Meshless collocation methods applied to problems with material discontinuities
Authors:
- Artur Krowiak
Abstract
The paper deals with the use of a kind ofmeshless method to solve the problem with material discontinuity on an interface. Such a problem is described by a differential equation with discontinuous coefficients. To solve the problem, the abovementioned method is associated with the subdomain approach that divides the whole domain into subdomains, in which the problem is continuous. To accurately address the analyzed problem, proper continuity conditions are imposed on the interface. The Gaussi an kernel, which belongs to the family of infinitely smooth radial basis functions, is taken into consideration as the basis function for the method. It is known that this type of method ca n provide very high rate of convergence and high accuracy but it suffers from instability. To avoid the instability, some recent advances in kernel methods, based on Mercer’s theorem, are involved in the present paper. The usefulness of the approaches are shown by benchmark proble ms described by ordinary as well as partial differential equations.
- Record ID
- CUT3a6ade9477674713a357114b610f6d33
- Publication categories
- ; ;
- Author
- Other language title versions
- Meshless collocation methods applied to problems with material discontinuities
- Pages
- [1-12]
- Other elements of collation
- rys.; wykr.; Bibliografia (na s.) - 12; Bibliografia (liczba pozycji) - 14; Oznaczenie streszczenia - Abstr.
- Substantive notes
- Ścieżka dostępu: dział 1000 - Manufacturing and Materials Processing
- Book
- Chinesta F., F. Chinesta Abgrall R., R. Abgrall Allix O. O. Allix [et al.] (eds.): 14th WCCM-ECCOMAS Congress 2020, January, 11-15, 2021 : virtual congress, 2021, Barcelona, International Centre for Numerical Methods in Engineering (CIMNE), 12 p.
- Keywords in English
- meshless method, material discontinuity, interface problem, stable RBF basis
- DOI
- DOI:10.23967/wccm-eccomas.2020.197 Opening in a new tab
- URL
- https://www.scipedia.com/public/Krowiak_2021a Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 5
- Additional fields
- Indeksowana w: Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT3a6ade9477674713a357114b610f6d33/
- URN
urn:pkr-prod:CUT3a6ade9477674713a357114b610f6d33
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