4,577 research outputs found
Multiscale Methods for Boundary Integral Equations and Their Application to Boundary Value Problems in Scattering Theory and Geodesy
No full textIn the present paper we give an overview on multiscale algorithms for the solution of boundary integral equations which are based on the use of wavelets. These methods have been introduced first by Beylkin, Coifman, and Rokhlin [5]. They have been developed and thoroughly investigated in the work of Alpert [1], Dahmen, Proessdorf, Schneider [16-19], Harten, Yad-Shalom [25], v.Petersdorff, Schwab [33-35], and Rathsfeld [39-40]. We describe the wavelet algorithm and the theoretical results on its stability, convergence, and complexity. Moreover, we discuss the application of the method to the solution of a two-dimensional scattering problem of acoustic or electromagnetic waves and to the solution of a fixed geodetic boundary value problem for the gravity field of the earth. The computational tests confirm the high compression rates and the saving of computation time predicted by the theory
Stylos kai edraiōma tēs ekklēsias, sive, Dissertatio de iustificatione hominis
No full textquam ... sub praesidio ... Ioh. Henrici Heideggeri ... placido eruditorum examini subiicit Andreas Steinerus, Vitod. author & respondens, ad diem Octobris loco horisque solitisDiss. Hohe Schule Zürich, 167
Author: Andreas Johannis Prytz
No full textAn edition of the consecration sermons in Gothenburg Cathedral 1633 by Superintendent Andreas Johannis Prytz, with introductory comments. The first sermon deals with the need for Church buildings, the second with the consecration of a new Church
We must combine conservation of nature with benefits to society. Interview by Gaby Allheilig with Andreas Heinimann on IPBES' Global Assessment Report on Biodiversity and Ecosystem Services
No full textOn 6 May 2019, the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) presented its report on the state of biodiversity and ecosystem services worldwide. The first such assessment since 2005, it concludes that biodiversity and ecosystem loss has reached the point where it threatens human well-being. The researchers involved recommend several urgent measures to political decision-makers. Andreas Heinimann of CDE was the one Swiss scientist who worked as a lead author on a chapter of the report
To athanaton tēs psychēs, sive, Dissertatio de animae immortalitate, ex naturae & sanae rationis lumine demonstrata
No full textquam ... sub praesidio ... Iohannis Lavateri ... publicae ac placidae disquisitioni submittit Andreas Steinerus, Vitod. author & respondens ...Dedikation an Johannes Lavater, Jacob Meyer, Joh. Jacob Schaedler und Jacob Hegner auf dem Titelbl. versoDiss. Hohe Schule Zürich, 167
Family Virtues and Social Critique: Andreas Latzko’s Anti-War Prose (1917-1918)
No full textBetween 1917 and 1918, the Austro-Hungarian author Andreas Latzko (1876-1943) wrote three separate publications against the Great War: Menschen im Krieg (1917), Friedensgericht (1918), and Der letzte Mann (published 1919). Literary historians tend to bypass these works, and the few who note them chiefly focus on the best-selling novella cycle Menschen im Krieg (1917). It is usually presented as an example of expressionist political prose, or as a mixture of social satire and aesthetic shock-tactics that chiefly remains indebted to realist traditions, albeit with occasional incursions into expressionistic styles..
A wavelet algorithm for the boundary element solution of a geodetic boundary value problem
No full textIn this paper we consider a piecewise bilinear collocation method for the solution of a singular integral equation over a part of the surface of the earth. This singular equation is the boundary integral equation corresponding to the oblique derivative boundary problem for Laplace's equation. We introduce special wavelet bases for the spaces of test and trial functions. Analogously to well-known results on wavelet algorithms, the stiffness matrices with respect to these bases can be reduced to sparse matrices such that the assembling of the matrices and the iterative solution of the matrix equations quicken. Though the theoretical results apply only to integral equations with ‘smooth’ solutions over ‘smooth’ manifolds, we present numerical tests for a geometry as difficult as the surface of the earth
A Wavelet Algorithm for the Solution of a Singular Integral Equation over a Smooth Two-Dimensional Manifold
No full textIn this paper we consider a piecewise bilinear collocation method for the solution of a singular integral equation over a smooth surface. Using a fixed set of parametrizations, we introduce special wavelet bases for the spaces of test and trial functions. The trial wavelets have two vanishing moments only if their supports do not intersect the lines belonging to the common boundary of two subsurfaces defined by different parameter representations. Nevertheless, analogously to well-known results on wavelet algorithms, the stiffness matrices with respect to these bases can be compressed to sparse matrices such that the iterative solution of the matrix equations becomes fast. Finally, we present a fast quadrature algorithm for the computation of the compressed stiffness matrix
Error estimates and extrapolation for the numerical solution of Mellin convolution equations
No full textIn this paper we consider a quadrature method for the numerical solution of a second-kind integral equation over the interval, where the integral operator is a compact perturbation of a Mellin convolution operator. This quadrature method relies upon a singularity subtraction and transformation technique. Stability and convergence order of the approximate solution are well known. We shall derive the first term in the asymptotics of the error which shows that, in the interior of the interval, the approximate solution converges with higher order than over the whole interval. This implies higher orders of convergence for the numerical calculation of smooth functionals to the exact solution. Moreover, the asymptotics allows us to define a new approximate solution extrapolated from the dilated solutions of the quadrature method over meshes with different mesh sizes. This extrapolated solution is designed to improve the low convergence order caused by the non-smoothness of the exact solution even when the transformation technique corresponds to slightly graded meshes. Finally, we discuss the application to the double-layer integral equation over the boundary of polygonal domains an
Short laws for finite groups and residual finiteness growth
No full text We prove that for every n ∈ N n \in \mathbb {N} and δ > 0 \delta >0 there exists a word w n ∈ F 2 w_n \in F_2 of length O ( n 2 / 3 log ( n ) 3 + δ ) O(n^{2/3} \log (n)^{3+\delta }) which is a law for every finite group of order at most n n . This improves upon the main result of Andreas Thom [Israel J. Math. 219 (2017), pp. 469–478] by the second named author. As an application we prove a new lower bound on the residual finiteness growth of non-abelian free groups. </p
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