共查询到20条相似文献,搜索用时 93 毫秒
1.
** Email: blanca{at}imati.cnr.it*** Email: frutos{at}mac.cie.uva.es**** Corresponding author. Email: julia.novo{at}uam.es
A technique to improve the accuracy of the mini-element approximationto incompressible the NavierStokes equations is introduced.Once the mini-element approximation has been computed at a fixedtime, the linear part of this approximation is postprocessedby solving a discrete Stokes problem. The bubble functions neededto stabilize the approximation to the NavierStokes equationsare not used at the postprocessing step. This postprocessingprocedure allows us to increase by one unit (up to a logarithmicterm) the H1 norm rate of convergence of the velocity and correspondinglythe L2 norm of the pressure. An error analysis of the algorithmis performed. 相似文献
2.
Algorithms for the computation of the pseudospectral radius and the numerical radius of a matrix 总被引:1,自引:0,他引:1
** Email: mengi{at}cs.nyu.edu*** Email: overton{at}cs.nyu.edu Two useful measures of the robust stability of the discrete-timedynamical system xk+1 = Axk are the -pseudospectral radius andthe numerical radius of A. The -pseudospectral radius of A isthe largest of the moduli of the points in the -pseudospectrumof A, while the numerical radius is the largest of the moduliof the points in the field of values. We present globally convergentalgorithms for computing the -pseudospectral radius and thenumerical radius. For the former algorithm, we discuss conditionsunder which it is quadratically convergent and provide a detailedaccuracy analysis giving conditions under which the algorithmis backward stable. The algorithms are inspired by methods ofByers, BoydBalakrishnan, HeWatson and BurkeLewisOvertonfor related problems and depend on computing eigenvalues ofsymplectic pencils and Hamiltonian matrices. 相似文献
3.
Kumar Anil; Joshi Mohan C.; Pani Amiya K. 《IMA Journal of Mathematical Control and Information》2007,24(1):115-136
** Email: anil{at}math.iitb.ac.in*** Email: mcj{at}math.iitb.ac.in**** Email: akp{at}math.iitb.ac.in In this paper, we consider the following control system governedby the non-linear parabolic differential equation of the form: [graphic: see PDF] where A is a linear operator with dense domain and f(t, y)is a non-linear function. We have proved that under Lipschitzcontinuity assumption on the non-linear function f(t, y), theset of admissible controls is non-empty. The optimal pair (u*,y*) is then obtained as the limit of the optimal pair sequence{(un*, yn*)}, where un* is a minimizer of the unconstrainedproblem involving a penalty function arising from the controllabilityconstraint and yn* is the solution of the parabolic non-linearsystem defined above. Subsequently, we give approximation theoremswhich guarantee the convergence of the numerical schemes tooptimal pair sequence. We also present numerical experimentwhich shows the applicability of our result. 相似文献
4.
Calvo Nati; Durany Jose; Munoz Ana I.; Schiavi Emanuele; Vazquez Carlos 《IMA Journal of Applied Mathematics》2006,71(1):62-91
** Email: nati{at}dma.uvigo.es*** Email: durany{at}dma.uvigo.es**** Email: anaisabel.munoz{at}urjc.es***** Email: emanuele.schiavi{at}urjc.es****** Email: carlosv{at}udc.es This paper deals with the numerical solution of a non-linearmodel describing a free-boundary problem arising in modern glaciology.Considering a shallow, viscous ice sheet flow along a soft,deformable bed, a coupled non-linear system of differentialequations can be obtained. Particularly, an obstacle problemis then deduced and solved in the framework of its complementarityformulation. We present the numerical solution of the resultingmultivalued system modelling the ice sheet non-Newtonian dynamicsdriven by the underlying drainage system. Our numerical resultsshow the existence of fast ice streams when positive wave-likeinitial conditions are considered. The solutions are numericallycomputed with a decoupling iterative method and finite-elementtechnique. A duality algorithm and a projected GaussSeidelmethod are the alternatives used to cope with the resultingvariational inequality while the explicit treatment, Newtonmethod or a duality method are proposed to deal with the non-linearsource term. Finally, the numerical solutions are physicallyinterpreted and some comparisons among the numerical methodsare then discussed. 相似文献
5.
