Cooling rate is a key factor that can drastically affect the phase transformation and thermal stress of duplex stainless steels. Therefore, in this research, different sand moulds were used to explore the influence of...Cooling rate is a key factor that can drastically affect the phase transformation and thermal stress of duplex stainless steels. Therefore, in this research, different sand moulds were used to explore the influence of cooling rate on the solidification of the 2304 duplex stainless steel (DSS). The macro and micro structures of the 2304 DSS were investigated. Small equiaxed grains are obtained in chromite sand mould sample with a lower pouring temperature and a higher cooling rate, whereas coarse columnar and equiaxed grains are found in silica sand and refractory powder mould samples. The size of austenite phase is significantly increased with decreasing cooling rate, while the ferrite phase content ranging from 51.6% to 53.9% does not change obviously. In addition, the linear contraction of the 2304 DSS decreases from 2.34% to 1.09% when the mean cooling rate above 1,173 K increases from 0.99 K·s-1 to 3.66 K·s-1.展开更多
In this paper, we study the contraction linearity for metric projection in L p spaces. A geometrical property of a subspace Y of L p is given on which P Y is a contraction projection.
Recently, we have proposed an iterative projection and contraction (PC) method for a class of linear complementarity problems (LCP)([4]). The method was showed to be globally convergent, but no statement could be made...Recently, we have proposed an iterative projection and contraction (PC) method for a class of linear complementarity problems (LCP)([4]). The method was showed to be globally convergent, but no statement could be made about the rate of convergence. In this paper, we develop a modified globally linearly convergent PC method for linear complementarity problems. Both the method and the convergence proofs are very simple. The method can also be used to solve some linear variational inequalities. Several computational experiments are presented to indicate that the method is surprising good for solving some known difficult problems.展开更多
The generalized successive overrelaxation （GSOR） method was presented and studied by Bai, Parlett and Wang [Numer. Math. 102（2005）, pp.1-38] for solving the augmented system of linear equations, and the optimal it...The generalized successive overrelaxation （GSOR） method was presented and studied by Bai, Parlett and Wang [Numer. Math. 102（2005）, pp.1-38] for solving the augmented system of linear equations, and the optimal iteration parameters and the corresponding optimal convergence factor were exactly obtained. In this paper, we further estimate the contraction and the semi-contraction factors of the GSOR method. The motivation of the study is that the convergence speed of an iteration method is actually decided by the contraction factor but not by the spectral radius in finite-step iteration computations. For the nonsingular augmented linear system, under some restrictions we obtain the contraction domain of the parameters involved, which guarantees that the contraction factor of the GSOR method is less than one. For the singular but consistent augmented linear system, we also obtain the semi-contraction domain of the parameters in a similar fashion. Finally, we use two numerical examples to verify the theoretical results and the effectiveness of the GSOR method.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 50904044)
文摘Cooling rate is a key factor that can drastically affect the phase transformation and thermal stress of duplex stainless steels. Therefore, in this research, different sand moulds were used to explore the influence of cooling rate on the solidification of the 2304 duplex stainless steel (DSS). The macro and micro structures of the 2304 DSS were investigated. Small equiaxed grains are obtained in chromite sand mould sample with a lower pouring temperature and a higher cooling rate, whereas coarse columnar and equiaxed grains are found in silica sand and refractory powder mould samples. The size of austenite phase is significantly increased with decreasing cooling rate, while the ferrite phase content ranging from 51.6% to 53.9% does not change obviously. In addition, the linear contraction of the 2304 DSS decreases from 2.34% to 1.09% when the mean cooling rate above 1,173 K increases from 0.99 K·s-1 to 3.66 K·s-1.
基金Supported by the natural science foundation of Hebei
文摘In this paper, we study the contraction linearity for metric projection in L p spaces. A geometrical property of a subspace Y of L p is given on which P Y is a contraction projection.
文摘Recently, we have proposed an iterative projection and contraction (PC) method for a class of linear complementarity problems (LCP)([4]). The method was showed to be globally convergent, but no statement could be made about the rate of convergence. In this paper, we develop a modified globally linearly convergent PC method for linear complementarity problems. Both the method and the convergence proofs are very simple. The method can also be used to solve some linear variational inequalities. Several computational experiments are presented to indicate that the method is surprising good for solving some known difficult problems.
基金supported by State Key Laboratory of Scientific/Engineering Computing,Chinese Academy of SciencesThe National Key Basic Research Program of China (973 program) under Grant 2005CB321701+2 种基金The National Natural Science Foundation (No. 10771168)The Natural Science and Technology Development Plan Research Project of Shaanxi Province (No. 2008K01-33)The Special Plan Research Project of Shaanxi Education Department (No. 09JK716),P.R.China
文摘The generalized successive overrelaxation （GSOR） method was presented and studied by Bai, Parlett and Wang [Numer. Math. 102（2005）, pp.1-38] for solving the augmented system of linear equations, and the optimal iteration parameters and the corresponding optimal convergence factor were exactly obtained. In this paper, we further estimate the contraction and the semi-contraction factors of the GSOR method. The motivation of the study is that the convergence speed of an iteration method is actually decided by the contraction factor but not by the spectral radius in finite-step iteration computations. For the nonsingular augmented linear system, under some restrictions we obtain the contraction domain of the parameters involved, which guarantees that the contraction factor of the GSOR method is less than one. For the singular but consistent augmented linear system, we also obtain the semi-contraction domain of the parameters in a similar fashion. Finally, we use two numerical examples to verify the theoretical results and the effectiveness of the GSOR method.
