Consistency of the Douglas – Rachford Splitting Algorithm for the Sum of Three Nonlinear Operators: Application to the Stefan Problem in Permafrost Soils
Taras A. Dauzhenka,
Igor A. Gishkeluk
Issue:
Volume 2, Issue 4, August 2013
Pages:
100-108
Received:
30 May 2013
Published:
10 August 2013
Abstract: 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.
Abstract: 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 applie...
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Analysis of Cracked Plates Using Localized Multi-Domain Differential Quadrature Method
Tharwat Osman,
Mohamed. S. Matbuly,
Salwa. A. Mohamed,
Mohamed Nassar
Issue:
Volume 2, Issue 4, August 2013
Pages:
109-114
Received:
5 August 2013
Published:
30 August 2013
Abstract: In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the irregular subdomains to regular ones. Then the differential quadrature method is employed to solve the problem over the transformed domains. Further, it’s focused on the crack regions by applying the localized version of differential quadrature method. The out of plane deflection is obtained at the immediate vicinity of the crack tips, such that the stress intensity factor can be calculated. The obtained results are compared with the previous analytical ones. Furthermore a parametric study is introduced to investigate the effects of elastic and geometric characteristics on the values of stress intensity factor.
Abstract: In this paper, A multi-domain differential quadrature method is employed to solve a mode III crack problem. The domain of the problem is assumed to be irregular rather than it possesses discontinuities, (cracks). The entire domain is divided into several subdomains, according to the crack locations. A conformal mapping is applied to transform the i...
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