Search results for "Jacobi"
showing 10 items of 106 documents
Topologinen aste
2017
Tämän tutkielman tarkoituksena on luoda perusta topologiselle asteelle, ja todistaa siihen liittyviä tuloksia. Topologinen aste määritellään aluksi jatkuvasti derivoituville funktioille jossakin kyseisen funktion kuvapisteessä. Nämä ovat useasti moniulotteisia funktioita, joiden määrittelyjoukko ja kuvapisteiden joukko ovat samassa ulottuvuudessa. Topologinen aste tarkastelee funktion kuvapisteen alkukuvien ympäristön kuvautumista derivaattamatriisin determinantin avulla. Mikäli Jacobin determinantti saa positiivisen arvon, lisätään topologiseen asteeseen kokonaisluku yksi. Jos taas derivaattamatriisin arvo on negatiivinen kyseisen kuvapisteen alkukuvassa, topologisesta asteesta vähennetään…
Elastoplastic analysis by active macro-zones with linear kinematic hardening and von Mises materials.
2014
In this paper a strategy to perform elastoplastic analysis with linear kinematic hardening for von Mises materials under plane strain conditions is shown. The proposed approach works with the Symmetric Galerkin Boundary Element Method applied to multidomain problems using a mixed variables approach, to obtain a more stringent solution. The elastoplastic analysis is carried out as the response to the loads and the plastic strains, the latter evaluated through the self-equilibrium stress matrix. This matrix is used both, in the predictor phase, for trial stress evaluation and, in the corrector phase, for solving a nonlinear global system which provides the elastoplastic solution of the active…
A new method for creating sparse design velocity fields
2006
We present a novel method for the computation of mesh node sensitivities with respect to the boundary node movement. The sensitivity field is sparse in a sense that movement of each boundary node affects only given amount of inner mesh nodes, which can result in considerable savings in the storage space. The method needs minimal control from the user, and it does not place any restrictions (such as block structure) on the mesh. Use of the method is demonstrated with a shape optimization problem using CAD-free parametrization. A solution to the classical die-swell free boundary problem by coupling the boundary node locations with the state variables is also presented. In that case, sparsity …
Using the witness method to detect rigid subsystems of geometric constraints in CAD
2010
International audience; This paper deals with the resolution of geometric constraint systems encountered in CAD-CAM. The main results are that the witness method can be used to detect that a constraint system is over-constrained and that the computation of the maximal rigid subsystems of a system leads to a powerful decomposition method. In a first step, we recall the theoretical framework of the witness method in geometric constraint solving and extend this method to generate a witness. We show then that it can be used to incrementally detect over-constrainedness. We give an algorithm to efficiently identify all maximal rigid parts of a geometric constraint system. We introduce the algorit…
Mappings of finite distortion: the degree of regularity
2005
This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)⩾1 be a measurable function defined on a domain Ω⊂Rn,n⩾2, and such that exp(βK(x))∈Lloc1(Ω), β>0. We show that there exist two universal constants c1(n),c2(n) with the following property: Let f be a mapping in Wloc1,1(Ω,Rn) with |Df(x)|n⩽K(x)J(x,f) for a.e. x∈Ω and such that the Jacobian determinant J(x,f) is locally in L1log−c1(n)βL. Then automatically J(x,f) is locally in L1logc2(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite disto…
The eigen-structure of the Jacobian in multi-class Lighthill-Whitham-Richards traffic flow models
2007
Characteristic-based High Resolution Shock Capturing schemes for hyperbolic systems of conservation laws require, in their basic design structure, knowledge on the complete eigen-decomposition of the Jacobian matrix of the system. For the Multi-Class Lighthill-Witham-Richards (MCLWR) Traffic flow model considered in [4], there is no explicit formula for the eigenvalues of the Jacobian matrix, which can only be determined numerically. However, once they are determined, the eigen-vectors are easily computed and straightforward formulas can be obtained by exploiting the specific structure of the Jacobian matrix in these models. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Response Power Spectrum of Multi-Degree-of-Freedom Nonlinear Systems by a Galerkin Technique
2003
This paper deals with the estimation of spectral properties of randomly excited multi-degree-of-freedom (MDOF) nonlinear vibrating systems. Each component of the vector of the stationary system response is expanded into a trigonometric Fourier series over an adequately long interval T. The unknown Fourier coefficients of individual samples of the response process are treated by harmonic balance, which leads to a set of nonlinear equations that are solved by Newton’s method. For polynomial nonlinearities of cubic order, exact solutions are developed to compute the Fourier coefficients of the nonlinear terms, including those involved in the Jacobian matrix associated with the implementation o…
On the implementation of weno schemes for a class of polydisperse sedimentation models
2011
The sedimentation of a polydisperse suspension of small rigid spheres of the same density, but which belong to a finite number of species (size classes), can be described by a spatially one-dimensional system of first-order, nonlinear, strongly coupled conservation laws. The unknowns are the volume fractions (concentrations) of each species as functions of depth and time. Typical solutions, e.g. for batch settling in a column, include discontinuities (kinematic shocks) separating areas of different composition. The accurate numerical approximation of these solutions is a challenge since closed-form eigenvalues and eigenvectors of the flux Jacobian are usually not available, and the characte…
A Flux-Split Algorithm Applied to Relativistic Flows
1998
The equations of RFD can be written as a hyperbolic system of conservation laws by choosing an appropriate vector of unknowns. We give an explicit formulation of the full spectral decomposition of the Jacobian matrices associated with the fluxes in each spatial direction, which is the essential ingredient of the techniques we propose in this paper. These techniques are based on the recently derived flux formula of Marquina, a new way to compute the numerical flux at a cell interface which leads to a conservative, upwind numerical scheme. Using the spectral decompositions in a fundamental way, we construct high order versions of the basic first-order scheme described by R. Donat and A. Marqu…
Indefinite integrals of some special functions from a new method
2015
A substantial number of indefinite integrals of special functions are presented, which have been obtained using a new method presented in a companion paper [Conway JT. A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015; submitted to]. The method was originally derived from the Euler–Lagrange equations but an elementary proof is also presented in [Conway JT. A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015; submitted to]. Sample results are presented here for Bessel functions, Airy functions and hypergeometric functions. More extensive results are given for th…