Order Approximation Technique Research Articles

Higher order meshless approximation applied to Finite Difference and Finite Element methods in selected thermomechanical problems

This paper is focused on the application of higher order meshless schemes in a numerical analysis of selected thermomechanical problems. Numerical investigation is based upon meshless Finite Difference method as well as its combinations with Finite Element method, performed at two different levels of analysis. The first variant assumes conjugation of element and meshless approximation schemes, while in the second one, the problem domain is divided into several disjoint subdomains, with a parallel and independent operating of coupled methods in each subdomain.The most important advantage of the applied approximation technique is no requirements of modification or enhancement of the existing discretization model. Therefore, high approximation orders may be assumed without providing new nodes, elements and degrees of freedom, maintaining the entire numerical model as simple as possible. This approach is especially convenient in coupled multi-field 2D and 3D problems, for instance stationary and non-stationary thermoelastic ones. In those problems, standard higher order approximation techniques may lead to complex numerical models caused by the rapid growth of a number of degrees of freedom and ill-conditioned schemes.The proposed approach is derived for three dimensional non-stationary thermoelastic problems. Moreover, it is examined on variety of 2D and 3D benchmark examples and engineering applications. Both solution accuracy and convergence rate are taken into account. Obtained results are very promising as they reflect the competitiveness of the approach comparing to other commonly applied higher order approaches.

A Second Order Approximation Technique for Robust Shape Optimization

We present a second order approximation for the robust counterpart of general uncertain nonlinear programs with state equation given by a partial di erential equation.We show how the approximated worst-case functions, which are the essential part of the approximated robust counterpart, can be formulated as trust-region problems that can be solved effciently using adjoint techniques. Further, we describe how the gradients of the worst-case functions can be computed analytically combining a sensitivity and an adjoint approach. This methodis applied to shape optimization in structural mechanics in order to obtain optimal solutions that are robust with respect to uncertainty in acting forces. Numerical results are presented.

Isogeometrical approach for cable type structures allowing large sliding contact

AbstractA special combination of two finite elements approaches is considered in order to derive a formulation suitable for cable type structures. First, a finite beam element allowing arbitrarily large rotations together with a high order approximation technique including a C1‐continuous approximation is used to model cable behavior. Afterwards, a covariant approach for a curve‐to‐curve contact is exploited to incorporate contact between a pair of cable elements. This leads to a cable type element with contact. In numerical examples both “soft” and “hard” cables are represented. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Design of adaptive supply voltage for sub-threshold logic based on sub-1 V bandgap reference circuit

This paper presents the design methodology to produce an adaptive supply voltage, which is used to drive digital sub-threshold logic system. Design guidelines to maintain constant speed and power via adaptive V DD regulation are presented first. Then the paper discusses modification of sub-1 V bandgap reference (BGR) circuits using dynamic threshold MOSFET technique to provide the necessary adaptive reference voltage. Another well-known sub-1 V BGR circuit using current mode technique is also fabricated and compared. Both circuits are implemented in CMOS 0.18 μm technology. Empirical data from SPICE simulation and first order approximation techniques are used to derive analytical design models used inside BGR circuit. Measurement results of both the fabricated circuits show reference voltage output of 500 mV range; which are in good match of SPICE simulation.

'EDCON': an educational control system analysis and design program

A PC-based software package called EDCON which is a useful tool for teaching basic control system theory is discussed. It provides a user friendly environment that allows students to vary system parameters and design requirements to see the effects on system response. The package is designed around the root locus plot of a unity feedback control system. It uses a second order approximation technique to calculate and graph the unit step response of the system for any value of gain, and gives all the time and frequency parameters of the system. The package was developed to be used as a complement to an undergraduate course in control systems analysis and design. >

A higher order approximation technique for restricted linear least-squares problems

An essential limitation for the method of weighting for equality constrained linear least-squares problems is the sub-optimality of the attainable convergence rate. In this paper, we propose a method, related to the method of iterated Tikhonov regularisation, that (under suitable conditions) gives rise to convergence rates which are arbitrarily near the optimal rate. As a by-product, we develop the theory of iterated Tikhonov regularisation for equations with unbounded linear operators.

Technical Note—Extension of the Luss-Gupta Resource Allocation Algorithm by Means of First Order Approximation Techniques

A resource allocation algorithm proposed by Luss and Gupta is extended by the introduction of a numerical method for the optimal distribution of a continous resource among preselected activities as an option to the analytical method applied in the original algorithm. The numerical method allows return functions which cannot be dealt with by the analytical method. An integral part of the numerical method is a composite recurrence relation obtained from the Kuhn-Tucker conditions of the problem with linear functions substituted for the derivatives of the return functions. The convergency of the recurrence process is proven for a class of return functions.

A method for estimating the sampling variances of multipliers derived from a from-to model

Interindustry models provide a) a simple, logical, and internally consistent way of portraying the interdependent structure of a region and b) an analytic framework which can be used to provide answers to a wide variety of questions. Many of these answers can be expressed as easily understood multipliers, but because the persons for whom these multipliers are most useful possess only limited understanding of the underlying model, they are often forced to accept (or reject) them on faith. In many cases it should be possible to supply these users with some indication of the reliability of estimated multipliers. Many factors affect reliability and these factors are not equally measurable. This paper has the limited objective of estimating that component of multiplier variance induced by the use of sample data to construct the basic model. The procedure adopted exploits a first order approximation technique. It is applied to the data used to construct a from-to model of Oklahoma Planning Region 9. Selected limitations and implications of the resulting estimates are examined.

The transient and steady-state response of a hereditary system

The distinctive features of the response of a system with limited slip and trigonometric excitation are discussed. Both the steady-state and transient behavior of this hereditary system are predicted using a first order approximation technique, and the predictions are compared with the results of “exact” numerical solutions.