In this paper, we present the analytical expressions for computing the minimum distance between a point and a torus, which is called the orthogonal projection point problem. If the test point is on the outside of the ...In this paper, we present the analytical expressions for computing the minimum distance between a point and a torus, which is called the orthogonal projection point problem. If the test point is on the outside of the torus and the test point is at the center axis of the torus, we present that the orthogonal projection point set is a circle perpendicular to the center axis of the torus;if not, the analytical expression for the orthogonal projection point problem is also given. Furthermore, if the test point is in the inside of the torus, we also give the corresponding analytical expression for orthogonal projection point for two cases.展开更多
The purpose of this paper is to study the convergence problem of the iteration scheme xn＋l = λn＋1y ＋ （1 - λn＋1）Tn＋1xn for a family of infinitely many nonexpansive mappings T1, T2,... in a Hilbert space. It is...The purpose of this paper is to study the convergence problem of the iteration scheme xn＋l = λn＋1y ＋ （1 - λn＋1）Tn＋1xn for a family of infinitely many nonexpansive mappings T1, T2,... in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results.展开更多
Material point method（MPM）was originally introduced for large deformation problems in solid mechanics applications.Later,it has been successfully applied to solve a wide range of material behaviors.However,previous ...Material point method（MPM）was originally introduced for large deformation problems in solid mechanics applications.Later,it has been successfully applied to solve a wide range of material behaviors.However,previous research has indicated that MPM exhibits numerical instabilities when resolving incompressible flow problems.We study Chorin＇s projection method in MPM algorithm to simulate material incompressibility.Two projection-type schemes,non-incremental projection and incremental projection,are investigated for their accuracy and stability within MPM.Numerical examples show that the non-incremental projection scheme provides stable results in single phase MPM framework.Further,it avoids artificial pressure oscillations and small time steps that are present in the explicit MPM approach.展开更多
文摘In this paper, we present the analytical expressions for computing the minimum distance between a point and a torus, which is called the orthogonal projection point problem. If the test point is on the outside of the torus and the test point is at the center axis of the torus, we present that the orthogonal projection point set is a circle perpendicular to the center axis of the torus;if not, the analytical expression for the orthogonal projection point problem is also given. Furthermore, if the test point is in the inside of the torus, we also give the corresponding analytical expression for orthogonal projection point for two cases.
基金Supported by The Research Foundation Grant of The Hong Kong Polytechnic University and Yibin University(2005Z3)
文摘The purpose of this paper is to study the convergence problem of the iteration scheme xn＋l = λn＋1y ＋ （1 - λn＋1）Tn＋1xn for a family of infinitely many nonexpansive mappings T1, T2,... in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results.
基金financially supported by the Cambridge Commonwealth Trust and the European Union’s Seventh Framework Programme 662 for research,Technological Development and Demonstration under Grant Agreement No.PIAP-GA-663 2012-324522 (MPM Dredge)
文摘Material point method（MPM）was originally introduced for large deformation problems in solid mechanics applications.Later,it has been successfully applied to solve a wide range of material behaviors.However,previous research has indicated that MPM exhibits numerical instabilities when resolving incompressible flow problems.We study Chorin＇s projection method in MPM algorithm to simulate material incompressibility.Two projection-type schemes,non-incremental projection and incremental projection,are investigated for their accuracy and stability within MPM.Numerical examples show that the non-incremental projection scheme provides stable results in single phase MPM framework.Further,it avoids artificial pressure oscillations and small time steps that are present in the explicit MPM approach.
