Showing papers on "Piecewise linear function published in 1993"
01 Jan 1993
TL;DR: In this article, an upwind finite-volume scheme was proposed for solving scalar advection-diffusion equations as well as the Euler and Navier-Stokes equations.
Abstract: This paper presents recent improvements in high-order K-exact reconstruction on unstructured meshes. The new reconstruction procedures are incorporated into a basic upwind finite-volume scheme suitable for solving scalar advection-diffusion equations as well as the Euler and Navier-Stokes equations. Numerical calculations are performed comparing the present method with lower order accurate reconstruction procedures (piecewise constant and piecewise linear) and various competing technologies such as the fluctuation splitting method of Roe (1987) and Deconinck et al. (1992) and a system-variant of the streamline diffusion Petrov-Galerkin method developed by Hansbo (1991) and Hansbo and Johnson (1991). Five test problems are used in the numerical comparisons: scalar circular advection, transonic and supersonic Euler flow, laminar boundary-layer flow, and general compressible Navier-Stokes flow.
316 citations
TL;DR: A recursive prediction error identification algorithm, based on the Wiener model, is derived and shows that the input signal should be such that there is signal energy in the whole range of the piecewise linear approximation.
292 citations
TL;DR: The features of Bilevel Linear Programming are reviewed by presenting prior results as well as providing new results, including the capability of the problem to formulate any piecewise linear function and its connection to other optimization problems.
178 citations
TL;DR: In this paper, upwind methods for the 1-D Euler equations are reinterpreted as residual distribution schemes, assuming continuous piecewise linear space variation of the unknowns defined at the cell vertices.
174 citations
TL;DR: This work considers the approximate solution of self-adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non-uniform tetrahedral mesh which is generated adaptively.
Abstract: We consider the approximate solution of self-adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non-uniform tetrahedral mesh which is generated adaptively. The arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner. Here, the accuracy of the iterative solution is coupled with the discretization error. As the performance of hierarchical bases preconditioners deteriorates in three space dimensions, the BPX preconditioner is used, taking special care of an efficient implementation. Reliable a posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements. To illustrate the theoretical results, we consider a familiar model problem involving reentrant corners and a real-life problem arising from hyperthermia, a recent clinical method for cancer therapy.
142 citations
TL;DR: A linearity check of data is used to choose between linear and nonlinear forms of Muskingum models and an example is illustrated using MUPERS, which is menu‐driven and user‐friendly, with graphics capabilities.
Abstract: The conventional method of parameter estimation of Muskingum flood‐routing models is based on a graphical bivariate curve‐fitting procedure. The subjectivity of this procedure may lead to problems of reproducibility. A software, called MUPERS (Muskingum parameter estimation and flood routing system) was developed for estimating the parameters of a linear or nonlinear Muskingum model of choice and for routing the flood through the river reach. Although 11 methods of parameter estimation‐eight for the linear, two for the piecewise linear, and one for the nonlinear model‐are included in the software, only six of them are discussed in this note. A linearity check of data is used to choose between linear and nonlinear forms of Muskingum models. An example is illustrated using MUPERS, which is menu‐driven and user‐friendly, with graphics capabilities. A comparison of the performance of the different parameter‐estimation methods is also discussed.
123 citations
TL;DR: Analytical methods for truncating and scaling lattices to be used in vector quantizations are given, and their utility is demonstrated for independent and identically distributed Gaussian and Laplacian sources.
Abstract: Lattice vector quantizer design procedures for nonuniform sources are presented. The procedures yield lattice vector quantizers with excellent performance and retaining the structure required for fast quantization. Analytical methods for truncating and scaling lattices to be used in vector quantizations are given, and their utility is demonstrated for independent and identically distributed (i.i.d.) Gaussian and Laplacian sources. An analytical technique for piecewise linear multidimensional compandor designs is evaluated for i.i.d. Gaussian and Laplacian sources by comparing its performance to that of the other vector quantizers. >
101 citations
TL;DR: In this article, a semianalytical quasilinear method based on the describing function formulation is proposed for the harmonic response analysis of structures with symmetrical nonlinearities, where the equations of motion are converted to a set of nonlinear algebraic equations.
