bluuebunny/crossref_metadata_2025_split huggingface dataset:
On The Analog Of The Monotone Error Rule For Parameter Choice In The (Iterated) Lavrentiev Regularization
Authors: HAMARIK U , PALM R. , RAUS T. 
Published: April 2013

AbstractWe consider linear ill-posed problems in Hilbert spaces with a noisy right hand side and a given noise level. To solve non-self-adjoint problems by the (it-erated) Tikhonov method, one effective rule for choosing the regularization parameter is the monotone error rule (Tautenhahn and Hamarik, Inverse Problems, 1999, 15, 1487– 1505). In this paper we consider the solution of self-adjoint problems by the (iterated) Lavrentiev method and propose for parameter choice an analog of the monotone error rule. We prove under certain mild assumptions the quasi-optimality of the proposed rule guaranteeing convergence and order optimal error estimates. Numerical examples show for the proposed rule and its modifications much better performance than for the modified discrepancy principle.
Dual Regularized Total Least Squares And Multi-Parameter Regularization
Authors: LU S. , PEREVERZEV S.V. , TAUTENHAHN U. 
Published: April 2013

AbstractIn this paper we continue our study of solving ill-posed problems with a noisy right-hand side and a noisy operator. Regularized approximations are obtained by Tikhonov regularization with differential operators and by dual regularized total least squares (dual RTLS) which can be characterized as a special multi-parameter regularization method where one of the two regularization parameters is negative. We report on order optimality results for both regularized approximations, discuss compu-tational aspects, provide special algorithms and show by experiments that dual RTLS is competitive to Tikhonov regularization with differential operators.
Performance Of H-Lu Preconditioning For Sparse Matrices
Authors: GRASEDYCK L. , HACKBUSCH W. , KRIEMANN R. 
Published: April 2013

AbstractIn this paper we review the technique of hierarchical matrices and put it into the context of black-box solvers for large linear systems. Numerical examples for several classes of problems from medium- to large-scale illustrate the applicability and efficiency of this technique. We compare the results with those of several direct solvers (which typically scale quadratically in the matrix size) as well as an iterative solver (algebraic multigrid) which scales linearly (if it converges in O(1) steps).
On The Stability Of Finite-Difference Schemes For Parabolic Equations Subject To Integral Conditions With Applications To Thermoelasticity
Authors: SAPAGOVAS M , JESEVICIUTE Z. 
Published: April 2013

Abstract The stability of implicit difference scheme for parabolic equations subject to integral conditions, which correspond to the quasi-static flexure of a thermoelastic rod is considered. The stability analysis is based on the spectral structure of matrix of the difference scheme. The stability conditions obtained here differ from those presented in the articles of other authors..
Domain Decomposition Methods With Overlapping Subdomains For The Time-Dependent Problems Of Mathematical Physics
Authors: VABISHCHEVICH P.N. 
Published: April 2013

AbstractAt the present time, the domain decomposition methods are considered as the most promising ones for parallel computer systems.
Nowadays success is attained mainly in solving approximately the classical boundary value problems for second-order elliptic equations.
As for the time-dependent problems of mathematical physics, there are, in common use, approaches based on ordinary implicit schemes and
implemented via iterative methods of the domain decomposition. An alternative technique is based on the non-iterative schemes
(region-additive schemes). On the basis of the general theory of additive schemes a wide class of difference schemes
(alternative directions, locally one-dimensional, factorized schemes, summarized approximation schemes, vec-tor additive schemes, etc.)
as applied to the domain decomposition technique for time-dependent problems with synchronous and asynchronous implementations has been
investigated. For nonstationary problems with self-adjoint operators, we have considered three dif-ferent types of decomposition operators
corresponding to the Dirichlet and Neumann conditions on the subdomain boundaries. General stability conditions have been obtained for the
region-additive schemes. We focused on the accuracy of domain decom-position schemes. In particular, the dependence of the convergence rate
on the width of subdomain overlapping has been investigated as the primary property. In the present paper, new classes of domain decomposition
schemes for nonstationary problems, based on the subdomain overlaping and minimal data exchange in solving problems in subdomains, have been
constructed.
Mixed Hybrid Finite Element Method for a Variational Inequality with a Quasi-linear Operator
Authors: Lapin A. 
Published: April 2013

