Convergence acceleration of the classical trigonometric interpolation by the Eckhoff method is considered, where the exact values of the ＂jumps＂ are approximated by solution of a system of linear equations. The accu...Convergence acceleration of the classical trigonometric interpolation by the Eckhoff method is considered, where the exact values of the ＂jumps＂ are approximated by solution of a system of linear equations. The accuracy of the ＂jump＂ approximation is explored and the corresponding asymptotic error of interpolation is derived. Numerical results validate theoretical estimates.展开更多
The polynomial acceleration method for time history analysis is presented,in which accelerations between several equal neighboring time steps were assumed to be a polynomial function of time interval.With a higher ord...The polynomial acceleration method for time history analysis is presented,in which accelerations between several equal neighboring time steps were assumed to be a polynomial function of time interval.With a higher order polynomial used,a higher accuracy can be obtained,but the stability field of the method becomes narrower.When stability field and computational accuracy are taken into account at the same time,the quadratic acceleration method is superior to linear and cubic acceleration methods in choosing the maximum acceptable time step size.It is also shown that the quadratic acceleration method has desirable arithmetic damp,amplitude decay rate and period elongation rate,though its conditional stability restricts its application in stiff structures.展开更多
A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite...A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite element discretizations of many second-order self-adjoint elliptic boundary value problems. This framework not only covers all known parallel algebraic multilevel preconditioning methods, but also yields new ones. It is shown that all preconditioners within this framework have optimal orders of complexities for problems in two-dimensional(2-D) and three-dimensional (3-D) problem domains, and their relative condition numbers are bounded uniformly with respect to the numbers of both levels and nodes.展开更多
A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of ...A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of second order elliptic boundary value problems by the finite elementmethod. This framework covers not only all known algebraic multilevel preconditioning methods,but yields also new ones. It is shown that all preconditioners within this framework have optimalorders of complexities for problems in two-dimensional (2-D) and three-dimensional(3-D) problemdomains, and their relative condition numbers are bounded uniformly with respect to the numbersof both the levels and the nodes.展开更多
基金Supported in part by grant PS 1867 from the Armenian National Science and Education Fund (ANSEF) based in New York, USA
文摘Convergence acceleration of the classical trigonometric interpolation by the Eckhoff method is considered, where the exact values of the ＂jumps＂ are approximated by solution of a system of linear equations. The accuracy of the ＂jump＂ approximation is explored and the corresponding asymptotic error of interpolation is derived. Numerical results validate theoretical estimates.
基金supported by the Foundation of Science and Technology Commission of Shanghai Municipality(No.07JC14051)。
文摘The polynomial acceleration method for time history analysis is presented,in which accelerations between several equal neighboring time steps were assumed to be a polynomial function of time interval.With a higher order polynomial used,a higher accuracy can be obtained,but the stability field of the method becomes narrower.When stability field and computational accuracy are taken into account at the same time,the quadratic acceleration method is superior to linear and cubic acceleration methods in choosing the maximum acceptable time step size.It is also shown that the quadratic acceleration method has desirable arithmetic damp,amplitude decay rate and period elongation rate,though its conditional stability restricts its application in stiff structures.
文摘A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite element discretizations of many second-order self-adjoint elliptic boundary value problems. This framework not only covers all known parallel algebraic multilevel preconditioning methods, but also yields new ones. It is shown that all preconditioners within this framework have optimal orders of complexities for problems in two-dimensional(2-D) and three-dimensional (3-D) problem domains, and their relative condition numbers are bounded uniformly with respect to the numbers of both levels and nodes.
文摘A framework for algebraic multilevel preconditioning methods is presented for solving largesparse systems of linear equations with symmetric positive definite coefficient matrices, whicharise in the discretization of second order elliptic boundary value problems by the finite elementmethod. This framework covers not only all known algebraic multilevel preconditioning methods,but yields also new ones. It is shown that all preconditioners within this framework have optimalorders of complexities for problems in two-dimensional (2-D) and three-dimensional(3-D) problemdomains, and their relative condition numbers are bounded uniformly with respect to the numbersof both the levels and the nodes.
