Consistency of the Douglas – Rachford Splitting Algorithm for the Sum of Three Nonlinear Operators: Application to the Stefan Problem in Permafrost Soils
Applied and Computational Mathematics
Volume 2, Issue 4, August 2013, Pages: 100-108
Received: May 30, 2013; Published: Aug. 10, 2013
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Taras A. Dauzhenka, R&D Dept., Simmakers Ltd., 1A-307 V. Kharuzhei str., 220005 Minsk, Belarus
Igor A. Gishkeluk, R&D Dept., Simmakers Ltd., 1A-307 V. Kharuzhei str., 220005 Minsk, Belarus
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Consistency of the Douglas – Rachford dimensional splitting scheme is proved for the sum of three nonlinear operators constituting an evolution equation. It is shown that the operators must be densely defined, maximal monotone and single valued on a real Hilbert space in order to satisfy conditions, under which the splitting algorithm can be applied. Numerical experiment conducted for a three-dimensional Stefan problem in permafrost soils suggests that the Douglas – Rachford scheme produces reasonable results, although the convergence rate remains unestablished.
Splitting Algorithms, Alternating Directions Scheme, Stefan Problem, Nonlinear Heat Equation, Consistent Approximation
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Taras A. Dauzhenka, Igor A. Gishkeluk, Consistency of the Douglas – Rachford Splitting Algorithm for the Sum of Three Nonlinear Operators: Application to the Stefan Problem in Permafrost Soils, Applied and Computational Mathematics. Vol. 2, No. 4, 2013, pp. 100-108. doi: 10.11648/j.acm.20130204.11
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