175 research outputs found
Guaranteed error bounds for a class of Picard-Lindelöf iteration methods
No full textWe present a new version of the Picard-Lindelof method for ordinary dif- ¨
ferential equations (ODEs) supplied with guaranteed and explicitly computable upper
bounds of an approximation error. The upper bounds are based on the Ostrowski
estimates and the Banach fixed point theorem for contractive operators. The estimates
derived in the paper take into account interpolation and integration errors
and, therefore, provide objective information on the accuracy of computed approximations.peerReviewe
Domain decomposition methods for continuous casting problem
No full textAbstractSeveral numerical methods and algorithms, for solving the mathematical model of a continuous casting process, are presented, and theoretically studied, in this work. The numerical algorithms can be divided in to three different groups: the Schwarz type overlapping methods, the nonoverlapping Splitting iterative methods, and the Predictor-Corrector type nonoverlapping methods. These algorithms are all so-called parallel algorithms i.e., they are highly suitable for parallel computers. Multiplicative, additive Schwarz alternating method and two asynchronous domain decomposition methods, which appear to be a two-stage Schwarz alternating algorithms, are theoretically and numerically studied. Unique solvability of the fully implicit and semi-implicit finite difference schemes as well as monotone dependence of the solution on the right-hand side are proved. Geometric rate of convergence for the iterative methods is investigated.Splitting iterative methods for the sum of maximal monotone and single-valued monotone operators in a finite-dimensional space are studied. Convergence, rate of convergence and optimal iterative parameters are derived. A two-stage iterative method with inner iterations is analyzed in the case when both operators are linear, self-adjoint and positive definite. Several new finite-difference schemes for a nonlinear convection-diffusion problem are constructed and numerically studied. These schemes are constructed on the basis of non-overlapping domain decomposition and predictor-corrector approach. Different non-overlapping decompositions of a domain, with cross-points and angles, schemes with grid refinement in time in some subdomains, are used. All proposed algorithms are extensively numerically tested and are founded stable and accurate under natural assumptions for time and space grid steps.The advantages and disadvantages of the numerical methods are clearly seen in the numerical examples. All of the algorithms presented are quite easy and straight forward, from an implementation point of view. The speedups show that splitting iterative method can be parallelized better than multiplicative or additive Schwarz alternating method. The numerical examples show that the multidecomposition method is a very effective numerical method for solving the continuous casting problem. The idea of dividing the subdomains to smaller subdomains seems to be very beneficial and profitable. The advantages of multidecomposition methods over other methods is obvious. Multidecomposition methods are extremely quick, while being just as accurate as other methods. The numerical results for one processor seem to be very promising.Academic Dissertation to be presented with the assent of the Faculty of Science, University of Oulu, for public discussion in Kajaaninsali (Auditorium L6), Linnanmaa, on November 27th, 2004, at 12 noon.Abstract
Several numerical methods and algorithms, for solving the mathematical model of a continuous casting process, are presented, and theoretically studied, in this work. The numerical algorithms can be divided in to three different groups: the Schwarz type overlapping methods, the nonoverlapping Splitting iterative methods, and the Predictor-Corrector type nonoverlapping methods. These algorithms are all so-called parallel algorithms i.e., they are highly suitable for parallel computers.
Multiplicative, additive Schwarz alternating method and two asynchronous domain decomposition methods, which appear to be a two-stage Schwarz alternating algorithms, are theoretically and numerically studied. Unique solvability of the fully implicit and semi-implicit finite difference schemes as well as monotone dependence of the solution on the right-hand side are proved. Geometric rate of convergence for the iterative methods is investigated.
Splitting iterative methods for the sum of maximal monotone and single-valued monotone operators in a finite-dimensional space are studied. Convergence, rate of convergence and optimal iterative parameters are derived. A two-stage iterative method with inner iterations is analyzed in the case when both operators are linear, self-adjoint and positive definite.
