How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linea...How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).展开更多
Pyramidal elements are often used to connect tetrahedral and hexahedral elements in the finite element method.In this paper we derive three new higher order numerical cubature formulae for pyramidal elements.
基金support provided by the Ministry of Science and Technology,Taiwan,ROC under Contract No.MOST 110-2221-E-019-044.
文摘How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).
基金This paper was supported by The National Natural Science Foundation of China(No.10771063)Key Laboratory ofHigh performance Computation and Stochastic Information Processing,Hunan Province and Ministry of Education,Institutional Research Plan No.AV0Z 10190503,Anhui Agricultural University(yj2012-03)Grant No.IAA 100190803 of the Academy of Sciences of the Czech Republic and The Natural Sciences and Engineering Research Council of Canada.The authors are indebted to Pavel Krızek and Kevin B.Davies for their help in preparation of Figs.1 and 2,and Jan Brandts for fruitful discussions.
文摘Pyramidal elements are often used to connect tetrahedral and hexahedral elements in the finite element method.In this paper we derive three new higher order numerical cubature formulae for pyramidal elements.
