A parallel strategy for the multiparametric analysis of structures with large contact and friction surfaces

The objective of this work is to develop an efficient strategy for the resolution of many configurations of a quasi-static problem with multiple contacts. Our approach is based on the multiscale LATIN method with domain decomposition. Here we propose to take advantage of the capability of the LATIN method to reuse the solution of a given problem in order to solve many similar problems. We firstly introduce the LATIN method and compare our approach to different strategies commonly used to solve contact problems. Then, we illustrate the capabilities of our method through two examples.     

A Splitting Method for Orthogonality Constrained Problems

Orthogonality constrained problems are widely used in science and engineering. However, it is challenging to solve these problems efficiently due to the non-convex constraints. In this paper, a splitting method based on Bregman iteration is represented to tackle the optimization problems with orthogonality constraints. With the proposed method, the constrained problems can be iteratively solved by computing the corresponding unconstrained problems and orthogonality constrained quadratic problems with analytic solutions. As applications, we demonstrate the robustness of our method in several problems including direction fields correction, noisy color image restoration and global conformal mapping for genus-0 surfaces construction. Numerical comparisons with existing methods are also conducted to illustrate the efficiency of our algorithms.     

集中谐载力作用下三边固定一边自由板的受迫振动

应用混合变量最小作用量原理求解了三边固定一边自由矩形板在任意集中谐载作用下的受迫振动问题，建立了求解这类问题受迫振动稳态解的新方法，对于结构工程抗震问题中的振动分析给出了一个新的解决途径，所获得的计算结果，跟现有的文献进行比较证明了其正确性，因此该方法不仅具有重要的理论价值，而且可以为工程实际直接采用。     

A Numerical Method for Solving Stochastic Optimal Control Problems with Linear Control

We introduce a numerical method to solve stochastic optimal control problems which are linear in the control. We facilitate the idea of solving two-point boundary value problems with spline functions in order to solve the resulting dynamic programming equation. We then show how to effectively reduce the dimension in the proposed algorithm, which improves computational time and memory constraints. An example, motivated as an invest problem with uncertain cost, is provided, and the effectiveness of our method demonstrated.     

A modified simple heuristic for the p-median problem, with facilities design applications

Facilities design is closely related to efficient use of available resources. This paper presents a heuristic approach to solve two core problems of a good facilities design: facility location and facility layout. The latter group of problems will be solved for warehouse and production systems in particular. All these problems can be formulated as p-median clustering problems. Teitz and Bart (Oper. Res. 16 (1968) 955–961) developed the vertex substitution method to solve those problems. This paper introduces effective improvements on this heuristic. The approach is tested on a large number of randomly generated cases and on problems taken from the literature. The results demonstrate the effectiveness and superiority of our method.     

Graph-based induction as a unified learning framework

We describe a graph-based induction algorithm that extracts typical patterns from colored digraphs. The method is shown to be capable of solving a variety of learning problems by mapping the different learning problems into colored digraphs. The generality and scope of this method can be attributed to the expressiveness of the colored digraph representation, which allows a number of different learning problems to be solved by a single algorithm. We demonstrate the application of our method to two seemingly different learning tasks: inductive learning of classification rules, and learning macro rules for speeding up inference. We also show that the uniform treatment of these two learning tasks enables our method to solve complex learning problems such as the construction of hierarchical knowledge bases.     

Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems

In this paper we propose an adaptive multilevel correction scheme to solve optimal control problems discretized with finite element method. Different from the classical adaptive finite element method (AFEM for short) applied to optimal control which requires the solution of the optimization problem on new finite element space after each mesh refinement, with our approach we only need to solve two linear boundary value problems on current refined mesh and an optimization problem on a very low dimensional space. The linear boundary value problems can be solved with well-established multigrid method designed for elliptic equation and the optimization problems are of small scale corresponding to the space built with the coarsest space plus two enriched bases. Our approach can achieve the similar accuracy with standard AFEM but greatly reduces the computational cost. Numerical experiments demonstrate the efficiency of our proposed algorithm.     

Numerically accurate code synthesis for Gauss pivoting method to solve linear systems coming from mechanics

In numerical analysis of mechanical problems, we usually have to solve huge linear systems, which may be non-symmetric or ill-conditioned. For these reasons, it is necessary to develop original and domain specific approaches to treat these family of systems. In this work, we introduce a new methodology to synthesize numerically accurate programs for the Gauss pivoting method. The synthesis is based on program transformation techniques and it is guided in its estimation of accuracy by interval arithmetic that computes the propagation of roundoff errors. We apply our code synthesis to the resolution of systems coming from finite element method arising from problems of Mechanics. We test our synthesizer on two problems concerning the flexion of a beam and the sliding contact of a viscoelastic body on a rigid foundation. Our experimental results show that the specialized synthesized code to solve the families of systems given in input is far more accurate and faster than the standard implementation of the Gauss method.     

Complete decomposition algorithm for nonconvex separable optimization problems and applications

In this paper, we present a complete decomposition algorithm for nonconvex separable optimization problems applied in the optimal control problems. This complete decomposition algorithm combines recursive quadratic programming with the dual method. When our algorithm is applied to discretized optimal control problems, a simple and parallel computation and a simple and regular data flow pattern between consecutive computational steps results. This paper also suggests an approach for developing a hardware implementation of our algorithm and gives an estimation of the execution time needed to solve a practical example.     

SCHOOL SCHEDULING USING THRESHOLD ACCEPTING

In this paper, we focus on solving problems modeled after a real-world high school timetable problem. It includes multiple objectives and a variety of constraints. It mainly involves producing an optimal schedule for each teacher and for each class. The conventional integer programming approach seems to have some difficulties with solving such problems. The versatility of our proposed heuristic based on a modification of the threshold accepting method is exemplified through our problem solving. For comparison sake, simulated annealing was also used to solve the same problems.