Journal ArticleDOI
Adaptive multilevel BEM for acoustic scattering
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TLDR
An abstract a-posteriori error estimate for indefinite problems which is based on stable multilevel decompositions of test and trial spaces is derived and an adaptive algorithm for h- or p-adaptivity is formulated.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 1997-12-01. It has received 57 citations till now. The article focuses on the topics: Boundary element method & Adaptive algorithm.read more
Citations
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Journal ArticleDOI
Convergence of adaptive BEM for some mixed boundary value problem
Markus Aurada,Samuel Ferraz-Leite,Petra Goldenits,Michael Karkulik,Markus Mayr,Dirk Praetorius +5 more
TL;DR: It is proved that the proposed adaptive scheme leads to a sequence of discrete solutions, for which the corresponding error estimators tend to zero, under a saturation assumption for the non-perturbed problem which is observed empirically.
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Sparse grids for boundary integral equations
TL;DR: Theoretical and numerical results on approximation rates, preconditioning, adaptivity and compression for piecewise constant and linear sparse grid spaces are obtained.
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On the techniques for constructing admissible stress fields in model verification: Performances on engineering examples
TL;DR: In this paper, the authors compared the performance and computational cost of three different error estimators, namely, element equilibration, star-patch and EESPT, with respect to three different criteria, namely the quality of associated error estimator, computational cost and easiness of practical implementation into commercial finite element codes.
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Error analysis of the moment method
Karl F. Warnick,Weng Cho Chew +1 more
TL;DR: This work reviews fundamental concepts such as types of error measures, properties of the problem and numerical method that affect error, the optimality principle, and basic approximation error estimates.
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Averaging Techniques for the Effective Numerical Solution of Symm's Integral Equation of the First Kind
TL;DR: A class of averaging error estimators for boundary integral methods is established which are proven to be reliable and efficient up to terms of higher order, and the [normally unknown] error is sharply estimated by the proposed estimators.
References
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Book
Non-homogeneous boundary value problems and applications
TL;DR: In this paper, the authors consider the problem of finding solutions to elliptic boundary value problems in Spaces of Analytic Functions and of Class Mk Generalizations in the case of distributions and Ultra-Distributions.
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A direct boundary integral equation method for transmission problems
Martin Costabel,Ernst P. Stephan +1 more
TL;DR: In this article, a system of integral equations for the field and its normal derivative on the boundary in acoustic or potential scattering by a penetrable homogeneous object in arbitrary dimensions is presented.
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A posteriori error estimates based on hierarchical bases
Randolph E. Bank,R. Kent Smith +1 more
TL;DR: In this paper, the authors present an analysis of a posteriors error estimator based on the use of hierarchical basis functions and apply the theory to some scalar elliptic equations and the Stokes system of equations.
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Concepts of an adaptive hierarchical finite element code
TL;DR: It is shown that this approach permits a flexible balance among iterative solver, local error estimator, and local mesh refinement device—the main components of an adaptive PDE code, making the method particularly attractive in view of parallel computing.
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Boundary integral equations for screen problems in IR3
TL;DR: In this paper, a new solution procedure for Helmholtz and Laplacian Neumann screen or Dirichlet screen problems in IR3 via boundary integral equations of the first kind having as unknown the jump of the field or of its normal derivative, respectively, across the screen S is presented.