Abstract: A semianalytical quasilinear method based on the describing function formulation is proposed for the harmonic response analysis of structures with symmetrical nonlinearities. The equations of motion are converted to a set of nonlinear algebraic equations. The linear and nonlinear parts of the structure are dealt with separately, the former being represented by the constant linear receptance matrix, and the latter by the generalized quasilinear matrix which is updated at each iteration. Several examples dealing with cubic stiffness, piecewise linear stiffness, and coulomb friction type of nonlinearities are presented
94 citations
TL;DR: In this article, an analysis is presented for determining exact steady state response for a class of strongly non-linear multiple-degree-of-freedom oscillators, which consist of a linear component, with an arbitrary number of degrees of freedom and configuration, incorporating a component with a geometric nonlinearity.
88 citations
Journal Article•
TL;DR: The behavior of the mean exit time for the piecewise constant potential is characterized by the absence of correlations between barrier crossings and barrier fluctuations.
Abstract: We investigate the thermally activated escape of a Brownian particle over a potential barrier whose height fluctuates with a rate α between the values E + and E - . We are mainly interested in the low temperature behavior where E + /T>>E - /T. We calculate the mean exit time as a function of the rate of the barrier fluctuations for the piecewise linear and the piecewise constant barrier, τ=τ(α). For the piecewise constant potential we find three different regimes:τ∼τ + for α τ - -1 =exp(-E - /T), and τ∼α -1 for τ + -1 <α<τ - -1
82 citations
TL;DR: An optimal order multigrid method is developed for the pure displacement problem in two-dimensional linear elasticity, based on a nonconforming mixed formulation, where the displacement is approximated by weakly continuous piecewise linear vector functions, and the pressure is approximating by piecewise constants.
Abstract: An optimal order multigrid method is developed for the pure displacement problem in two-dimensional linear elasticity. It is based on a nonconforming mixed formulation, where the displacement is approximated by weakly continuous piecewise linear vector functions, and the pressure is approximated by piecewise constants. The full multigrid convergence is proved. The performance of the multigrid method does not deteriorate as the material becomes nearly incompressible.
TL;DR: In this paper, iterative dynamic programming is extended to provide piecewise linear continuous control policies to systems described by sets of ordinary differential equations, and only a single grid point is used for the state at each time stage.
Abstract: Iterative dynamic programming is extended to provide piecewise linear continuous control policies to systems described by sets of ordinary differential equations. To ensure continuity in the optimal control policy, only a single grid point is used for the state at each time stage. Three examples (optimal control of a continuous stirred tank reactor (CSTR), nondifferentiable system, fed-batch fermenter) that are used to test the viability of the procedure show that the proposed procedure is attractive from the computational point of view and provides reliable results even for highly nonlinear systems that exhibit singular control
TL;DR: An entirely new algorithm to find all the equilibrium points of piecewise-linear (PWL) circuits is presented, which is structured as a genealogical tree, whose nodes represent specific polyhedral circuits.
Abstract: An entirely new algorithm to find all the equilibrium points of piecewise-linear (PWL) circuits is presented. To this aim, the new class of the so-called polyhedral circuits, associated to the PWL ones, are defined by replacing the PWL elements with the polyhedral elements. The algorithm is structured as a genealogical tree, whose nodes represent specific polyhedral circuits. All the equilibrium points of the original PWL circuit can be captured by the analysis of these nodes. This analysis requires the solution of the phase I of linear programming (LP) problems, one problem for each node. An example shows the capabilities of this algorithm. >
01 Jul 1993
TL;DR: An approach toward path-oriented timing-driven placement is proposed, which first transforms the placement with timing constraints to a Lagrange problem, and a primal-dual approach is used to find the optimal relative module locations.
Abstract: An approach toward path-oriented timing-driven placement is proposed. We first transform the placement with timing constraints to a Lagrange problem. A primal-dual approach is used to find the optimal relative module locations. In each primal dual iteration, the primal problem is solved by a piecewise linear resistive network method, while the dual process is used to update the Lagrange multiplier. The sparsity of the piecewise linear resistive network is exploited to obtain dramatic improvement on the efficiency of the calculation. Up to 22.0% of clock cycle reduction was observed for Primary2 test case.
TL;DR: In this article, a Monte Carlo study was conducted to evaluate the effects of modelling assumptions and design parameters on the behaviour of interactive methods for the discrete choice MCDM problem, based on explicit value function models.
