The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth ...The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.展开更多
According to a mathematical model which describes the curing process of composites constructed from continuous fiber-reinforced, thermosetting resin matrix prepreg materials, and the consolidation of the composites, t...According to a mathematical model which describes the curing process of composites constructed from continuous fiber-reinforced, thermosetting resin matrix prepreg materials, and the consolidation of the composites, the solution method to the model is made and a computer code is developed, which for flat-plate composites cured by a specified cure cycle, provides the variation of temperature distribution, the cure reaction process in the resin, the resin flow and fibers stress inside the composite, the void variation and the residual stress distribution.展开更多
In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will...In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal.展开更多
We propose an alternating direction method of multipliers(ADMM)for solving the state constrained optimization problems governed by elliptic equations.The unconstrained as well as box-constrained cases of the Dirichlet...We propose an alternating direction method of multipliers(ADMM)for solving the state constrained optimization problems governed by elliptic equations.The unconstrained as well as box-constrained cases of the Dirichlet boundary control,Robin boundary control,and right-hand side control problems are considered here.These continuous optimization problems are transformed into discrete optimization problems by the finite element method discretization,then are solved by ADMM.The ADMM is an efficient first order algorithm with global convergence,which combines the decomposability of dual ascent with the superior convergence properties of the method of multipliers.We shall present exhaustive convergence analysis of ADMM for these different type optimization problems.The numerical experiments are performed to verify the efficiency of the method.展开更多
基金the Youth Fund of Zhoukou Normal University(ZKnuqn200606)
文摘The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.
文摘According to a mathematical model which describes the curing process of composites constructed from continuous fiber-reinforced, thermosetting resin matrix prepreg materials, and the consolidation of the composites, the solution method to the model is made and a computer code is developed, which for flat-plate composites cured by a specified cure cycle, provides the variation of temperature distribution, the cure reaction process in the resin, the resin flow and fibers stress inside the composite, the void variation and the residual stress distribution.
基金This research is supported by the Special Funds for Major State Research Projects of China(G 1999032804)
文摘In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal.
基金supported by National Natural Science Foundation of China (Grant No. 11471141)the Basic Research of the Science and Technology Development Program of Jilin Province (Grant No. 20150101058JC)
文摘We propose an alternating direction method of multipliers(ADMM)for solving the state constrained optimization problems governed by elliptic equations.The unconstrained as well as box-constrained cases of the Dirichlet boundary control,Robin boundary control,and right-hand side control problems are considered here.These continuous optimization problems are transformed into discrete optimization problems by the finite element method discretization,then are solved by ADMM.The ADMM is an efficient first order algorithm with global convergence,which combines the decomposability of dual ascent with the superior convergence properties of the method of multipliers.We shall present exhaustive convergence analysis of ADMM for these different type optimization problems.The numerical experiments are performed to verify the efficiency of the method.
