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Some practical aspects of parallel adaptive BDDC method
Šístek, Jakub; Mandel, J.; Sousedík, B.
2012 - English
We describe a parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method enhanced by an adaptive construction of coarse problem. The method is designed for numerically difficult problems, where standard choice of continuity of arithmetic averages across faces and edges of subdomains fails to maintain the low condition number of the preconditioned system. Problems of elasticity analysis of bodies consisting of different materials with rapidly changing stiffness may represent one class of such challenging problems. The adaptive selection of constraints is shown to significantly increase the robustness of the method for this class of problems. However, since the cost of the set-up of the preconditioner with adaptive constraints is considerably larger than for the standard choices, computational feasibility of the presented implementation is obtained only for large contrasts of material coefficients.
Keywords:
substructuring methods; BDDC; Feti methods
Available in digital repository of the ASCR
Some practical aspects of parallel adaptive BDDC method
We describe a parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method enhanced by an adaptive construction of coarse problem. The method is designed for numerically ...
Algebraic classification of the Weyl tensor
Pravdová, Alena
2012 - English
Alignment classification of tensors on Lorentzian manifolds of arbitrary dimension is summarized. This classification scheme is then applied to the case of the Weyl tensor and it is shown that in four dimensions it is equivalent to the well known Petrov classification. The approaches using Bel-Debever criteria and principal null directions of the superenergy tensor are also discussed.
Keywords:
algebraic classification of tensors; Lorentzian manifolds
Fulltext is available at external website.
Algebraic classification of the Weyl tensor
Alignment classification of tensors on Lorentzian manifolds of arbitrary dimension is summarized. This classification scheme is then applied to the case of the Weyl tensor and it is shown that in four ...
Algebraic classification of the Weyl tensor : selected applications
Pravda, Vojtěch
2012 - English
Selected applications of the algebraic classification of tensors on Lorentzian manifolds of arbitrary dimension are discussed. We clarify some aspects of the relationship between invariants of tensors and their algebraic class, discuss generalization of Newman-Penrose and Geroch-Held-Penrose formalisms to arbitrary dimension and study an application of the algebraic classification to the case of quadratic gravity.
Keywords:
Einstein spacetimes; algebraic classification
Fulltext is available at external website.
Algebraic classification of the Weyl tensor : selected applications
Selected applications of the algebraic classification of tensors on Lorentzian manifolds of arbitrary dimension are discussed. We clarify some aspects of the relationship between invariants of tensors ...
On the motion of rigid bodies in a compressible viscous fluid under the action of gravitational forces
Ducomet, B.; Nečasová, Šárka
2012 - English
The global existence of weak solution is proved for the problem of the motion of several rigid bodies in a barotropic compressible fluid, under the influence of gravitational forces.
Keywords:
compressible viscous fluid; motion
Fulltext is available at external website.
On the motion of rigid bodies in a compressible viscous fluid under the action of gravitational forces
The global existence of weak solution is proved for the problem of the motion of several rigid bodies in a barotropic compressible fluid, under the influence of gravitational forces.
Recent development of the DML-CZ and its current state
Rákosník, Jiří
2011 - English
The project DML-CZ: The Czech Digital Mathematics Library has been implemented since 2005 and in 2010 switched over to routine operation. This report describes progress, growth and usage of the DML-CZ, the experience from cooperation with content providers in the designed editorial workflow, some newly implemented features, adjustments of the workflow following from both the ongoing practical experience and the requirements of the advancing EuDML project, the general public acceptance and attendance and the suggested economic model for sustainable development.
Keywords:
digital mathematics library; retrodigitization; DML-CZ
Available in digital repository of the ASCR
Recent development of the DML-CZ and its current state
The project DML-CZ: The Czech Digital Mathematics Library has been implemented since 2005 and in 2010 switched over to routine operation. This report describes progress, growth and usage of the ...
The search for ways of enhancement of knowledge base for teaching
Tichá, Marie
2011 - English
Poster shows a problem posing as a significant way to improving teachers' knowledge. The presentation focused on the division of fractions. The presentation displayed examples of common misconceptions and their probable cause.
Keywords:
teachers' competence; teachers' knowledge; problem posing
Available on request at various institutes of the ASCR
The search for ways of enhancement of knowledge base for teaching
Poster shows a problem posing as a significant way to improving teachers' knowledge. The presentation focused on the division of fractions. The presentation displayed examples of common misconceptions ...
Representtion of basic isometries through square ornaments
Roubíček, Filip
2011 - English
The poster deals with basic isometries: point reflection, rotation and translation as composition of two line reflections. It presents some activities that support observation and intuitive cognition of isometries. Square ornaments were designed by composing mosaics, cutting folder paper, drawing, printing.
Keywords:
teaching; geometry; isometry
Available at various institutes of the ASCR
Representtion of basic isometries through square ornaments
The poster deals with basic isometries: point reflection, rotation and translation as composition of two line reflections. It presents some activities that support observation and intuitive cognition ...
Neumann problem for the Stokes system
Medková, Dagmar
2011 - English
the Neumann problem for the Stokes systems is studied by the boundary integral equation method. The successive approximation converges for bounded Lipschitz domains.
Keywords:
Stokes system; Neumann problem; integral equation method
Available on request at various institutes of the ASCR
Neumann problem for the Stokes system
the Neumann problem for the Stokes systems is studied by the boundary integral equation method. The successive approximation converges for bounded Lipschitz domains.
Computational and analytical a posteriori error estimates for finite element methods
Segeth, Karel
2010 - English
The analytical a posteriori error estimates are oriented to the use in h-methods, are usually constructed only for lowest-order polynomial approximation, and often depend on unknown constatns or functions. In this review paper, we present several error estimation procedures for some particular linear partial differential problems with special regards to the needs of the hp-method. We compare the advantages and drawbacks of a posteriori error estimators including computational ones.
Keywords:
hp-adaptive finite element method; a posteriori error estimator; computational error estimate; reference solution
Available at various institutes of the ASCR
Computational and analytical a posteriori error estimates for finite element methods
The analytical a posteriori error estimates are oriented to the use in h-methods, are usually constructed only for lowest-order polynomial approximation, and often depend on unknown constatns or ...
Application of the BDDC method to the Stokes problem
Šístek, Jakub; Burda, P.; Mandel, J.; Novotný, J.; Sousedík, B.
2010 - English
Application of BDDC method to problems of Stokes flow is explored. BDDC is applied to several 3D problems and is shown to be a competitive method.
Keywords:
BDDC; domain decomposition; iterative substructuring; Stokes flow
Available at various institutes of the ASCR
Application of the BDDC method to the Stokes problem
Application of BDDC method to problems of Stokes flow is explored. BDDC is applied to several 3D problems and is shown to be a competitive method.
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