Piecewise linear function

About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.

Numerical simulation of three-dimensional free surface flows

Abstract: A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2):439) is extended to three dimensional situations. The mathematical formulation of the model is similar to that of the volume of fluid (VOF) method, but the numerical procedures are different. A splitting method is used for the time discretization. At each time step, two advection problems-one for the predicted velocity field and the other for the volume fraction of liquid-are to be solved. Then, a generalized Stokes problem is solved and the velocity field is corrected. Two different grids are used for the space discretization. The two advection problems are solved on a fixed, structured grid made out of small cubic cells, using a forward characteristic method. The generalized Stokes problem is solved using continuous, piecewise linear stabilized finite elements on a fixed, unstructured mesh of tetrahedrons. The three-dimensional implementation is discussed. Efficient postprocessing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces memory requirements. Numerical results are presented for complex geometries arising in mold filling. Copyright (C) 2003 John Wiley Sons, Ltd.

Methods of nonlinear programming

Abstract: This chapter focuses on the methods of solution for general nonlinear programs. Several methods have been developed where either f or all g i are nonlinear or only f is nonlinear. The chapter states various methods including separable programming, Kelley's cutting plane algorithm, Zoutendijk's method of feasible direction, Rosen's Gradient projection method, Wolfe's reduced gradient method, Zangwill's Convex–Simplex Method, and Dantzig's method for convex programming. Separable programming is a special technique for obtaining solutions of a class of nonlinear programming problems where the functions involved can be expressed as a sum of functions each of a single variable only—that is, the functions f(X) and g i (X) are of the form. The linear function and the nonlinear function are examples of separable function. There are some functions, which are not directly separable can also be made so by transformation of variables. To be able to make use of the simplex method for finding a solution of the problem, the separable functions f j (x j ) and g ij (x j ), i = 1,2..m are first approximated by piecewise linear functions.

Control and Dynamics of Quarter-Car Models With Dual-Rate Damping

Abstract: Dynamics of a controlled quarter-car model is investigated. In this model, the damping coefficient of the car suspension is selected in a way that the resulting semiactive system approximates the performance of an active suspension system designed to produce sky-hook damping. According to this control strategy, the damping coefficient switches between two different values, leading to a piecewise linear dynamical model. For this model, the equation of motion is first presented in a general normalized form. Then, an appropriate methodology is applied for obtaining exact periodic motions for the case of forcing resulting from a road with harmonic profile. This methodology is based on employing the exact solution form within response intervals where the damping coefficient remains constant. The unknowns of the problem are then determined by imposing a set of periodicity and matching conditions. The stability analysis of the located motions is also performed by applying a method that is suitable for piecewise ...