共查询到20条相似文献,搜索用时 31 毫秒
1.
Hyun Woo Park Soobong Shin Hae Sung Lee 《International journal for numerical methods in engineering》2001,51(10):1211-1230
This paper presents a geometric mean scheme (GMS) to determine an optimal regularization factor for Tikhonov regularization technique in the system identification problems of linear elastic continua. The characteristics of non‐linear inverse problems and the role of the regularization are investigated by the singular value decomposition of a sensitivity matrix of responses. It is shown that the regularization results in a solution of a generalized average between the a priori estimates and the a posteriori solution. Based on this observation, the optimal regularization factor is defined as the geometric mean between the maximum singular value and the minimum singular value of the sensitivity matrix of responses. The validity of the GMS is demonstrated through two numerical examples with measurement errors and modelling errors. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
2.
Y. Zhang P. Forssén T. Fornstedt M. Gulliksson X. Dai 《Inverse Problems in Science & Engineering》2018,26(10):1464-1489
We present here the theoretical results and numerical analysis of a regularization method for the inverse problem of determining the rate constant distribution from biosensor data. The rate constant distribution method is a modern technique to study binding equilibrium and kinetics for chemical reactions. Finding a rate constant distribution from biosensor data can be described as a multidimensional Fredholm integral equation of the first kind, which is a typical ill-posed problem in the sense of J. Hadamard. By combining regularization theory and the goal-oriented adaptive discretization technique, we develop an Adaptive Interaction Distribution Algorithm (AIDA) for the reconstruction of rate constant distributions. The mesh refinement criteria are proposed based on the a posteriori error estimation of the finite element approximation. The stability of the obtained approximate solution with respect to data noise is proven. Finally, numerical tests for both synthetic and real data are given to show the robustness of the AIDA. 相似文献
3.
S. Mukherjee C. S. Krishnamoorthy 《International journal for numerical methods in engineering》1998,43(3):507-532
A hybrid error estimator using a priori interior region estimates in an a posteriori framework is presented for linear elastostatics problems in FEA. It is shown that local rates of convergence are augmented by this technique and global rates are not adversely affected. The effects of pollution for this estimator are explained and a pollution error estimator is derived using the concept of error loads. It is shown that pollution error estimation can improve the performance of both the conventional a posteriori and the hybrid techniques. A series of numerical results are presented which demonstrate the superior performance of the proposed method over previously published interior error estimation techniques. © 1998 John Wiley & Sons, Ltd. 相似文献
4.
In this paper, we consider the backward problem for diffusion equation with space fractional Laplacian, i.e. determining the initial distribution from the final value measurement data. In order to overcome the ill-posedness of the backward problem, we present a so-called negative exponential regularization method to deal with it. Based on the conditional stability estimate and an a posteriori regularization parameter choice rule, the convergence rate estimate are established under a-priori bound assumption for the exact solution. Finally, several numerical examples are proposed to show that the numerical methods are effective. 相似文献
5.
F. T. Suttmeier 《Computational Mechanics》2005,35(6):401-408
In this note, we focus on optimised mesh design for the Finite Element (FE) method for variational inequalities using global norm estimates for local error control. The strategies are based on the so called dual-weighted-residual (DWR) approach to a posteriori error control for FE-schemes (see, e.g., Rannacher et al. [19, 6, 2]), where error control for the primal problem is established by solving an auxiliary (dual) problem. In this context we blamed (cf. e.g., Rannacher and Suttmeier [18, 19]) global norm estimates being not that useful in applications. But having a closer look at the DWR-concept, one observes that in fact global (energy) error bounds can be employed to establish local error control. Our ideas and techniques are illustrated at the socalled obstacle problem.It turns out, that reliable and efficient energy error control is one main ingredient to establish useful a posteriori error bounds for local quantities. Therefore, in addition, we derive an unified approach to a posteriori error control in the energy norm for elliptic variational inequalities of first kind. Eventually, this framework is applied to Signorinis problem. 相似文献
6.
In this paper, numerical solutions are investigated based on the Trefftz method for an over-specified boundary value problem contaminated with artificial noise. The main difficulty of the inverse problem is that divergent results occur when the boundary condition on over-specified boundary is contaminated by artificial random errors. The mechanism of the unreasonable result stems from its ill-posed influence matrix. The accompanied ill-posed problem is remedied by using the Tikhonov regularization technique and the linear regularization method, respectively. This remedy will regularize the influence matrix. The optimal parameter λ of the Tikhonov technique and the linear regularization method can be determined by adopting the adaptive error estimation technique. From this study, convergent numerical solutions of the Trefftz method adopting the optimal parameter can be obtained. To show the accuracy of the numerical solutions, we take the examples as numerical examination. The numerical examination verifies the validity of the adaptive error estimation technique. The comparison of the Tikhonov regularization technique and the linear regularization method was also discussed in the examples. 相似文献
7.