Abstract A mixed hybrid finite element method has been applied to a variational inequality with a potential second-order quasi-linear differential operator. The
Lagrange multiplier method for a dual problem has been used to construct this finite
element scheme. The existence and uniqueness of a solution for the resulting finite-
dimensional problem has been proved, the solution iterative methods are discussed.
The non-overlapping domain decomposition method combined with the mixed hybrid
finite element approximation is analyzed.
Some Remarks on Residual-based Stabilisation of Inf-sup Stable Discretisations of the Generalised Oseen Problem
Authors: Matthies G. , Ionkin Nikolai I. , Lube G. , Röhe L. 
Published: April 2013

AbstractWe consider residual-based stabilised finite element methods for the generalised
Oseen problem. The unique solvability based on a modified stability condition
and an error estimate are proved for inf-sup stable discretisations of velocity and pressure.
The analysis highlights the role of an additional stabilisation of the incompressibility
constraint. It turns out that the stabilisation terms of the streamline-diffusion
(SUPG) type play a less important role. In particular, there exists a conditional stability
problem of the SUPG stabilisation if two relevant problem parameters tend to zero.
The analysis extends a recent result to general shape-regular meshes and to discontinuous
pressure interpolation. Some numerical observations support the theoretical
results.
A Fourier Pseudospectral Method for Solving Coupled Viscous Burgers Equations
Authors: Rashid Abdur , Ismail Ahmad Izani Bin Md. 
Published: April 2013

AbstractThe Fourier pseudo-spectral method has been studied for a one-
dimensional coupled system of viscous Burgers equations. Two test problems with
known exact solutions have been selected for this study. In this paper, the rate of con-
vergence in time and error analysis of the solution of the first problem has been studied,
while the numerical results of the second problem obtained by the present method are
compared to those obtained by using the Chebyshev spectral collocation method. The
numerical results show that the proposed method outperforms the conventional one in
terms of accuracy and convergence rate.
Additive Average Schwarz Methods for Discretization of Elliptic Problems with Highly Discontinuous Coefficients
Authors: Dryja M. , Sarkis M. 
Published: April 2013

AbstractA second order elliptic problem with highly discontinuous coefficients
has been considered. The problem is discretized by two methods: 1) continuous finite
element method (FEM) and 2) composite discretization given by a continuous
FEM inside the substructures and a discontinuous Galerkin method (DG) across the
boundaries of these substructures. The main goal of this paper is to design and analyze
parallel algorithms for the resulting discretizations. These algorithms are additive
Schwarz methods (ASMs) with special coarse spaces spanned by functions that are
almost piecewise constant with respect to the substructures for the first discretization
and by piecewise constant functions for the second discretization. It has been established
that the condition number of the preconditioned systems does not depend on the
jumps of the coefficients across the substructure boundaries and outside of a thin layer
along the substructure boundaries. The algorithms are very well suited for parallel
computations.
Runge-Kutta Nystrom Method of Order Three for Solving Fuzzy Differential Equations
Authors: Kanagarajan K. , Sambath M. 
Published: April 2013

AbstractIn this paper we present a numerical algorithm for solving fuzzy differential
equations based on Seikkala’s derivative of a fuzzy process. We discuss in detail
a numerical method based on a Runge-Kutta Nystrom method of order three. The
algorithm is illustrated by solving some fuzzy differential equations.
A Flux-Corrected Finite Element Method for Chemotaxis Problems
Authors: Strehl R. , Sokolov A. , Kuzmin D. , Turek S. 
Published: April 2013

AbstractAn implicit flux-corrected transport (FCT) algorithm has been developed
for a class of chemotaxis models. The coefficients of the Galerkin finite element
discretization has been adjusted in such a way as to guarantee mass conservation and
keep the cell density nonnegative. The numerical behaviour of the proposed highresolution
scheme is tested on the blow-up problem for a minimal chemotaxis model
with singularities. It has also been shown that the results for an Escherichia coli
chemotaxis model are in good agreement with the experimental data reported in the
literature.
Method for the Calculation of All Non-Multiple Zeros of an Analytic Function
Authors: Semenov Vasyl 
Published: April 2013

