Search results for "Numerical Analysis"
showing 10 items of 883 documents
A direct impedance tomography algorithm for locating small inhomogeneities
2003
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 documen…
Solving a model for 1-D, three-phase flow vertical equilibrium processes in a homogeneous porous medium by means of a Weighted Essentially Non Oscill…
2013
Mathematical models of multi-phase flow are useful in some engineering applications like enhanced oil recovery, filtration of pollutants into subsurface, etc. In this work, we derive a mathematical model for the motion of one-dimensional three-phase flow in a porous medium under the condition of vertical equilibrium, which can be viewed as an extension of some two-phase flow models described in the literature. Our model involves a system of two partial differential equations in the form of viscous conservation laws, whose solutions may contain very sharp transitions. We show that a high-order/high resolution Weighted Essentially Non Oscillatory scheme is an appropriate tool to discretize th…
On a topology optimization problem governed by two-dimensional Helmholtz equation
2015
The paper deals with a class of shape/topology optimization problems governed by the Helmholtz equation in 2D. To guarantee the existence of minimizers, the relaxation is necessary. Two numerical methods for solving such problems are proposed and theoretically justified: a direct discretization of the relaxed formulation and a level set parametrization of shapes by means of radial basis functions. Numerical experiments are given.
Finite element analysis of varitional crimes for a quasilinear elliptic problem in 3D
2000
We examine a finite element approximation of a quasilinear boundary value elliptic problem in a three-dimensional bounded convex domain with a smooth boundary. The domain is approximated by a polyhedron and a numerical integration is taken into account. We apply linear tetrahedral finite elements and prove the convergence of approximate solutions on polyhedral domains in the $W^1_2$ -norm to the true solution without any additional regularity assumptions.
Vereinfachte Rekursionen zur Richardson-Extrapolation in Spezialf�llen
1975
Recursions are given for Richardson-extrapolation based on generalized asymptotic expansions for the solution of a finite algorithm depending upon a parameterh>0. In particular, these expansions may contain terms likeh ?·log(h), (?>0). Simplified formulae are established in special cases. They are applicable to numerical integration of functions with algebraic or logarithmic endpoint singularities and provide a Romberg-type quadrature.
Ein Verfahren zur Behandlung von Ausgleichsaufgaben mit Intervallkoeffizienten
1976
Es wird ein Verfahren beschrieben, das die Berechnung einer Intervalleinschliesung der Losungsmenge einer linearen Ausgleichsaufgabe mit Intervallkoeffizienten erlaubt. Es stellt eine Ubertragung des Bjorckschen Algorithmus der iterativen Verbesserung einer Naherungslosung zu einer linearen Ausgleichsaufgabe [5] auf ein bekanntes Verfahren zur Behandlung von Intervallgleichungssystemen dar.
Enhancing Attention’s Explanation Using Interpretable Tsetlin Machine
2022
Explainability is one of the key factors in Natural Language Processing (NLP) specially for legal documents, medical diagnosis, and clinical text. Attention mechanism has been a popular choice for such explainability recently by estimating the relative importance of input units. Recent research has revealed, however, that such processes tend to misidentify irrelevant input units when explaining them. This is due to the fact that language representation layers are initialized by pre-trained word embedding that is not context-dependent. Such a lack of context-dependent knowledge in the initial layer makes it difficult for the model to concentrate on the important aspects of input. Usually, th…
A-stabile Kollokationsverfahren mit mehrfachen Knoten
1982
Die Kollokationsmethoden, die vom Autor in [3] untersucht werden, liefern Spline-Approximationen fur die Losungen von Anfangswertproblemen bei gewohnlichen Differentialgleichungen. Einige allgemeine Resultate uber A-Stabilitat von Wanner, Hairer und Norsett [6] werden fur diese Methoden in dem Fall formuliert, wo sie mit gewissen impliziten Runge-Kutta-Methoden aquivalent sind. Hierbei wird die Abhangigkeit der A-Stabilitat von den Knoten und ihren Vielfachheiten offensichtlich.
Numerische Lösung gewöhnlicher Differentialgleichungen mit Splinefunktionen
1980
In dieser Arbeit wird ein allgemeines Verfahren zur Erzeugung von Splineapproximationen fur die Losungen von Anfangswertproblemen bei gewohnlichen Differentialgleichungen vorgestellt. Einige der bekannten Spline-approximationsmethoden sind als Spezialfalle enthalten. Eine gangige Vorgehensweise besteht darin, das Intervall, uber dem das Anfangswertproblem gegeben ist, in aquidistante Teilintervalle zu zerlegen und dann sukzessive die Splineapproximation zu definieren. Hierbei wird gefordert, das die Spline-approximation in den Knoten gewisse Bedingungen erfullt. Bei dem hier betrachteten allgemeinen Verfahren werden in den einzelnen Teilintervallen noch zusatzliche Zwischenknoten eingefuhrt…
Einige Bemerkungen zur Dualität in der konvexen Optimierung
1975
Die allgemeine Rockafellarsche Dualitatstheorie wird auf eine Reihe konvexer Optimierungsprobleme angewandt, um Dualitats-, Existenz-und Charakterisierungssatze fur Optimallosungen zu erhalten. Unter anderem werden auf diesem Wege einige schon bekannte Ergebnisse in sehr einfacher Weise wiedergewonnen.