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991.
992.
We analyze a single step method for solving second-order parabolic initial-boundary value problems. The method uses a step-doubling extrapolation scheme in time based on backward Euler and a Galerkin approximation in space. The technique is shown to be a second-order correct approximation in time. Since step-doubling can be used as a mechanism for step-size control, the analysis is done for variable time steps. The stability properties of step-doubling are contrasted with those of Crank-Nicolson, as well as those of more general extrapolated theta-weighted schemes. We provide an example computation that illustrates both the use of step-doubling for adaptive time step control and the application of step-doubling to a nonlinear system.
993.
Todd Munson 《Mathematical Programming》2007,110(3):561-590
Meshes containing elements with bad quality can result in poorly conditioned systems of equations that must be solved when
using a discretization method, such as the finite-element method, for solving a partial differential equation. Moreover, such
meshes can lead to poor accuracy in the approximate solution computed. In this paper, we present a nonlinear fractional program
that relocates the vertex coordinates of a given mesh to optimize the average element shape quality as measured by the inverse
mean-ratio metric. To solve the resulting large-scale optimization problems, we apply an efficient implementation of an inexact
Newton algorithm that uses the conjugate gradient method with a block Jacobi preconditioner to compute the direction. We show
that the block Jacobi preconditioner is positive definite by proving a general theorem concerning the convexity of fractional
functions, applying this result to components of the inverse mean-ratio metric, and showing that each block in the preconditioner
is invertible. Numerical results obtained with this special-purpose code on several test meshes are presented and used to
quantify the impact on solution time and memory requirements of using a modeling language and general-purpose algorithm to
solve these problems. 相似文献
994.
995.
Michael J. Todd 《Mathematical Programming》1983,26(1):1-20
This paper is concerned with linear programming problems in which many of the constraints are handled implicitly by requiring that the vector of decision variables lie in a polyhedronX. It is shown that the simplex method can be implemented using a working basis whose size is the number of explicit constraints as long as the local structure ofX around the current point is known. Various ways of describing this local structure lead to known implementations whenX is defined by generalized or variable upper bounds or flow conservation constraints. In the general case a decomposition principle can be used to generate this local structure. We also show how to update factorizations of the working basis. 相似文献
996.
Michael J Todd 《Journal of Combinatorial Theory, Series B》1985,39(2):105-133
We prove constructively duality theorems of linear and quadratic programming in the combinatorial setting of oriented matroids. One version of our algorithm for linear programing has the interesting feature of maintaining feasibility. The development of the quadratic programming duality result suggests the study of properties of square matrices such as symmetry and positive semi-definiteness in the context of oriented matroids. 相似文献
997.
Syntheses of morpholine-2,3-diones and 2-hydroxymorpholin-3-ones: intermediates in the synthesis of aprepitant 总被引:1,自引:0,他引:1
Todd D. Nelson Jonathan D. Rosen Bridgette Craig James M. McNamara 《Tetrahedron letters》2004,45(48):8917-8920
The preparation of morpholine-2,3-diones and 2-hydroxymorpholin-3-ones from N-substituted β-amino alcohols is reported. These were useful intermediates in the synthesis and development of aprepitant. 相似文献
998.
999.
1000.
Deposits of Ag on Si(111), at room temperature, have yielded a linear Auger signal-time characteristic to a gradient break point at (7.6 ± 0.9) × 1014 atoms ofAg cm?2, which is very close to the Si surface state density of (8–10) × 1014 cm?2, and which supports a Stranski-Krastanov growth mechanism. Analysis of the Auger spectra at the monolayer end point revealed a new peak at 82 ± 1 eV. This peak is believed to arise from an Auger process involving an induced Ag-Si interface state. A model is proposed for this state arising from the chemisorption of Ag on Si. 相似文献