Surface mesh regeneration considering curvatures

This work describes an automatic algorithm for unstructured mesh regeneration on arbitrarily shaped three-dimensional surfaces. The arbitrary surface may be: a triangulated mesh, a set of points, or an analytical surface (such as a collection of NURBS patches). To be generic, the algorithm works directly in Cartesian coordinates, as opposed to generating the mesh in parametric space, which might not be available in all the cases. In addition, the algorithm requires the implementation of three generic functions that abstractly represent the supporting surface. The first, given a point location, returns the desired characteristic size of a triangular element at this position. The second method, given the current edge in the boundary-contraction algorithm, locates the ideal apex point that forms a triangle with this edge. And the third method, given a point in space and a projection direction, returns the closest point on the geometrical supporting surface. This work also describes the implementation of these three methods to re-mesh an existing triangulated mesh that might present regions of high curvature. In this implementation, the only information about the surface geometry is a set of triangles. In order to test the efficiency of the proposed algorithm of surface mesh generation and implementation of the three abstract methods, results of performance and quality of generated triangular element examples are presented.     

Aggregation in hub location problems

Because of their widespread use in real-world transportation situations, hub location models have been extensively studied in the last two decades. Many types of hub location problems are NP-hard and remain unmanageable when the number of nodes exceeds 200. We present a way to tackle large-sized problems using aggregation, explore the resulting error, and show how to reduce it. Furthermore, we develop a heuristic based on aggregation for k-hub center problems and present computational results.     

The study of forced oscillations of shells under circumfluent flow effect

The influence of rigidity and damping properties on roll wave phase speed in large-dimension shells, streamlined with fluid flow is investigated. It is shown that the roll wave in the finite-length shell can exist only with the presence of damping. The phase speed estimations under varied flexural rigidity are obtained.     

Stability independent of delay using rational functions

This paper is concerned with the problem of assessing the stability of linear systems with a single time-delay. Stability analysis of linear systems with time-delays is complicated by the need to locate the roots of a transcendental characteristic equation. In this paper we show that a linear system with a single time-delay is stable independent of delay if and only if a certain rational function parameterized by an integer k and a positive real number T has only stable roots for any finite T≥0 and any k≥2. We then show how this stability result can be further simplified by analyzing the roots of an associated polynomial parameterized by a real number δ in the open interval (0,1). The paper is closed by showing counterexamples where stability of the roots of the rational function when k=1 is not sufficient for stability of the associated linear system with time-delay. We also introduce a variation of an existing frequency-sweeping necessary and sufficient condition for stability independent of delay which resembles the form of a generalized Nyquist criterion. The results are illustrated by numerical examples.     

A tracking problem for mechanical systems with delay in control

A problem of tracking for mechanical systems described by nonstationary nonlinear equations is studied at relay control with delay is studied. An approach that makes it possible to solve problems of tracking for mechanical systems whose parameters may continuously vary with time is developed. This approach is based on the transformation of the system and construction of a Lyapunov vector-function with components of the form of vector norm.     

Reducing conservativeness in recent stability conditions of TS fuzzy systems

In this correspondence a new simple strategy for reducing the conservativeness in stability analysis of continuous-time Takagi-Sugeno fuzzy systems based on fuzzy Lyapunov functions is proposed. This new strategy generalizes previous results.     

Medial axis computation for planar free-form shapes

We present a simple, efficient, and stable method for computing—with any desired precision—the medial axis of simply connected planar domains. The domain boundaries are assumed to be given as polynomial spline curves. Our approach combines known results from the field of geometric approximation theory with a new algorithm from the field of computational geometry. Challenging steps are (1) the approximation of the boundary spline such that the medial axis is geometrically stable, and (2) the efficient decomposition of the domain into base cases where the medial axis can be computed directly and exactly. We solve these problems via spiral biarc approximation and a randomized divide & conquer algorithm.     

ALTDSE: An Arnoldi–Lanczos program to solve the time-dependent Schrödinger equation

We describe a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom. While the field-free Hamiltonian and the dipole matrices may be generated using an arbitrary primitive basis, they are assumed to have been transformed to the eigenbasis of the problem before the solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. Probabilities for survival of the ground state, excitation, and single ionization can be extracted from the propagated wavefunction.

Program summary

Program title: ALTDSECatalogue identifier: AEDM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2154No. of bytes in distributed program, including test data, etc.: 30 827Distribution format: tar.gzProgramming language: Fortran 95. [A Fortran 2003 call to “flush” is used to simplify monitoring the output file during execution. If this function is not available, these statements should be commented out.].Computer: Shared-memory machinesOperating system: Linux, OpenMPHas the code been vectorized or parallelized?: YesRAM: Several Gb, depending on matrix size and number of processorsSupplementary material: To facilitate the execution of the program, Hamiltonian field-free and dipole matrix files are provided.Classification: 2.5External routines: LAPACK, BLASNature of problem: We describe a computer program for a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom [1,2]. The probabilities for survival of the initial state, excitation of discrete states, and single ionization due to multi-photon processes can be obtained.Solution method: The solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. The field-free Hamiltonian and the dipole matrices, originally generated in an arbitrary basis (e.g., the flexible B-spline R-matrix (BSR) method with non-orthogonal orbitals [3]), must be provided in the eigenbasis of the problem as input.Restrictions: The present program is restricted to a ¹S^e initial state and linearly polarized light. This is the most common situation experimentally, but a generalization is straightforward.Running time: Several hours, depending on the number of threads used.References: [1] X. Guan, O. Zatsarinny, K. Bartschat, B.I. Schneider, J. Feist, C.J. Noble, Phys. Rev. A 76 (2007) 053411. [2] X. Guan, C.J. Noble, O. Zatsarinny, K. Bartschat, B.I. Schneider, Phys. Rev. A 78 (2008) 053402. [3] O. Zatsarinny, Comput. Phys. Comm. 174 (2006) 273.     

Implementation and analysis of multigrid schemes with finite elements for elliptic optimal control problems

The detailed implementation and analysis of a finite element multigrid scheme for the solution of elliptic optimal control problems is presented. A particular focus is in the definition of smoothing strategies for the case of constrained control problems. For this setting, convergence of the multigrid scheme is discussed based on the BPX framework. Results of numerical experiments are reported to illustrate and validate the optimal efficiency and robustness of the performance of the present multigrid strategy.     

A Simplified Design for Strict Lyapunov Functions Under Matrosov Conditions

We construct strict Lyapunov functions for broad classes of nonlinear systems satisfying Matrosov type conditions. Our new constructions are simpler than the designs available in the literature. We illustrate the practical interest of our designs using a globally asymptotically stable biological model.