Abstract: This paper describes a Monte Carlo study conducted to evaluate the effects of modelling assumptions and design parameters on the behaviour of interactive methods for the discrete choice MCDM problem, based on explicit value function models. The purpose of the study is to identify those assumptions and parameters which lead to the most efficient use of preference judgements made by the decision maker, and to the greatest robustness to judgmental errors. It is concluded that nonlinearities in the value function need to be modelled, achieved here by use of a piecewise linear form. It was also found that search for indifference points, rather than using simple preference judgements alone, is of great advantage, best realized by expressing judgements in terms of pairwise trade-offs. Methods incorporating these features are highly robust to judgmental errors. Interactive methods of this class are compared with a priori fitting of similar value functions, and found to give a very similar quality of solution.
TL;DR: In this article, the authors propose a decomposition technique for linear programs which proposes a new treatment of the master program in the classical Dantzig-Wolfe algorithm, exploiting the relationship between the master programs and the minimization of a convex piecewise linear function.
TL;DR: In this article, the authors present an efficient algorithm for finding all solutions of piecewise-linear resistive circuits using two types of sign tests; one is a new test that is proposed in this paper, and the other is the test proposed by Yamamura and Ochiai (1992).
Abstract: This paper presents an efficient algorithm for finding all solutions of piecewise-linear resistive circuits. The algorithm uses two types of sign tests; one is a new test that is proposed in this paper, and the other is the test proposed by Yamamura and Ochiai (1992). The computational complexity of the new test is much smaller than that of Yamamura and Ochiai's test. These tests eliminate many linear regions that do not contain a solution. Therefore, the number of simultaneous linear equations to be solved is substantially reduced. The proposed algorithm is very simple and efficient. >
TL;DR: In this paper, the authors present a universal method to design n-dimensional piecewise linear circuits, which are described by a system of differential equation associated with a piece-wise linear continuous vector-field in the ndimensional state-space.
Abstract: In this paper, we present a universal method to design n-dimensional piecewise linear circuits. These circuits are described by a system of differential equation associated with a piecewise linear continuous vector-field in the n-dimensional state-space, which consists of two different linear regions. The circuits contain only two-terminal elements, one piecewise linear resistor and a number of linear resistors, capacitors and inductors. The developed method leads to a variety of structures. It is possible to design n-dimensional canonical circuits containing a minimum number of inductors as well as inductor-free circuits. A surprising result is the transformation of the 3-D Chua circuit into an inductor-free circuit that exhibits the double scroll as well. Using our approach, a theorem that specifies the restriction of eigenvalue patterns associated with a piecewise linear vector-field having at least two equilibrium points can be proved. >
TL;DR: In this article, a piecewise-linear circuit is presented which exhibits a chaotic attractor similar to that observed from the Lorenz equation, and the nonlinearities in the circuit consists of two piecewise linear terms.
Abstract: In this paper we present a simple piecewise-linear circuit which exhibits a chaotic attractor similar to that observed from the Lorenz equation. Whereas the nonlinearities in the Lorenz equation consists of two product terms between two state variables, the nonlinearities in our circuit consists of two piecewise-linear terms.
TL;DR: In this paper, a theoretical analysis of stick-slip instability with reference to systems with one degree of freedom is proposed, where the friction force is approximated with a piecewise linear function, i.e. straight line segments with a suitable slope, assuming that the static friction coefficient is greater than the kinetic one.
TL;DR: In this article, a numerical method to compute free surfaces in electromagnetic shaping and levitation of liquid metals is described, where the surfaces are represented by piecewise linear finite elements and each step requires solving an elliptic boundary value problem in the exterior of the intermediate surfaces.
Abstract: We describe a numerical method to compute free surfaces in electromagnetic shaping and levitation of liquid metals. We use an energetic variational formulation and optimization techniques to compute, a critical point. The surfaces are represented by piecewise linear finite elements. Each step of the algorithm requires solving an elliptic boundary value problem in the exterior of the intermediate surfaces. This is done by using an integral representation on these surfaces.
14 Jun 1993
TL;DR: This work presents a continuation method in which the correct function Φ* is approached through a sequence of smooth Φ functions, and shows a means of generalizing this formalism to the less restrictive case of piecewise linear rather than piecewise flat priors.
