共查询到20条相似文献,搜索用时 31 毫秒
1.
Summary. Impedance tomography seeks to recover the electrical conductivity distribution inside a body from measurements of current
flows and voltages on its surface. In its most general form impedance tomography is quite ill-posed, but when additional a-priori
information is admitted the situation changes dramatically. In this paper we consider the case where the goal is to find a
number of small objects (inhomogeneities) inside an otherwise known conductor. Taking advantage of the smallness of the inhomogeneities,
we can use asymptotic analysis to design a direct (i.e., non-iterative) reconstruction algorithm for the determination of
their locations. The viability of this direct approach is documented by numerical examples.
Received May 28, 2001 / Revised version received March 15, 2002 / Published online July 18, 2002
RID="⋆"
ID="⋆" Supported by the Deutsche Forschungsgemeinschaft (DFG) under grant HA 2121/2-3
RID="⋆⋆"
ID="⋆⋆" Supported by the National Science Foundation under grant DMS-0072556
Mathematics Subject Classification (2000): 65N21, 35R30, 35C20 相似文献
2.
Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows 总被引:1,自引:0,他引:1
Summary. We propose and analyze a semi-discrete (in time) scheme and a fully discrete scheme for the Allen-Cahn equation u
t
−Δu+ɛ−2
f(u)=0 arising from phase transition in materials science, where ɛ is a small parameter known as an ``interaction length'. The
primary goal of this paper is to establish some useful a priori error estimates for the proposed numerical methods, in particular,
by focusing on the dependence of the error bounds on ɛ. Optimal order and quasi-optimal order error bounds are shown for the
semi-discrete and fully discrete schemes under different constraints on the mesh size h and the time step size k and different regularity assumptions on the initial datum function u
0
. In particular, all our error bounds depend on only in some lower polynomial order for small ɛ. The cruxes of the analysis are to establish stability estimates for the
discrete solutions, to use a spectrum estimate result of de Mottoni and Schatzman [18, 19] and Chen [12] and to establish
a discrete counterpart of it for a linearized Allen-Cahn operator to handle the nonlinear term. Finally, as a nontrivial byproduct,
the error estimates are used to establish convergence and rate of convergence of the zero level set of the fully discrete
solution to the motion by mean curvature flow and to the generalized motion by mean curvature flow.
Received April 30, 2001 / Revised version received March 20, 2002 / Published online July 18, 2002
Mathematics Subject Classification (1991): 65M60, 65M12, 65M15, 35B25, 35K57, 35Q99, 53A10
Correspondence to: A. Prohl 相似文献
3.
Summary. In this paper, global optimization (GO) Lipschitz problems are considered where the multi-dimensional multiextremal objective
function is determined over a hyperinterval. An efficient one-dimensional GO method using local tuning on the behavior of
the objective function is generalized to the multi-dimensional case by the diagonal approach using two partition strategies.
Global convergence conditions are established for the obtained diagonal geometric methods. Results of a wide numerical comparison
show a strong acceleration reached by the new methods working with estimates of the local Lipschitz constants over different
subregions of the search domain in comparison with the traditional approach.
Received July 13, 2001 / Revised version received March 14, 2002 / Published online October 29, 2002
Mathematics Subject Classification (1991): 65K05, 90C30
Correspondence to: Yaroslav D. Sergeyev 相似文献
4.
Susanne C. Brenner 《Numerische Mathematik》2003,94(1):1-31
Summary. A new additive Schwarz preconditioner for the Finite Element Tearing and Interconnecting (FETI) method is analyzed in this
paper. This preconditioner has the unique feature that the coefficient matrix of its ``coarse grid' problem is mesh independent.
For a model second order heterogeneous elliptic boundary value problem in two dimensions, the condition number of the preconditioned
system is shown to be bounded by C[1+ln(H/h)]2, where h is the mesh size, H is the typical diameter of the subdomains, and the constant C is independent of h, H, the number of subdomains and the coefficients of the boundary value problem.
Received May 8, 2000 / Revised version received January 2, 2002 / Published online July 18, 2002
Mathematics Subject Classification (1991): 65N55, 65N30 相似文献
5.
Summary Using the argument principle higher order methods for simultaneous computation of all zeros of generalized polynomials (like algebraic, trigonometric and exponential polynomials or exponential sums) are derived. The methods can also be derived following the continuation principle from [3]. Thereby, the unified approach of [7] is enlarged to arbitrary orderN. The local convergence as well as a-priori and a-posteriori error estimates for these methods are treated on a general level. Numerical examples are included. 相似文献
6.
