciences and techniques of general use
stability
Two dimensional equation
Parallel algorithm
Error estimation
Method of lines
Dirichlet problem
Diffusion equation
Numerical method
Padé approximation
Partial differential equation
Numerical stability
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Summary:An efficient L 0 -stable parallel algorithm is developed for the two-dimensional diffusion equation with non-local time-dependent boundary conditions. The algorithm is based on subdiagonal Padé approximation to the matrix exponentials arising from the use of the method of lines and may be implemented on a parallel architecture using two processors running concurrently with each processor employing the use of tridiagonal solvers at every time-step. The algorithm is tested on two model problems from the literature for which discontinuities between initial and boundary conditions exist. The CPU times together with the associated error estimates are compared.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207169708804580