Several new finite-difference schemes for a nonlinear convection-diffusion problem are constructed and numerically studied. These schemes are constructed on the basis of non-overlapping domain decomposition and predictor-corrector approach. Different non-overlapping decompositions of a domain, with cross-points and angles, schemes with grid refinement in time in some subdomains, are used. All proposed algorithms are extensively numerically tested and are founded stable and accurate under natural assumptions for time and space grid steps.
The advantages and disadvantages of the numerical methods are clearly seen in the numerical examples. All of the algorithms presented are quite easy and straight forward, from an implementation point of view. The speedups show that splitting iterative method can be parallelized better than multiplicative or additive Schwarz alternating method.
The numerical examples show that the multidecomposition method is a very effective numerical method for solving the continuous casting problem. The idea of dividing the subdomains to smaller subdomains seems to be very beneficial and profitable. The advantages of multidecomposition methods over other methods is obvious. Multidecomposition methods are extremely quick, while being just as accurate as other methods. The numerical results for one processor seem to be very promising
Preservation and popularization of the artistic heritage of I. Yu. Repin in the Kharkiv region
No full textНе дивлячись на значну
дослідженість життя та творчості Рєпіна поза увагою дослідників залишилося
питання вшанування його пам’яті та популяризація творчості видатного
земляка на Харківщині.
Виходячи з цього автор мав на меті заповнити цю прогалину й
відтворити хронологію подій та проаналізувати практики вшанування пам’яті
видатного земляка харків’янами та продемонструвати їх туристичну
привабливість. The article is devoted to
to the question of commemorating and popularizing the work of Ilya Yukhymovich Repin, an artist who gave the world
hundreds of paintings written in the genre of realism. Author
recreated the chronology of events and analyzed the practice of commemoration
prominent countryman by Kharkiv residents and demonstrate their tourism
attractiveness
International Conference for Mathematical Modeling and Optimization in Mechanics, 6-7 March, 2014, Jyväskylä, Finland : honor of the 70th anniversary of Prof. Nikolay Banichuk
No full textThis book of abstracts presents materials of the International Conference for Mathematical Modeling
and Optimization in Mechanics (MMOM 2014) 6-7 March 2014, Jyväskylä, Finland. This event is
dedicated to Professor Nikolay Banichuk in occasion of his 70th anniversary.
It is aimed to present the latest results of leading scientists in mathematical modeling, numerical
analysis, and optimization theory and to discuss the state of the art and open problems in the field.
The book is divided in five sections:
1. Mathematical Modelling of Complex Systems
2. Stability Analysis and Vibration
3. Optimization
4. Methods of Numerical Analysis
5. Shape Optimizationunknown accessibilityei tietoa saavutettavuudest
Functional Approach to Locally Based A Posteriori Error Estimates for Elliptic and Parabolic Problems
No full text
Poincaré Type Inequalities for Vector Functions with Zero Mean Normal Traces on the Boundary and Applications to Interpolation Methods
No full text
Poincaré Type Inequalities for Vector Functions with Zero Mean Normal Traces on the Boundary and Applications to Interpolation Methods
No full textWe consider inequalities of the Poincaré–Steklov type for subspaces of H1 -functions defined in a bounded domain Ω∈Rd with Lipschitz boundary ∂Ω . For scalar valued functions, the subspaces are defined by zero mean condition on ∂Ω or on a part of ∂Ω having positive d−1 measure. For vector valued functions, zero mean conditions are applied to normal components on plane faces of ∂Ω (or to averaged normal components on curvilinear faces). We find explicit and simply computable bounds of constants in the respective Poincaré type inequalities for domains typically used in finite element methods (triangles, quadrilaterals, tetrahedrons, prisms, pyramids, and domains composed of them). The second part of the paper discusses applications of the estimates to interpolation of scalar and vector valued functions on macrocells and on meshes with non-overlapping and overlapping cells.peerReviewe
- …
