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Ivanov, Tjavdar
Publications (4 of 4) Show all publications
Ivanov, T., Maz'ya, V. & Schmidt, G. (2000). Boundary Layer Approximate Approximations for Cubature of Potentials. In: M. Bonnet, A.-M. Sändig, W.L. Wendland (Ed.), Mathematical Aspects of Boundary Element Methods (pp. 165-177). London: Chapman & Hall
Open this publication in new window or tab >>Boundary Layer Approximate Approximations for Cubature of Potentials
2000 (English)In: Mathematical Aspects of Boundary Element Methods / [ed] M. Bonnet, A.-M. Sändig, W.L. Wendland, London: Chapman & Hall , 2000, p. 165-177Chapter in book (Other academic)
Place, publisher, year, edition, pages
London: Chapman & Hall, 2000
Series
Pitman research notes in mathematics series, ISSN 0269-3674 ; 414
Identifiers
urn:nbn:se:hj:diva-3161 (URN)1-58488-006-6 (ISBN)
Available from: 2007-08-02 Created: 2007-08-02 Last updated: 2010-05-24Bibliographically approved
Ivanov, T., Maz'ya, V. & Schmidt, G. (1999). Boundary Layer Approximate Approximations and Cubature of Potentials in Domains. Advances in Computational Mathematics, 10(3-4), 311-342
Open this publication in new window or tab >>Boundary Layer Approximate Approximations and Cubature of Potentials in Domains
1999 (English)In: Advances in Computational Mathematics, ISSN 1019-7168, E-ISSN 1572-9044, Vol. 10, no 3-4, p. 311-342Article in journal (Refereed) Published
Identifiers
urn:nbn:se:hj:diva-3150 (URN)10.1023/A:1018990918531 (DOI)
Available from: 2007-08-02 Created: 2007-08-02 Last updated: 2017-12-12Bibliographically approved
Ivanov, T. (1997). Boundary Layer Approximate Approximations and Cubature of Potentials in Domains. (Doctoral dissertation). Linköping: Department of Mathematics, Linköping University
Open this publication in new window or tab >>Boundary Layer Approximate Approximations and Cubature of Potentials in Domains
1997 (English)Doctoral thesis, monograph (Other scientific)
Abstract [en]

The goal of this thesis is to develop efficient numerical algorithms for approximation of functions defined on domains and apply these algorithms to obtain accurate semi-analytic cubature formulae for various integral operators. These algorithms are based on the method of "approximate approximations", introduced by V. Maz'ya in 1991. Approximate approximations are quasi-interpolants using generating functions which form an approximate partition of unity. The lack of convergence, which is not perceptible in practical computations, is compensated for by the flexibility in the choice of generating functions and the simplicity of the generalisation to the multivariate case.

In the present thesis, we develop multi-resolution schemes for accurate approximation of functions up to the boundary using iterative application of quasi-interpolants on finer grids. The mesh refinement is obtained automatically through analytical factorization of the approximate approximations operator. The structure of the schemes makes it possible to perform mesh refinement locally, in particular, near the boundary. In the latter case, one obtains good accuracy on the whole domain, except on a thin boundary layer of width decreasing exponentially with the number of iterations.

Using these properties we derive high-order cubature formulae for approximation of potentials acting on densities defined in domains. We give error estimates in suitable norms both for the approximation of functions and the approximation of integral operators. Special attention is paid to the construction of anisotropic schemes on affine meshes, which leads to reduced computational complexity. We conclude by deducing anisotropic formulae for approximation of the logarithmic, two-dimensional elastic and Newtonian potentials.

Place, publisher, year, edition, pages
Linköping: Department of Mathematics, Linköping University, 1997
Series
Linköping Studies in Science and Technology. Dissertations , ISSN 0345-7524 ; 507
Identifiers
urn:nbn:se:hj:diva-3172 (URN)91-7219-105-8 (ISBN)
Public defence
(English)
Available from: 2007-08-02 Created: 2007-08-02Bibliographically approved
Ivanov, T. (1995). Boundary Layer: Approximate Approximations and Cubature of Potentials in Domains. (Licentiate dissertation). Linköping: Linköping university
Open this publication in new window or tab >>Boundary Layer: Approximate Approximations and Cubature of Potentials in Domains
1995 (English)Licentiate thesis, monograph (Other scientific)
Place, publisher, year, edition, pages
Linköping: Linköping university, 1995. p. 87
Series
Linköping studies in science and technology. Thesis, ISSN 0280-7971 ; 516
Identifiers
urn:nbn:se:hj:diva-3183 (URN)91-7871-613-6 (ISBN)
Available from: 2007-08-02 Created: 2007-08-02Bibliographically approved
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