Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.

Evaluation of Computational Complexity of Finite Element Analysis Using Gaussian Elimination

Abstract: This paper describes the evaluation of computational complexity of software implementation of finite element method. It has been used to predict the approximate time in which the given tasks will be solved. Also illustrates the increasing of computational complexity in transition from two to three dimensional problem.

Generalized non-linear elastic inversion with constraints in model and data spaces

Abstract: SUMMARY Seismic data are non-linearly related to model parameters such as seismic velocities However, seismic inversion is usually considered in a linear approximation Such techniques as the Born inversion were recently applied to seismic data Non-linear inversion is more complicated and involves extensive calculations Non-linear inversion was developed in the frame work of an unconstrained optimization procedure It uses as a priori information an initial model and probability distribution functions in the data and model spaces (This a priori information is called ‘soft’ bounds) In this paper, we propose a new technique for solving a constrained non-linear inversion This technique will allow us to use a priori information not only in terms of ‘soft’ bounds, but ‘hard’ bounds as well (usually giving more stable and accurate solutions) Non-linear inversion is considered as an iterative procedure which involves a dual transform at each iteration A dual transform allows for considering the problem in terms of the Lagrangian multipliers The number of Lagrangian multipliers is equal to the number of available data and thus, significantly reduces the dimension of the problem (this is true for underdetermined problems only) However, the most important property of the dual transform is that it allows us to consider a constrained problem as an unconstrained problem Another important property is that proper constraints incorporate small-wave numbers in the generalized inversion It is shown that conventional (unconstrained non-linear inversion) is a special case of the constrained non-linear inversion developed in this paper if the truncation operator is represented by the identity matrix

Lax–Wendroff-type schemes of arbitrary order in several space dimensions

Abstract: The second-order accurate Lax-Wendroff scheme is based on the first three terms of a Taylor expansion in time in which the time derivatives are replaced by space derivatives using the governing evolution equations. The space derivatives are then approximated by central differencing. In this paper, we extend this idea and truncate the Taylor expansion at an arbitrary order. One main building block is the so-called Cauchy-Kovalevskaya procedure to replace all the time derivatives by space derivatives which can be formulated for a general system of linear equations with arbitrary order and in two- or three-space dimensions. The linear case is the main focus of this paper because the proposed high-order schemes are good candidates for the approximation of linear wave motion over long distances and times with important applications in aeroacoustics and electromagnetics. The stability and the efficiency of Lax-Wendroff-type schemes are examined. The numerical results are compared with a standard scheme for aeroacoustical applications with respect to their quality and the computational effort. The extensions of the schemes to general grids, nonconstant and nonlinear cases are also addressed.

H-Infinity Attitude Control System Design for a Small-Scale Autonomous Helicopter with Nonlinear Dynamics and Uncertainties

Abstract: The paper focuses on the design of a robust H-infinity attitude controller for an unmanned small-scale helicopter. To take into account the salient nonlinearities, a model with six-degrees-of-freedom nonlinear dynamics and some linear approximation of the aerodynamic parts are used when extracting a linear model and performing simulations to check the performance of the designed controller. To design a robust H-infinity controller, an augmented plant is constructed by adjusting several weighting functions. Then, a robust controller is synthesized utilizing the augmented system with the weighting functions and H-infinity control methodology. Using computer simulation it is shown that the H-infinity controller works well when applied to the nonlinear model even though it is designed using a linear model approximation. Through frequency response analysis, it is shown that the proposed controller can overcome more than half of the uncertainty variations around a nominal point at the input side. The time-domain simulation with the nonlinear model demonstrates that the proposed controller is very robust in relation to the uncertainties, as was expected, overcoming large gain uncertainties and time delay in each input channel. The analysis and simulation results also show that the control system satisfies the Level 1 handling requirements, as defined in Aeronautical Design Standard ADS-33E-PRF.