To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based syn- chronous multisplitting iteration method and the corres...To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based syn- chronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an H＋-matrix, which improve the existing convergence theory. Numeri- cal results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation.展开更多
Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive d...Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive diagonal elements. Moreover, block and multi-parameter variants of the new methods, together with their convergence properties, are investigated in detail. Numerical results show that these new methods can achieve high parallel efficiency for solving the large sparse linear complementarity problems on multiprocessor systems.展开更多
The main purpose of this paper is to present a linear complementarity problem （LCP） method for a planar passive dynamic walker with round feet based on an event-driven scheme. The passive dynamic walker is treated a...The main purpose of this paper is to present a linear complementarity problem （LCP） method for a planar passive dynamic walker with round feet based on an event-driven scheme. The passive dynamic walker is treated as a planar multi-rigid-body system. The dynamic equations of the passive dynamic walker are obtained by using Lagrange＇s equations of the second kind. The normal forces and frictional forces acting on the feet of the passive walker are described based on a modified Hertz contact model and Coulomb＇s law of dry friction. The state transition problem of stick-slip between feet and floor is formulated as an LCR which is solved with an event-driven scheme. Finally, to validate the methodology, four gaits of the walker are simulated： the stance leg neither slips nor bounces; the stance leg slips without bouncing; the stance leg bounces without slipping; the walker stands after walking several steps.展开更多
文摘To reduce the communication among processors and improve the computing time for solving linear complementarity problems, we present a two-step modulus-based syn- chronous multisplitting iteration method and the corresponding symmetric modulus-based multisplitting relaxation methods. The convergence theorems are established when the system matrix is an H＋-matrix, which improve the existing convergence theory. Numeri- cal results show that the symmetric modulus-based multisplitting relaxation methods are effective in actual implementation.
基金Subsidized by The Special Funds For Major State Basic Research Projects G1999032803.
文摘Asynchronous parallel multisplitting relaxation methods for solving large sparse linear complementarity problems are presented, and their convergence is proved when the system matrices are H-matrices having positive diagonal elements. Moreover, block and multi-parameter variants of the new methods, together with their convergence properties, are investigated in detail. Numerical results show that these new methods can achieve high parallel efficiency for solving the large sparse linear complementarity problems on multiprocessor systems.
基金supported by the National Natural Science Foundation of China (Grants 11372018, 11772021)
文摘The main purpose of this paper is to present a linear complementarity problem （LCP） method for a planar passive dynamic walker with round feet based on an event-driven scheme. The passive dynamic walker is treated as a planar multi-rigid-body system. The dynamic equations of the passive dynamic walker are obtained by using Lagrange＇s equations of the second kind. The normal forces and frictional forces acting on the feet of the passive walker are described based on a modified Hertz contact model and Coulomb＇s law of dry friction. The state transition problem of stick-slip between feet and floor is formulated as an LCR which is solved with an event-driven scheme. Finally, to validate the methodology, four gaits of the walker are simulated： the stance leg neither slips nor bounces; the stance leg slips without bouncing; the stance leg bounces without slipping; the walker stands after walking several steps.