Karam Alejandro; Caporossi Gilles; Hansen Pierre 《IMA Journal of Management Mathematics》2007,18(2):173-189
** Email: alejandro.karam{at}hec.ca*** Email: gilles.caporossi{at}gerad.ca**** Email: pierre.hansen{at}gerad.ca We consider the problem of separating two sets of points ina Euclidean space with a hyperplane that minimizes the sum ofp-norm distances to the plane of points lying on the wrongside of the plane. A variable neighbourhood search heuristicis used to determine the plane coefficients. For a set of exampleswith L1-norm, L2-norm and L-norm, for which the exact solutioncan be computed, we show that our algorithm finds it in mostcases and gets good approximations in the others. The use ofour heuristic solutions for problems in these norms can dramaticallyaccelerate exact algorithms. Our method can be applied on verylarge instances that are intractable by exact algorithms. Sincethe proposed approach works for truly arbitrary norms (otherthan the traditional 1, 2 and ), we can explore for the firsttime the effects of the choice of p on the generalization propertiesof p-norm hyperplane separation. 相似文献
6.
Duran Mario; Muga Ignacio; Nedelec Jean-Claude 《IMA Journal of Applied Mathematics》2006,71(6):853-876
** Email: mduran{at}ing.puc.cl*** Email: ignacio.muga{at}ucv.cl**** Email: nedelec{at}cmapx.polytechnique.fr
In this article, we study the existence and uniqueness of outgoingsolutions for the Helmholtz equation in locally perturbed half-planeswith passive boundary. We establish an explicit outgoing radiationcondition which is somewhat different from the usual Sommerfeld'sone due to the appearance of surface waves. We work with thehelp of Fourier analysis and a half-plane Green's function framework.This is an extended and detailed version of the previous articleDurán et al. (2005, The Helmholtz equation with impedancein a half-plane. C. R. Acad. Sci. Paris, Ser. I, 340, 483488). 相似文献
7.
Variable neighbourhood search for redundancy allocation problems 总被引:1,自引:0,他引:1
** Email: ycliang{at}saturn.yzu.edu.tw*** Email: s929512{at}mail.yzu.edu.tw**** Email: s927522{at}mail.yzu.edu.tw A variable neighbourhood search (VNS) algorithm has been developedto solve the redundancy allocation problem (RAP). The VNS methodis perfectly suited to those combinatorial problems with potentialneighbourhood structures, as in the case of the RAP. The moststudied configuration of the RAP is a series system of s-independentk-out-of-n:G subsystems the so-called seriesparallelsystem. The RAP is to select the optimal combination and redundancylevels of components to meet system-level constraints. Two typesof objectives are considered in this studysystem reliabilitymaximization and system cost minimization. The VNS algorithmis tested on sets of benchmark problems and compared to thebest heuristics in the literature such as tabu search, multipleweighted objective heuristic, ant colony optimization and geneticalgorithm. Computational results show the advantages and benefitsof VNS for solving both types of RAP while considering bothsolution quality and computational efficiency. 相似文献
8.
Barcenas Diomedes; Leiva Hugo; Urbina Wilfredo 《IMA Journal of Mathematical Control and Information》2006,23(1):1-9
** Email: Leiva{at}ula.ve In this paper we study the controllability of the followingcontrolled OrnsteinUhlenbeck equation [graphic: see PDF] then the system is approximately controllable on [0, t1]. Moreover,the system can never be exactly controllable. 相似文献
9.
Sakthivel Rathinasamy; Ito Hiroshi 《IMA Journal of Mathematical Control and Information》2007,24(1):47-55
** Email: krsakthivel{at}rediffmail.com*** Email: hiroshi{at}ces.kyutech.ac.jp This paper considers the problem of robust global stabilizationof the KuramotoSivashinsky equation subject to Neumannand Dirichlet boundary conditions. The aim is to derive non-linearrobust boundary control laws which make the system robustlyglobally asymptotically stable in spite of uncertainty in boththe instability parameter and the anti-diffusion parameter.A unique approach this paper introduces for achieving the requiredrobustness is spatially dependent scaling of uncertain elementsin Lyapunov-based stabilization. An important advantage of thisapproach is flexibility to obtain robust control laws with smallcontrol effort. The control laws can be implemented as Dirichlet-likeboundary control as well as Neumann-like boundary control. Furthermore,it is shown that they guarantee the stability and boundednessin terms of both L2 and L. 相似文献
10.
