Numerical Methods for Black-Box Software in Computational Continuum Mechanics : : Parallel High-Performance Computing / / Sergey I. Martynenko.
The organization of the material is presented as follows: This introductory chapter I represents a theoretical analysis of the computational algorithms for a numerical solution of the basic equations in continuum mechanics. In this chapter, the general requirements for computational grids, discretiz...
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Superior document: | Title is part of eBook package: De Gruyter DG Plus DeG Package 2023 Part 1 |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2023] ©2023 |
Year of Publication: | 2023 |
Language: | English |
Series: | De Gruyter Textbook
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Online Access: | |
Physical Description: | 1 online resource (XII, 136 p.) |
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024 | 7 | |a 10.1515/9783111319568 |2 doi | |
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072 | 7 | |a MAT041000 |2 bisacsh | |
082 | 0 | 4 | |a 518.6 |
100 | 1 | |a Martynenko, Sergey I., |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
245 | 1 | 0 | |a Numerical Methods for Black-Box Software in Computational Continuum Mechanics : |b Parallel High-Performance Computing / |c Sergey I. Martynenko. |
264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2023] | |
264 | 4 | |c ©2023 | |
300 | |a 1 online resource (XII, 136 p.) | ||
336 | |a text |b txt |2 rdacontent | ||
337 | |a computer |b c |2 rdamedia | ||
338 | |a online resource |b cr |2 rdacarrier | ||
347 | |a text file |b PDF |2 rda | ||
490 | 0 | |a De Gruyter Textbook | |
505 | 0 | 0 | |t Frontmatter -- |t Preface -- |t Acknowledgments -- |t Contents -- |t Notation -- |t I Forward to black-box software -- |t II Sequential robust multigrid technique -- |t III Parallel robust multigrid technique -- |t IV Background in iterative methods -- |t Conclusions -- |t Bibliography -- |t Index |
506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
520 | |a The organization of the material is presented as follows: This introductory chapter I represents a theoretical analysis of the computational algorithms for a numerical solution of the basic equations in continuum mechanics. In this chapter, the general requirements for computational grids, discretization, and iterative methods for black-box software are examined. Finally, a concept of a two-grid algorithm for (de-)coupled solving multidimensional non-linear (initial-)boundary value problems in continuum mechanics (multiphysics simulation) in complex domains is presented. Chapter II contains descriptions of the sequential Robust Multigrid Technique which is developed as a general-purpose solver in black-box codes. This chapter presents the main components of the Robust Multigrid Technique (RMT) used in the two-grid algorithm (Chapter I) to compute the auxiliary (structured) grid correction. This includes the generation of multigrid structures, computation of index mapping, and integral evaluation. Finite volume discretization on the multigrid structures will be explained by studying a 1D linear model problem. In addition, the algorithmic complexity of RMT and black-box optimization of the problem-dependent components of RMT are analysed. Chapter III provides a description of parallel RMT. This chapter introduces parallel RMT-based algorithms for solving the boundary value problems and initial-boundary value problems in unified manner. Section 1 presents a comparative analysis of the parallel RMT and the sequential V-cycle. Sections 2 and 3 present a geometric and an algebraic parallelism of RMT, i.e. parallelization of the smoothing iterations on the coarse and the levels. A parallel multigrid cycle will be considered in Section 4. A parallel RMT for the time-dependent problems is given in Section 5. Finally, the basic properties of parallel RMT will be summarized in Section 6. Theoretical aspects of the used algorithms for solving multidimensional problems are discussed in Chapters IV. This chapter contains the theoretical aspects of the algorithms used for the numerical solving of the resulting system of linear algebraic equations obtained from discrete multidimensional (initial-)boundary value problems. | ||
530 | |a Issued also in print. | ||
538 | |a Mode of access: Internet via World Wide Web. | ||
546 | |a In English. | ||
588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 02. Jun 2024) | |
650 | 4 | |a Berechnungs-Grids. | |
650 | 4 | |a Black-Box-Optimierung. | |
650 | 4 | |a Multiphysikalische Simulation. | |
650 | 4 | |a Paralleles und Hochleistungsrechnen. | |
650 | 4 | |a Robustes Multigrid. | |
650 | 7 | |a MATHEMATICS / Numerical Analysis. |2 bisacsh | |
653 | |a Multiphysics simulation, Robust multigrid, Parallel and high-performance computing, Computational grids, Black-box optimization. | ||
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t DG Plus DeG Package 2023 Part 1 |z 9783111175782 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2023 English |z 9783111319292 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2023 |z 9783111318912 |o ZDB-23-DGG |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2023 English |z 9783111319209 |
773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2023 |z 9783111318608 |o ZDB-23-DMA |
776 | 0 | |c EPUB |z 9783111319759 | |
776 | 0 | |c print |z 9783111317298 | |
856 | 4 | 0 | |u https://doi.org/10.1515/9783111319568 |
856 | 4 | 0 | |u https://www.degruyter.com/isbn/9783111319568 |
856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9783111319568/original |
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912 | |a 978-3-11-131929-2 EBOOK PACKAGE COMPLETE 2023 English |b 2023 | ||
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