8.
Djordje Peri Jianguo Yu D. R. J. Owen 《International journal for numerical methods in engineering》1994,37(8):1351-1379
The a posteriori error estimates based on the post-processing approach are introduced for elastoplastic solids. The standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy. This is known to represent a natural metric for the class of elastoplastic problems of evolution. In addition, the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates. A posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem. As a model problem, the constitutive equations describing a generalization of standard J2-elastoplasticity within the Cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post-instability region. The proposed a posteriori error estimates are appropriately modified to account for the Cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems. Superior behaviour of the Cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material, resulting in convergent solutions with an h-refinement and almost uniform error distribution in all considered error norms. 相似文献
9.
Gangan Prathap 《Sadhana》1999,24(3):199-214
The quality of finite element computational results can be assessed only by providing rational criteria for evaluating errors.
Most exercises in this direction are based ona posteriori error estimates, based primarily on experience and intuition. If finite element analysis has to be considered a rational
science, it is imperative that procedures to computea priori error estimates from first principles are made available. This paper captures some efforts in this direction. 相似文献
10.
Jintai Chung Eun‐Hyoung Cho Keeyoung Choi 《International journal for numerical methods in engineering》2003,57(4):537-554
An a priori error estimator for the generalized‐α time‐integration method is developed to solve structural dynamic problems efficiently. Since the proposed error estimator is computed with only information in the previous and current time‐steps, the time‐step size can be adaptively selected without a feedback process, which is required in most conventional a posteriori error estimators. This paper shows that the automatic time‐stepping algorithm using the a priori estimator performs more efficient time integration, when compared to algorithms using an a posteriori estimator. In particular, the proposed error estimator can be usefully applied to large‐scale structural dynamic problems, because it is helpful to save computation time. To verify efficiency of the algorithm, several examples are numerically investigated. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
11.
Håkan Jakobsson Fredrik Bengzon Mats G. Larson 《International journal for numerical methods in engineering》2011,86(7):829-844
Component mode synthesis (CMS) is a classical method for the reduction of large‐scale finite element models in linear elasticity. In this paper we develop a methodology for adaptive refinement of CMS models. The methodology is based on a posteriori error estimates that determine to what degree each CMS subspace influence the error in the reduced solution. We consider a static model problem and prove a posteriori error estimates for the error in a linear goal quantity as well as in the energy and L2 norms. Automatic control of the error in the reduced solution is accomplished through an adaptive algorithm that determines suitable dimensions of each CMS subspace. The results are demonstrated in numerical examples. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
12.
The boundary-element method for the determination of a heat source dependent on one variable 总被引:1,自引:0,他引:1
This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions of the direct problem and a supplementary condition, called an overdetermination. In this problem, if the heat source is taken to be space-dependent only, then the overdetermination is the temperature measurement at a given single instant, whilst if the heat source is time-dependent only, then the overdetermination is the transient temperature measurement recorded by a single thermocouple installed in the interior of the heat conductor. These measurements ensure that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method with the discrepancy principle or the L-curve criterion for the choice of the regularization parameter. The boundary-element method (BEM) is developed for solving numerically the inverse problem and numerical results for some benchmark test examples are obtained and discussed 相似文献
13.
Nguyen Huy Tuan Le Dinh Long Van Thinh Nguyen Thanh Tran 《Inverse Problems in Science & Engineering》2017,25(9):1367-1395
In this paper, we consider an inverse problem for the time-fractional diffusion equation with inhomogeneous source to determine an initial data from the observation data provided at a later time. In general, this problem is ill-posed, therefore we construct a regularizing solution using the quasi-boundary value method. We also proposed both parameter choice rule methods, the a-priori and the a-posteriori methods, to estimate the convergence rate of the regularized methods. In addition, the proposed regularized methods have been verified by numerical experiments, and a comparison of the convergence rate between the a-priori and the a-posteriori choice rule methods is also given. 相似文献
14.
Huan Liu 《Inverse Problems in Science & Engineering》2017,25(11):1601-1617
This paper studies an inverse problem of determining the unknown source term in a space-fractional diffusion equation. Three types of spectral regularization method are proposed to deal with the ill-posed problem and the corresponding error estimates are obtained with an a priori strategy to find the regularization parameter. We verify the efficiency of the proposed numerical method with some numerical experiments. 相似文献
15.