Dai Yu-Hong; Hager William W.; Schittkowski Klaus; Zhang Hongchao 《IMA Journal of Numerical Analysis》2006,26(3):604-627
** Email: dyh{at}lsec.cc.ac.cn*** Email: hager{at}math.ufl.edu**** Email: klaus.schittkowski{at}uni-bayreuth.de***** Email: hzhang{at}math.ufl.edu In the cyclic BarzilaiBorwein (CBB) method, the sameBarzilaiBorwein (BB) stepsize is reused for m consecutiveiterations. It is proved that CBB is locally linearly convergentat a local minimizer with positive definite Hessian. Numericalevidence indicates that when m > n/2 3, where n is the problemdimension, CBB is locally superlinearly convergent. In the specialcase m = 3 and n = 2, it is proved that the convergence rateis no better than linear, in general. An implementation of theCBB method, called adaptive cyclic BarzilaiBorwein (ACBB),combines a non-monotone line search and an adaptive choice forthe cycle length m. In numerical experiments using the CUTErtest problem library, ACBB performs better than the existingBB gradient algorithm, while it is competitive with the well-knownPRP+ conjugate gradient algorithm. 相似文献
11.
Houston Paul; Perugia Ilaria; Schotzau Dominik 《IMA Journal of Numerical Analysis》2007,27(1):122-150
** Email: paul.houston{at}nottingham.ac.uk*** Corresponding author. Email: ilaria.perugia{at}unipv.it**** Email: schoetzau{at}math.ubc.ca
We introduce a residual-based a posteriori error indicator fordiscontinuous Galerkin discretizations of H(curl; )-ellipticboundary value problems that arise in eddy current models. Weshow that the indicator is both reliable and efficient withrespect to the approximation error measured in terms of a naturalenergy norm. We validate the performance of the indicator withinan adaptive mesh refinement procedure and show its asymptoticexactness for a range of test problems. 相似文献
12.
A cell-centred finite-volume approximation for anisotropic diffusion operators on unstructured meshes in any space dimension 总被引:2,自引:0,他引:2
** Email: eymard{at}math.univ-mlv.fr*** Email: gallouet{at}cmi.univ-mrs.fr**** Corresponding author. Email: herbin{at}cmi.univ-mrs.fr Finite-volume methods for problems involving second-order operatorswith full diffusion matrix can be used thanks to the definitionof a discrete gradient for piecewise constant functions on unstructuredmeshes satisfying an orthogonality condition. This discretegradient is shown to satisfy a strong convergence property forthe interpolation of regular functions, and a weak one for functionsbounded in a discrete H1-norm. To highlight the importance ofboth properties, the convergence of the finite-volume schemefor a homogeneous Dirichlet problem with full diffusion matrixis proven, and an error estimate is provided. Numerical testsshow the actual accuracy of the method. 相似文献
13.
** Email: wei.97{at}osu.edu*** Email: murray.308{at}osu.edu**** Email: xiao.37{at}osu.edu The Voronoi diagram heuristic has been proposed for solvingthe p-centre problem in continuous space. However, importantassumptions underlie this heuristic and may be problematic forpractical applications. These simplifying assumptions includeuniformly distributed demand, representing a region as a rectangle;analysis of a simple Voronoi polygon in solving associated one-centreproblems and no restrictions on potential facility locations.In this paper, we explore the complexity of solving the continuousspace p-centre problem in location planning. Considering theissue of solution space feasibility, we present a spatiallyrestricted version of this problem and propose methods for solvingit heuristically. Theoretical and empirical results are provided. 相似文献
14.
Belhachmi Zakaria; Bucur Dorin; Sac-Epee Jean-Marc 《IMA Journal of Numerical Analysis》2006,26(4):790-810
** Email: belhach{at}poncelet.univ-metz.fr*** Email: bucur{at}math.univ-metz.fr**** Email: jmse{at}math.univ-metz.fr We study the NeumannLaplacian eigenvalue problem in domainswith multiple cracks. We derive a mixed variational formulationwhich holds on the whole geometric domain (including the cracks)and implements efficient finite-element discretizations forthe computation of eigenvalues. Optimal error estimates aregiven and several numerical examples are presented, confirmingthe efficiency of the method. As applications, we numericallyinvestigate the behaviour of the low eigenvalues in domainswith a large number of cracks. 相似文献
15.