Abstract: In emission tomography, a principled means of incorporating a piecewise smooth prior on the source f is via a mixed variable objective function E(f, l) defined on f and binary valued line processes l. MAP estimation on E(f, l) results in the difficult problem of minimizing an objective function that includes a nonsmooth Gibbs prior Φ* defined on the spatial derivatives of f. Previous approaches have used heuristic Gibbs potentials Φ that incorporate line processes, but only approximately. In this work, we present a continuation method in which the correct function Φ* is approached through a sequence of smooth Φ functions. Our continuation method is implemented using a GEM-ICM procedure. Simulation results show improvement using our continuation method relative to using Φ* alone, and to conventional EM reconstructions. Finally, we show a means of generalizing this formalism to the less restrictive case of piecewise linear instead of piecewise flat priors.
TL;DR: A novel architecture for nonlinear adaptive filters that inherits the robust estimation and fast adaptation of linear adaptive filters, along with the approximation and model-fitting properties of tree-structured regression models is proposed and analyzed.
Abstract: The authors propose and analyze a novel architecture for nonlinear adaptive filters These nonlinear filters are piecewise linear filters obtained by arranging linear filters and thresholds in a tree structure A training algorithm is used to adaptively update the filter coefficients and thresholds at the nodes of the tree, and to prune the tree The resulting tree-structured piecewise linear adaptive filter inherits the robust estimation and fast adaptation of linear adaptive filters, along with the approximation and model-fitting properties of tree-structured regression models A rigorous analysis of the training algorithm for the tree-structured filter is performed Some techniques are developed for analyzing hierarchically organized stochastic gradient algorithms with fixed gains and nonstationary dependent data Simulation results show the significant advantages of the tree-structured piecewise linear filter over linear and polynomial filters for adaptive echo cancellation >
TL;DR: In this article, a class of one-dimensional piecewise linear maps admitting fractal invariant sets and uncountably many invariant measures is constructed, and a physical measure is selected as the invariant measure with maximum information dimension.
TL;DR: It is demonstrated that data-dependent triangulations can improve significantly the quality of approximation and that long and thin triangles, which are traditionally avoided, are sometimes necessary to have.
TL;DR: It is proven that the weights and biases generated with certain constraints based on the piecewise linear principle result in an initial neural network which is better able to form a function approximation of an arbitrary function.
Abstract: It is proven that the weights and biases generated with certain constraints based on the piecewise linear principle result in an initial neural network which is better able to form a function approximation of an arbitrary function. Use of these initial constraints greatly shortens the training time and avoids the local minima usually associated with an arbitrary random choice of initial weights.
03 Nov 1993
TL;DR: This work gives a compact representation of the Voronoi diagram, using O(k) line segments, that is sufficient for logarithmic time post-office location queries and motion planning.
Abstract: In the plane, the post-office problem, which asks for the closest site to a query site, and retraction motion planning, which asks for a one-dimensional retract of the free space of a robot, are both classically solved by computing a Voronoi diagram. When the sites are k disjoint convex sets, we give a compact representation of the Voronoi diagram, using O(k) line segments, that is sufficient for logarithmic time post-office location queries and motion planning. If these sets are polygons with n total vertices, we compute this diagram optimally in O(klog n) deterministic time for the Euclidean metric and in O(klog nlog m) deterministic time for the convex distance function defined by a convex m-gon. >
TL;DR: In this article, the authors studied a class of piecewise linear functions from R n to R n, namely Robinson's normal maps induced by linear mappings and polyhedral convex sets, called pl-normal maps.
TL;DR: It is proved that accumulation points of sequences of discrete optimal sequences of extremal controls are optimal for the continuous problem and necessary conditions for optimality are derived for both the continuous and the discrete problem.
Abstract: We consider a relaxed optimal control problem for systems defined by nonlinear parabolic partial differential equations with distributed control. The problem is completely discretized by using a finite-element approximation scheme with piecewise linear states and piecewise constant controls. Existence of optimal controls and necessary conditions for optimality are derived for both the continuous and the discrete problem. We then prove that accumulation points of sequences of discrete optimal [resp. extremal] controls are optimal [resp. extremal] for the continuous problem.