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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

Intersections of Sequences of Ideals Generated by Polynomials: Dedicated to Professor Stanis law Lojasiewicz on his 70th birthday

Apel, Joachim, Tworzewski, Piotr, Winiarski, Tadeusz, Stückrad, Jürgen 22 November 2018 (has links)
We present a method for determining the reduced Gröbner basis with respect to a given admissible term order of order type ! of the intersection ideal of an infinite sequence of polynomial ideals. As an application we discuss the Lagrange type interpolation on algebraic sets and the 'approximation' of the ideal I of an algebraic set by zero dimensional ideals, whose affine Hilbert functions converge towards the affine Hilbert function of I.

Term Bases for Multivariate Interpolation of Hermite Type

Apel, Joachim, Stückrad, Jürgen, Tworzewski, Piotr, Winiarski, Tadeusz 22 November 2018 (has links)
No description available.

Distance Desert Automata and Star Height Substitutions

Kirsten, Daniel 06 February 2019 (has links)
We introduce the notion of nested distance desert automata as a joint generalization and further development of distance automata and desert automata. We show that limitedness of nested distance desert automata is PSPACE-complete. As an application, we show that it is decidable in 22O(n2) space whether the language accepted by an n-state non-deterministic automaton is of a star height less than a given integer h (concerning rational expressions with union, concatenation and iteration). We also show some decidability results for some substitution problems for recognizable languages.

Efficient time step parallelization of full multigrid techniques

Weickert, J., Steidten, T. 30 October 1998 (has links)
This paper deals with parallelization methods for time-dependent problems where the time steps are shared out among the processors. A Full Multigrid technique serves as solution algorithm, hence information of the preceding time step and of the coarser grid is necessary to compute the solution at each new grid level. Applying the usual extrapolation formula to process this information, the parallelization will not be very efficient. We developed another extrapolation technique which causes a much higher parallelization effect. Test examples show that no essential loss of exactness appears, such that the method presented here shall be well-applicable.

Local inequalities for anisotropic finite elements and their application to convection-diffusion problems

Apel, Thomas, Lube, Gert 30 October 1998 (has links)
The paper gives an overview over local inequalities for anisotropic simplicial Lagrangian finite elements. The main original contributions are the estimates for higher derivatives of the interpolation error, the formulation of the assumptions on admissible anisotropic finite elements in terms of geometrical conditions in the three-dimensional case, and an anisotropic variant of the inverse inequality. An application of anisotropic meshes in the context of a stabilized Galerkin method for a convection-diffusion problem is given.

Navier-Stokes equations as a differential-algebraic system

Weickert, J. 30 October 1998 (has links)
Nonsteady Navier-Stokes equations represent a differential-algebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differential-algebraic equation (DAE). We investigate for several discretization schemes for the Navier-Stokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE.

A note on anisotropic interpolation error estimates for isoparametric quadrilateral finite elements

Apel, Th. 30 October 1998 (has links)
Anisotropic local interpolation error estimates are derived for quadrilateral and hexahedral Lagrangian finite elements with straight edges. These elements are allowed to have diameters with different asymptotic behaviour in different space directions. The case of affine elements (parallelepipeds) with arbitrarily high degree of the shape functions is considered first. Then, a careful examination of the multi-linear map leads to estimates for certain classes of more general, isoparametric elements. As an application, the Galerkin finite element method for a reaction diffusion problem in a polygonal domain is considered. The boundary layers are resolved using anisotropic trapezoidal elements.

Two-point boundary value problems with piecewise constant coefficients: weak solution and exact discretization

Windisch, G. 30 October 1998 (has links)
For two-point boundary value problems in weak formulation with piecewise constant coefficients and piecewise continuous right-hand side functions we derive a representation of its weak solution by local Green's functions. Then we use it to generate exact three-point discretizations by Galerkin's method on essentially arbitrary grids. The coarsest possible grid is the set of points at which the piecewise constant coefficients and the right- hand side functions are discontinuous. This grid can be refined to resolve any solution properties like boundary and interior layers much more correctly. The proper basis functions for the Galerkin method are entirely defined by the local Green's functions. The exact discretizations are of completely exponentially fitted type and stable. The system matrices of the resulting tridiagonal systems of linear equations are in any case irreducible M-matrices with a uniformly bounded norm of its inverse.

Variable preconditioning procedures for elliptic problems

Jung, M., Nepomnyaschikh, S. V. 30 October 1998 (has links)
For solving systems of grid equations approximating elliptic boundary value problems a method of constructing variable preconditioning procedures is presented. The main purpose is to discuss how an efficient preconditioning iterative procedure can be constructed in the case of elliptic problems with disproportional coefficients, e.g. equations with a large coefficient in the reaction term (or a small diffusion coefficient). The optimality of the suggested technique is based on fictitious space and multilevel decom- position methods. Using an additive form of the preconditioners, we intro- duce factors into the preconditioners to optimize the corresponding conver- gence rate. The optimization with respect to these factors is used at each step of the iterative process. The application of this technique to two-level $p$-hierarchical precondi- tioners and domain decomposition methods is considered too.

A new method for computing the stable invariant subspace of a real Hamiltonian matrix or Breaking Van Loans curse?

Benner, P., Mehrmann, V., Xu., H. 30 October 1998 (has links)
A new backward stable, structure preserving method of complexity O(n^3) is presented for computing the stable invariant subspace of a real Hamiltonian matrix and the stabilizing solution of the continuous-time algebraic Riccati equation. The new method is based on the relationship between the invariant subspaces of the Hamiltonian matrix H and the extended matrix /0 H\ and makes use \H 0/ of the symplectic URV-like decomposition that was recently introduced by the authors.

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