Summary. When a system of linear equations is ill-conditioned, regularization techniques provide a quite useful tool for trying to
overcome the numerical inherent difficulties: the ill-conditioned system is replaced by another one whose solution depends
on a regularization term formed by a scalar and a matrix which are to be chosen. In this paper, we consider the case of several
regularizations terms added simultaneously, thus overcoming the problem of the best choice of the regularization matrix. The
error of this procedure is analyzed and numerical results prove its efficiency.
Received January 15, 2002 / Revised version received July 31, 2002 / Published online October 29, 2002
Mathematics Subject Classification (1991): 65F05 – 65F22 相似文献
7.
Summary. We construct and analyze combinations of rational implicit and explicit multistep methods for nonlinear evolution equations
and extend thus recent results concerning the discretization of nonlinear parabolic equations. The resulting schemes are linearly
implicit and include as particular cases implicit–explicit multistep schemes as well as the combination of implicit Runge–Kutta
schemes and extrapolation. We establish optimal order error estimates. The abstract results are applied to a third–order evolution
equation arising in the modelling of flow in a fluidized bed. We discretize this equation in space by a Petrov–Galerkin method.
The resulting fully discrete schemes require solving some linear systems to advance in time with coefficient matrices the
same for all time levels.
Received October 22, 2001 / Revised version received April 22, 2002 /
Published online December 13, 2002
Mathematics Subject Classification (1991): Primary 65M60, 65M12; Secondary 65L06
Correspondence to: G. Akrivis 相似文献
8.
Peter K. Moore 《Numerische Mathematik》2003,94(2):367-401
Summary. Hp-adaptive finite element codes require methods for estimating the error at several spatial orders and for interpolating solutions
between grids. Lobatto polynomial-based techniques are presented for both. An interpolation error-based error estimation strategy
for a posteriori error estimates is generalized to yield asymptotically exact error estimates one order higher than the computed solution.
The estimates involve high-order derivatives of the solution that must be approximated from the computed solution. Differentiating
a ``Taylor-like' series for error in the Lobatto interpolant and using the weak form of the equations yields the correct
derivative approximations. This leads to a more robust order selection strategy. Interpolation between grids is done over
each element using the Lobatto interpolating polynomial. Explicit formulas for the inverse of the resulting Lobatto interpolation
matrices are given. Computational results illustrate the theory.
Received June 25, 2001 / Revised version received February 12, 2002 / Published online October 29, 2002
Mathematics Subject Classification (1991): 65M15,65M20,65M60
This research was partially supported by NSF Grant #DMS-0196108. 相似文献
9.
Georgios K. Alexopoulos 《Probability Theory and Related Fields》2002,124(1):112-150
We study the asymptotic behavior of the convolution powers of a centered density on a connected Lie group G of polynomial volume growth. The main tool is a Harnack inequality which is proved by using ideas from Homogenization theory
and by adapting the method of Krylov and Safonov. Applying this inequality we prove that the positive -harmonic functions are constant. We also characterise the -harmonic functions which grow polynomially. We give Gaussian estimates for , as well as for the differences and . We give estimates, similar to the ones given by the classical Berry-Esseen theorem, for and . We use these estimates to study the associated Riesz transforms.
Received: 5 July 1999 / Revised version: 8 April 2002 / Published online: 22 August 2002 相似文献
10.
Summary. We use the integral equation approach to study electromagnetic scattering by perfectly conducting (non-orientable) Lipschitz
screens. The well-posedness of the electric field integral equation is derived. The Galerkin method for this problem is analysed
in a general setting and optimal error bounds are proved for conforming finite elements in natural norms.
Received September 7, 2001 / Revised version received May 15, 2002 Published online October 29, 2002
Mathematics Subject Classification (1991): 65R20
Work of the second author was sponsored by Thales Airborne Systems. 相似文献
11.
Wensheng Wang 《Probability Theory and Related Fields》2003,126(2):203-220
Kesten and Spitzer have shown that certain random walks in random sceneries converge to stable processes in random sceneries.
In this paper, we consider certain random walks in sceneries defined using stationary Gaussian sequence, and show their convergence
towards a certain self-similar process that we call fractional Brownian motion in Brownian scenery.
Received: 17 April 2002 / Revised version: 11 October 2002 /
Published online: 15 April 2003
Research supported by NSFC (10131040).