AbstractA method for calculating all nonmultiple zeros of the complex function in a given rectangle is proposed. The main idea of the method is to construct a covering of the initial rectangle by subsets where either there no solutions or there is only one solution. The algorithm for the construction of such a covering is presented and its convergence is proved. The implementation of the method is shown using different examples.
Computing the sinp function via the inverse power method
Authors: Biezuner Rodney Josué , Ercole Grey , Martins Eder Marinho 
Published: April 2013

AbstractIn this paper, we discuss a new iterative method for computing sinp. This function
was introduced by Lindqvist in connection with the unidimensional nonlinear Dirichlet
eigenvalue problem for the p-Laplacian. The iterative technique was inspired by the
inverse power method in finite dimensional linear algebra and is competitive with other
methods available in the literature. Keywords: p-Laplacian, eigenvalues, eigenfunctions,
sinp, inverse power method.
A Substructuring Domain Decomposition Scheme for Unsteady Problems
Authors: Vabishchevich Petr 
Published: April 2013

AbstractDomain decomposition methods are used for the approximate solution of boundary-value
problems for partial differential equations on parallel computing systems. Specific features
of unsteady problems are fully taken into account in iteration-free domain decomposition
schemes. Regionally-additive schemes are based on various classes of splitting schemes. In
this paper we highlight a class of domain decomposition schemes which are based on the
partition of the initial domain into subdomains with common boundary nodes. Using a partition
of unity we construct and analyze unconditionally stable schemes for domain decomposition
based on a two-component splitting: the problem within each subdomain and the problem at
their boundaries. As an example we consider a Cauchy problem of first or second order in time
with a non-negative self-adjoint second order operator in space. The theoretical discussion
is supplemented with the numerical solution of a model problem for a two-dimensional parabolic
equation.
Quantized-TT-Cayley Transform for Computing the Dynamics and the Spectrum of High-Dimensional Hamiltonians
Authors: Gavrilyuk Ivan , Khoromskij Boris 
Published: April 2013

Abstract In the present paper, we propose and analyse a class of tensor methods for the efficient
numerical computation of the dynamics and spectrum of high-dimensional Hamiltonians. We focus
on the complex-time evolution problems. We apply the quantized-TT (QTT) matrix product states
type tensor approximation that allows to represent N-d tensors generated by the grid
representation of d-dimensional functions and operators with log-volume complexity, O(d log N),
where N is the univariate discretization parameter in space. Making use of the truncated
Cayley transform method allows us to recursively separate the time and space variables and
then introduce the efficient QTT representation of both the temporal and the spatial parts of
the solution to the high-dimensional evolution equation. We prove the exponential convergence
of the m-term time-space separation scheme and describe the efficient tensor-structured
preconditioners for the arising system with multidimensional Hamiltonians. For the class of
"analytic" and low QTT-rank input data, our method allows to compute the solution at a fixed
point in time t=T>0 with an asymptotic complexity of order O(d log N ln^q (1/ε)), where ε>0
is the error bound and q is a fixed small number. The time-and-space separation method via
the QTT-Cayley-transform enables us to construct a global m-term separable (x,t)-representation
of the solution on a very fine time-space grid with complexity of order O(dm^4 log N_t log N),
where N_t is the number of sampling points in time. The latter allows efficient energy
spectrum calculations by FFT (or QTT-FFT) of the autocorrelation function computed on a
sufficiently long time interval [0,T]. Moreover, we show that the spectrum of the Hamiltonian
can also be represented by the poles of the t-Laplace transform of a solution. In particular,
the approach can be an option to compute the dynamics and the spectrum in the time-dependent
molecular Schrödinger equation.
An Introduction to Hierarchical (H-) Rank and TT-Rank of Tensors with Examples
Authors: Grasedyck Lars , Hackbusch Wolfgang 
Published: April 2013

