A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of ...A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of high time cost in adopting a rational-based optimal design method for ship structural design. Furthermore,the method was verified by its effective application in optimization of the mid-ship section of a container ship. A full 3-D FEM model of a ship,suffering static and quasi-static loads, was used as the analyzing object for evaluating the structural performance of the mid-ship module, including static strength and buckling performance. Research results reveal that this new method could substantially reduce the computational cost of the rational-based optimization problem without decreasing its accuracy, which increases the feasibility and economic efficiency of using a rational-based optimal design method in ship structural design.展开更多
The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numeri...The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numerical results show the efficiency of this new approach.展开更多
Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by u...Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by using the extended Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.展开更多
对高阶紧致(high order compact)方法进行了详细的讨论和简洁的评述．这就是:回顾了方法的发展历史,指出了方法优点,分析了方法的基本特征、构造方式和应用现状,预示了它的近期发展和研究形势．特别地,就方法的数学基础——有理逼近和P...对高阶紧致(high order compact)方法进行了详细的讨论和简洁的评述．这就是:回顾了方法的发展历史,指出了方法优点,分析了方法的基本特征、构造方式和应用现状,预示了它的近期发展和研究形势．特别地,就方法的数学基础——有理逼近和Pade逼近进行了归纳．在文章中提供了丰富的方法信息和大量的有关公式．展开更多
In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the （2＋ 1 ）-dimensional Nizhnik-Novikov-Veselov equati...In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the （2＋ 1 ）-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.展开更多
基金Supported by the Project of Ministry of Education and Finance(No.200512)the Project of the State Key Laboratory of ocean engineering(GKZD010053-10)
文摘A new multi-level analysis method of introducing the super-element modeling method, derived from the multi-level analysis method first proposed by O. F. Hughes, has been proposed in this paper to solve the problem of high time cost in adopting a rational-based optimal design method for ship structural design. Furthermore,the method was verified by its effective application in optimization of the mid-ship section of a container ship. A full 3-D FEM model of a ship,suffering static and quasi-static loads, was used as the analyzing object for evaluating the structural performance of the mid-ship module, including static strength and buckling performance. Research results reveal that this new method could substantially reduce the computational cost of the rational-based optimization problem without decreasing its accuracy, which increases the feasibility and economic efficiency of using a rational-based optimal design method in ship structural design.
文摘The Legendre rational approximation is investigated. Some approximation results are established, which form the mathematical foundation of a new spectral method on the whole line. A model problem is considered. Numerical results show the efficiency of this new approach.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004CB318000
文摘Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by using the extended Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.
文摘对高阶紧致(high order compact)方法进行了详细的讨论和简洁的评述．这就是:回顾了方法的发展历史,指出了方法优点,分析了方法的基本特征、构造方式和应用现状,预示了它的近期发展和研究形势．特别地,就方法的数学基础——有理逼近和Pade逼近进行了归纳．在文章中提供了丰富的方法信息和大量的有关公式．
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004CB318000 .
文摘In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the （2＋ 1 ）-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.