Gabriel N. Gatica Luis F. Gatica 《International journal for numerical methods in engineering》2006,68(8):861-892
In this paper, we reconsider the a priori and a posteriori error analysis of a new mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions. The approach, being based only on the fact that the resulting variational formulation becomes a two‐fold saddle‐point operator equation, simplifies the analysis and improves the results provided recently in a previous work. Thus, a well‐known generalization of the classical Babu?ka–Brezzi theory is applied to show the well‐posedness of the continuous and discrete formulations, and to derive the corresponding a priori error estimate. In particular, enriched PEERS subspaces are required for the solvability and stability of the associated Galerkin scheme. In addition, we use the Ritz projection operator to obtain a new reliable and quasi‐efficient a posteriori error estimate. Finally, several numerical results illustrating the good performance of the associated adaptive algorithm are presented. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
16.
M. Bertero P. Boccacci F. Maggio 《International journal of imaging systems and technology》1995,6(4):376-386
The mathematic problem of restoring an image degraded by blurring and noise is ill-posed, so that the solution is affected by numeric instability. As a consequence, the solution provided by the so-called inverse filter is completely contaminated by noise and, in general, is deprived of any physical meaning. If one looks for approximate solutions, the ill-posedness of the problem implies that the set of these solutions is too broad. For this reason, one must look for approximate solutions satisfying some kind of a priori constraints, the so-called a priori information. This fact explains the variety of methods, usually called regularization methods, which have been designed for solving this kind of problems. In this article we briefly review some of the most widely used methods, both deterministic and probabilistic, and show their effectiveness in the restoration of some HST images. 相似文献
17.
Recently a refined approach to error control in finite element (FE) discretisations has been proposed, Becker and Rannacher
(1995b), (1996), which uses weighted a posteriori error estimates derived via duality arguments. The conventional strategies for mesh refinement in FE models of problems from
elasticity theory are mostly based on a posteriori error estimates in the energy norm. Such estimates reflect the approximation properties of the finite element ansatz by local
interpolation constants while the stability properties of the continuous model enter through a global coercivity constant.
However, meshes generated on the basis of such global error estimates are not appropriate in cases where the domain consists of very heterogeneous materials and for the computation
of local quantities, e.g., point values or contour integrals. This deficiency is cured by using certain local norms of the
dual solution directly as weights multiplying the local residuals of the computed solution. In general, these weights have
to be evaluated numerically in the course of the refinement process, yielding almost optimal meshes for various kinds of error
measures. This feed-back approach is developed here for primal as well as mixed FE discretisations of the fundamental problem
in linear elasticity. 相似文献
18.
I. Babuka F. Ihlenburg T. Strouboulis S. K. Gangaraj 《International journal for numerical methods in engineering》1997,40(21):3883-3900
In part I of this investigation, we proved that the standard a posteriori estimates, based only on local computations, may severely underestimate the exact error for the classes of wave-numbers and the types of meshes employed in engineering analyses. We showed that this is due to the fact that the local estimators do not measure the pollution effect inherent to the FE-solutions of Helmholtz' equation with large wavenumber. Here, we construct a posteriori estimates of the pollution error. We demonstrate that these estimates are reliable and can be used to correct the standard a posteriori error estimates in any patch of elements of interest. © 1997 John Wiley & Sons, Ltd. 相似文献
19.
Trond Kvamsdal Knut Morten Okstad 《International journal for numerical methods in engineering》1998,42(3):443-472
In this paper we investigate an approach for a posteriori error estimation based on recovery of an improved stress field. The qualitative properties of the recovered stress field necessary to obtain a conservative error estimator, i.e. an upper bound on the true error, are given. A specific procedure for recovery of an improved stress field is then developed. The procedure can be classified as Superconvergent Patch Recovery (SPR) enhanced with approximate satisfaction of the interior equilibrium and the natural boundary conditions. Herein the interior equilibrium is satisfied a priori within each nodal patch. Compared to the original SPR-method, which usually underestimates the true error, the present approach gives a more conservative estimate. The performance of the developed error estimator is illustrated by investigating two plane strain problems with known closed-form solutions. © 1998 John Wiley & Sons, Ltd. 相似文献
20.
Gustavo C. Buscaglia Ricardo Durn Eduardo A. Fancello Raúl A. Feijo Claudio Padra 《International journal for numerical methods in engineering》2001,50(2):395-418
The derivation of an a posteriori error estimator for frictionless contact problems under the hypotheses of linear elastic behaviour and infinitesimal deformation is presented. The approximated solution of this problem is obtained by using the finite element method. A penalization or augmented‐Lagrangian technique is used to deal with the unilateral boundary condition over the contact boundary. An a posteriori error estimator suitable for adaptive mesh refinement in this problem is proposed, together with its mathematical justification. Up to the present time, this mathematical proof is restricted to the penalization approach. Several numerical results are reported in order to corroborate the applicability of this estimator and to compare it with other a posteriori error estimators. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献