Abstract We review two similar concepts of hierarchical rank of tensors (which extend the matrix
rank to higher order tensors): the TT-rank and the H-rank (hierarchical or H-Tucker rank).
Based on this notion of rank, one can define a data-sparse representation of tensors
involving O(dnk + dk^3) data for order d tensors with mode sizes n and rank k. Simple
examples underline the differences and similarities between the different formats and ranks.
Finally, we derive rank bounds for tensors in one of the formats based on the ranks in the
other format.
Fast Quadrature Techniques for Retarded Potentials Based on TT/QTT Tensor Approximation
Authors: Khoromskij Boris , Sauter Stefan , Veit Alexander 
Published: April 2013

AbstractWe consider the Galerkin approach for the numerical solution of retarded boundary integral
formulations of the three dimensional wave equation in unbounded domains. Recently smooth and
compactly supported basis functions in time were introduced which allow the use of standard
quadrature rules in order to compute the entries of the boundary element matrix. In this
paper, we use TT and QTT tensor approximations to increase the efficiency of these quadrature
rules. Various numerical experiments show the substantial reduction of the computational
cost that is needed to obtain accurate approximations for the arising integrals.
Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems
Authors: Kressner Daniel , Tobler Christine 
Published: April 2013

AbstractWe consider elliptic PDE eigenvalue problems on a tensorized domain, discretized such that
the resulting matrix eigenvalue problem Ax=λx exhibits Kronecker product structure. In
particular, we are concerned with the case of high dimensions, where standard approaches to
the solution of matrix eigenvalue problems fail due to the exponentially growing degrees of
freedom. Recent work shows that this curse of dimensionality can in many cases be addressed
by approximating the desired solution vector x in a low-rank tensor format. In this paper, we
use the hierarchical Tucker decomposition to develop a low-rank variant of LOBPCG, a classical
preconditioned eigenvalue solver. We also show how the ALS and MALS (DMRG) methods known from
computational quantum physics can be adapted to the hierarchical Tucker decomposition.
Finally, a combination of ALS and MALS with LOBPCG and with our low-rank variant is proposed.
A number of numerical experiments indicate that such combinations represent the methods of
choice.
DMRG Approach to Fast Linear Algebra in the TT-Format
Authors: Oseledets Ivan 
Published: April 2013

AbstractIn this paper, the concept of the DMRG minimization scheme is extended to several
important operations in the TT-format, like the matrix-by-vector product and the conversion
from the canonical format to the TT-format. Fast algorithms are implemented and a
stabilization scheme based on randomization is proposed. The comparison with the direct
method is performed on a sequence of matrices and vectors coming as approximate solutions
of linear systems in the TT-format. A generated example is provided to show that
randomization is really needed in some cases. The matrices and vectors used are available
from the author or at http://spring.inm.ras.ru/osel
Full discretisation of second-order nonlinear evolution equations: strong convergence and applications
Authors: Emmrich Etienne , Šiška David 
Published: April 2013

Abstract Recent results on convergence of fully discrete approximations combining the Galerkin
method with the explicit-implicit Euler scheme are extended to strong convergence under
additional monotonicity assumptions. It is shown that these abstract results, formulated in
the setting of evolution equations, apply, for example, to the partial differential equation
for vibrating membrane with nonlinear damping and to another partial differential equation
that is similar to one of the equations used to describe martensitic transformations in
shape-memory alloys. Numerical experiments are performed for the vibrating membrane equation
with nonlinear damping which support the convergence results.
Efficient implementation of adaptive P1-FEM in Matlab
Authors: Funken Stefan , Praetorius Dirk , Wissgott Philipp 
Published: April 2013

Abstract We provide a MATLAB package p1afem for an adaptive P1-finite element method (AFEM).
This includes functions for the assembly of the data, different error estimators, and
an indicator-based adaptive meshrefining algorithm. Throughout, the focus is on an efficient
realization by use of MATLAB built-in functions and vectorization. Numerical experiments
underline the efficiency of the code which is observed to be of almost linear complexity
with respect to the runtime. Although the scope of this paper is on AFEM, the general ideas
can be understood as a guideline for writing efficient MATLAB code.
The Effect of Regulating Elements on Convective Heat Transfer along Shaped Heat Exchange Surfaces
Authors: Cernecky Jozef , Koniar Jan , Brodnianska Zuzana 
Published: April 2013