Mathematics Subject Classification (2002): 60J55, 60J15, 60J65
Key words or phrases: Weak convergence – Random walk in random scenery – Local time – Fractional Brownian motion in Brownian scenery 相似文献
12.
Felix Schlenk 《manuscripta mathematica》2002,109(3):329-348
We extend the ``Extension after Restriction Principle' for symplectic embeddings of bounded starlike domains to a large
class of symplectic embeddings of unbounded starlike domains.
Received: 21 January 2002 / Revised version: 5 July 2002
Mathematics Subject Classification (2000): Primary 53D35, Secondary 54C20 相似文献
13.
Sharp two-sided estimates for Green functions of censored α-stable process Y in a bounded C
1,1
open set D are obtained, where α (1, 2). It is shown that the Martin boundary and minimal Martin boundary of Y can all be identified with the Euclidean boundary of D. Sharp two-sided estimates for the Martin kernel of Y are also derived.
Received: 27 January 2002 / Revised version: 10 June 2002 / Published online: 24 October 2002
This research is supported in part by NSF Grant DMS-0071486.
Mathematics Subject Classification (2002): Primary: 60J45, 31C35; Secondary: 60G52, 31C15
Keywords or phrases: Censored stable process – Green function – Capacity – Martin boundary – Martin kernel – Harmonic function 相似文献
14.
In this paper we try to generalize the notion of a minimal polynomial of an algebraic number to a class of transcendental
elements from where is the completion of the algebraic closure of ℚ in ℂ, relative to the spectral norm on : ([PPP], [PPZ1], [PPZ2], [PPZ3]).
Received: 2 July 2002 / Revised version: 13 January 2003 Published online: 20 March 2003
Mathematics Subject Classification (2000): 11R99 相似文献
15.
Collet Pierre Martínez Servet Martín Jaime San 《Probability Theory and Related Fields》2003,125(3):350-364
Using a new inequality relating the heat kernel and the probability of survival, we prove asymptotic ratio limit theorems
for the heat kernel (and survival probability) in general Benedicks domains. In particular, the dimension of the cone of positive
harmonic measures with Dirichlet boundary conditions can be derived from the rate of convergence to zero of the heat kernel
(or the survival probability).
Received: 31 March 2002 / Revised version: 12 August 2002 / Published online: 19 December 2002
Mathematics Subject Classification (2000): 60J65, 31B05
Key words or phrases: Positive harmonic functions – Ratio limit theorems – Survival probability 相似文献
16.
A family of plate elements introduced by Falk and Tu [25] is considered. A new stability and a-priori error analysis is given.
In addition, an a-posteriori error estimate is proved. The analysis is confirmed by numerical benchmark computations.
AMS subject classification (2000) 65F20 相似文献
17.
Mihai Prunescu 《Archive for Mathematical Logic》2003,42(3):293-302
Simple observations on diophantine definability over finite commutative rings lead to a characterization of those rings in
terms of their diophantine behavior.
Received: 28 March 2001 / Published online: 12 July 2002
Mathematics Subject Classification (2000): 13M10, 11T06, 03G99 相似文献
18.
Starting from the definition of `amorphous set' in set theory without the axiom of choice, we propose a notion of rank (which
will only make sense for, at most, the class of Dedekind finite sets), which is intended to be an analogue in this situation
of Morley rank in model theory.
Received: 22 September 2000 / Revised version: 14 May 2002 Published online: 19 December 2002
The research of the first author was supported by the SERC.
Mathematics Subject Classification (2000): 03E25
Key words or phrases: Rank – Degree – Amorphous 相似文献
19.
Ikuo Yoneda 《Archive for Mathematical Logic》2003,42(5):423-433
We show that any relational generic structure whose theory has finite closure and amalgamation over closed sets is stable
CM-trivial with weak elimination of imaginaries.
Received: 21 December 2001 /
Published online: 5 November 2002
Mathematics Subject Classification (2000): 03C45
Key words or phrases: CM-triviality – Generic structures – Stability 相似文献
20.
The Belavkin equation, describing the continuous measurement of the position of a quantum particle, is studied. A rigorous
representation of its solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on
the complex Cameron-Martin space is given.
Received: 7 January 2002 / Revised version: 20 June 2002 / Published online: 19 December 2002
Mathematics Subject Classification (2000): 81, 81S40, 60H15
Key words or phrases: Belavkin equation – Continuous measurement – Quantum theory – Oscillatory integrals – Feynman path integrals 相似文献