Tsachouridis Vassilios A.; Karcanias Nicos; Postlethwaite Ian 《IMA Journal of Mathematical Control and Information》2007,24(2):259-287
** Email: vassilios.tsachouridis{at}ieee.org*** Email: N.karcanias{at}city.ac.uk**** Email: ixp{at}le.ac.uk Algebraic quadratic equations are special cases of a singlegeneralized algebraic quadratic matrix equation (GQME). Thispaper focuses on the numerical solution of the GQME using probability-1homotopy methods. A synoptic review of these methods and theirapplication to algebraic matrix equations is provided as background.A large variety of analysis and design problems in systems andcontrol are reported as special cases of the presented frameworkand some of them are illustrated via numerical examples fromthe literature. 相似文献
16.
** Email: lyle{at}maths.uwa.edu.au*** Email: popiet01{at}maths.uwa.edu.au Riemannian cubics in tension in the rotation group SO(3) arevariational curves with applications to interpolation problemsin computer graphics and rigid-body trajectory planning. Theyare related by a linking equation to Lie quadratics in tension(LQT) in the Lie algebra so(3). This paper provides a qualitativeanalysis of the null case of LQT in so(3). 相似文献
17.
On the solvability for the mixed-type Lyapunov equation 总被引:3,自引:0,他引:3
** Email: xsf{at}math.pku.edu.cn*** Email: mscheng{at}math.pku.edu.cn In this paper, the linear matrix equation X = AXB* + BXA* +Q is considered, which is called the mixed-type Lyapunov equation.Some necessary and sufficient conditions for the existence ofa unique solution are presented. Since a Hermitian positivesemidefinite solution is important from the application pointof view, some sufficient conditions for the existence of a Hermitianpositive semidefinite solution are derived. 相似文献
18.
Bonnans J. Frederic; Maroso Stefania; Zidani Housnaa 《IMA Journal of Numerical Analysis》2006,26(1):188-212
** Email: frederic.bonnans{at}inria.fr*** Email: stefania.maroso{at}inria.fr**** Email: zidani{at}ensta.fr We obtain error bounds for monotone approximation schemes ofa particular Isaacs equation. This is an extension of the theoryfor estimating errors for the HamiltonJacobiBellmanequation. To obtain the upper error bound, we consider the Krylovregularization of the Isaacs equation to build an approximatesub-solution of the scheme. To get the lower error bound, weextend the method of Barles & Jakobsen (2005, SIAM J. Numer.Anal.) which consists in introducing a switching system whosesolutions are local super-solutions of the Isaacs equation. 相似文献
19.
Coughlan James J.; Hill Adrian T.; Logemann Hartmut 《IMA Journal of Numerical Analysis》2007,27(1):45-73
** Email: mapjjc{at}maths.bath.ac.uk*** Corresponding author. Email: ath{at}maths.bath.ac.uk**** Email: hl{at}maths.bath.ac.uk
This paper makes systematic use of control-theoretic methodssuch as the -transform, small-gain theorems and frequency-domainstability criteria in the analysis of the stability behaviourof linear multistep methods. Some of the results in Nevanlinna'swork are recovered and a number of new boundedness and asymptoticproperties of solutions of numerical schemes are obtained. Inparticular, we give a careful and detailed analysis of the nonlinearstability properties of strictly zero-stable methods. 相似文献
20.
** Email: gqxu{at}tju.edu.cn*** Email: Jiajg{at}mailst.xjtu.edu.cn The group property of a string system with time delay in boundaryand the Riesz basis property of eigenvectors of the system arediscussed in the present paper. It is proved that, when thefeedback with delay > 0, the system also associates a C0group, and its eigenvectors (generalized eigenvectors) forma Riesz basis in Hilbert space . This result shows that timedelay may destroy the stability of the system, but the groupand Riesz basis properties are kept. As a consequence, the exactcontrollability of the system with boundary control is given. 相似文献