Abstract
The paper deals with a study of the effect of regulating elements on local values of heat transfer coefficients along shaped heat exchange surfaces with forced air convection. The use of combined methods of heat transfer intensification, i.e. a combination of regulating elements with appropriately shaped heat exchange areas seems to be highly effective. The study focused on the analysis of local values of heat transfer coefficients in indicated cuts, in distances expressed as a ratio x/s for 0; 0.33; 0.66 and 1. As can be seen from our findings, in given conditions the regulating elements can increase the values of local heat transfer coefficients along shaped heat exchange surfaces. An optical method of holographic interferometry was used for the experimental research into temperature fields in the vicinity of heat exchange surfaces. The obtained values correspond very well with those of local heat transfer coefficients αx, recorded in a CFD simulation.
Process Engineering in Iron Production
Authors: Pustějovská Pavlína , Jursová Simona 
Published: April 2013

Abstract
Balance, thermodynamic and mainly kinetic approaches using methods of process engineering enable to determine conditions under which iron technology can actually work in limiting technological states, at the lowest reachable fuel consumption (reducing factor) and the highest reachable productivity accordingly. Kinetic simulation can be also used for variant prognostic calculations. The paper deals with thermodynamics and kinetics of iron making process. It presents a kinetic model of iron oxide reduction in a low temperature area. In the experimental part it deals with testing of iron ore feedstock properties. The theoretical and practical limits determined by heat conditions, feedstock reducibility and kinetics of processes are calculated.
Effect of Impeller Shape on Solid Particle Suspension
Authors: Rieger František , Jirout Tomáš , Ceres Dorin , Seichter Pavel 
Published: April 2013

Abstract
This paper deals with the effect of impeller shape on off-bottom particle suspension. On the basis of numerous suspension measurements, correlations are proposed for calculating the just-suspended impeller speed for a standard pitched four-blade turbine and three types of hydrofoil impellers produced by TECHMIX for several particle sizes and for a wide range of particle concentrations. The suspension efficiency of the tested impellers is compared with the efficiency of a standard pitched blade turbine on the basis of the power consumption required for off-bottom suspension of solid particles. It is shown that the standard pitched blade turbine needs highest power consumption, i.e. it exhibits less efficiency for particle suspension than hydrofoil impellers produced by TECHMIX.
The Impact of Migration Policy on Migrants’ Education Structure: Evidence from Austrian Policy Reform
Authors: Huber Peter , Bock-Schappelwein Julia 
Published: April 2013

Abstract
We ask how reform of migration law intended to increase the selectivity of migration (the so-called integration agreement regulation in 2003) in Austria impacted on the education structure of migrants to Austria. To identify the effects of this reform, we use the fact that it applied only to migrants from third countries and not those from EEA-countries.We find no compelling evidence that this regulation improved the education structure of migrants to Austria. Our interpretation of this is that the implicit positive impact of the reforms on the education structure of migrants was countervailed by the increased restrictiveness of the migration regime overall, or that other developments in the migration regime were more important for changes in education structure in the time period considered.
The Never-Ending Fight: Economic and Political Corruption in Hungary
Authors: Kőhalmi László 
Published: April 2013

Abstract
Every society must pay the “price of democracy” and in this price are “calculated” the rising number of crimes and the change in their quality, and also the unique alterations of corruption, among other things. The fight against economic-political corruption is a risky question, because the hunters and the hunted, those who conduct and those who undergo impeachment, are often members of the same political elite. It is in the interest of tax-payers that public funds should not become cash bribes, and furthermore that the rule of corruption should not grow dominant in even a single sphere. If we consider the moral weakness of politicians as the genesis of economic and political corruption, then the appropriate anti-corruption strategy would be the right combination of penalty policy and payment policy.