A unified framework of multi-objective cost functions for partitioning unstructured finite element meshes

Good performance of parallel finite element computations on unstructured meshes requires high-quality mesh partitioning. Such a decomposition task is normally done by a graph-based partitioning approach. However, the main shortcoming of graph partitioning algorithms is that minimizing the so-called edge cut is not entirely the same as minimizing the communication overhead. This paper thus proposes a unified framework of multi-objective cost functions, which take into account several factors that are not captured by the graph-based partitioning approach. Freely adjustable weighting parameters in the framework also promote a flexible treatment of different optimization objectives. A greedy-style post-improvement procedure is designed to use these cost functions to improve the quality of subdomain meshes arising from the graph-based partitioning approach. Both serial and parallel implementation of the post-improvement procedure have been done. Numerical experiments show that communication overhead can indeed be reduced by this improvement procedure, thereby increasing the performance of parallel finite element computations.     

Additive Schwarz domain decomposition methods for elliptic problems on unstructured meshes

We give several additive Schwarz domain decomposition methods for solving finite element problems which arise from the discretizations of elliptic problems on general unstructured meshes in two and three dimensions. Our theory requires no assumption (for the main results) on the substructures which constitute the whole domain, so each substructure can be of arbitrary shape and of different size. The global coarse mesh is allowed to be non-nested to the fine grid on which the discrete problem is to be solved and both the coarse meshes and the fine meshes need not be quasi-uniform. In this general setting, our algorithms have the same optimal convergence rate of the usual domain decomposition methods on structured meshes. The condition numbers of the preconditioned systems depend only on the (possibly small) overlap of the substructures and the size of the coares grid, but is independent of the sizes of the subdomains.Revised version on Sept. 20, 1994. Original version: CAM Report 93-40, Dec. 1993, Dept. of Math., UCLA.The work of this author was partially supported by the National Science Foundation under contract ASC 92-01266, the Army Research Office under contract DAAL03-91-G-0150, and ONR under contract ONR-N00014-92-J-1890.The work of this author was partially supported by the National Science Foundation under contract ASC 92-01266, the Army Research Office under contract DAAL03-91-G-0150, and subcontract DAAL03-91-C-0047.     

A posteriori error estimation of the new mixed element schemes for second order elliptic problem on anisotropic meshes

This paper presents a posteriori residual error estimator for the new mixed element scheme for second order elliptic problem on anisotropic meshes. The reliability and efficiency of our estimator are established without any regularity assumption on the mesh.     

A simple cost minimization procedure for the (Q, r) inventory system with a specified fixed cost per stockout occasion

For fast-moving A items, Silver et al. [E.A. Silver, D.F. Pyke, R. Peterson, Inventory Management and Production Planning and Scheduling, third ed., John Wiley & Sons, New York, NY, 1998] explore the (Q, r) inventory system with a specified cost per stockout occasion. However, a number of difficulties have impeded the implement of their solution procedure. That is, the total relevant cost function is not convex in general, so the convergence of the Silver et al.’s solution procedure to the optimal solution of the total relevant cost function is not necessarily true. An easier and more accurate solution procedure is proposed to overcome the shortcoming of the Silver et al.’s solution procedure.     

一类单位圆上的Chebyshev权的Cauchy型求积公式

在本文中,我们首先给出一些基本的结果和一些概念,然后给出单位圆上带Cheby shev权的一些Cauchy主值积分的求积公式,最后给出了它们的误差估计.     

A note on “New kink-shaped solutions and periodic wave solutions for the (2 + 1)-dimensional Sine-Gordon equation”

Exact solutions of the Nizhnik-Novikov-Veselov equation by Li [New kink-shaped solutions and periodic wave solutions for the (2 + 1)-dimensional Sine-Gordon equation, Appl. Math. Comput. 215 (2009) 3777-3781] are analyzed. We have observed that fourteen solutions by Li from 30 do not satisfy the equation. The other 16 exact solutions by Li can be found from the general solutions of the well-known solution of the equation for the Weierstrass elliptic function.