Homogenization method and multiscale modeling:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Fukuoka
Kyushu Univ.
2011
|
| Series: | COE lecture note
34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 72 S. Ill., graph. Darst. |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
List of Figures
vii
Acknowledgments
ix
Chapter
1.
Introduction
1
1.1.
Aim of these notes. Choice of the teaching material
1
1.2.
What means homogenization in this context?
1
1.3.
Organization of the material
2
1.4.
Note
3
Chapter
2.
Formal asymptotic homogenization
5
2.1.
Guessing the averaged model: A direct approach
5
2.2.
A model problem: Stationary diffusion and chemical reactions in perforated media
5
2.3.
The asymptotics homogenization procedure or How to guess macroscopic models?
6
2.4.
Structure of the macroscopic equation. Effective coefficients
8
2.5.
Exercises
10
Chapter
3.
What should one know before thinking to applying homogenization?
13
3.1.
Weak convergence
13
3.2.
Compactness
14
3.3.
Two-scale convergence. Definition and properties
14
3.4.
Exercises
16
Chapter
4.
Homogenization of a linear
2nd
order elliptic equation. A two-scale approach
19
4.1.
Setting of the problem. Working hypotheses
19
4.2.
A corrector estimate
22
4.3.
Exercises
24
Chapter
5.
Homogenization in periodically perforated media
25
5.1.
Linear elliptic equation in periodically perforated domains
25
5.2.
Averaging boundary processes in perforated media
27
5.3.
Exercises
30
Chapter
6.
Multiscale approximation
33
6.1.
Multiscale concrete corrosion
33
6.2.
Background and statement of the mathematical problem
33
6.3.
Numerical scheme
37
6.4.
Approximation estimates
43
6.5.
Interpolation and compactness
48
6.6.
Numerical illustration of the two-scale FD scheme
50
6.7.
Exercises
51
Chapter
7.
Computer implementation in
С
53
7.1.
Introduction
53
vi
CONTENTS
7.2. Review
of the numerical scheme
53
7.3.
Implementation
54
7.4.
Exercises
ßl
Appendix A. Source code
63
Bibliography
71
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:10:23Z |
| institution | BVB |
| language | English |
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| owner_facet | DE-703 |
| physical | IX, 72 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Kyushu Univ. |
| record_format | marc |
| series | COE lecture note |
| series2 | COE lecture note |
| spelling | Homogenization method and multiscale modeling [Ed.:] Adrian Muntean ... Fukuoka Kyushu Univ. 2011 IX, 72 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier COE lecture note 34 Mehrskalenmodell (DE-588)7600619-0 gnd rswk-swf Homogenisierungsmethode (DE-588)4257770-6 gnd rswk-swf Homogenisierungsmethode (DE-588)4257770-6 s Mehrskalenmodell (DE-588)7600619-0 s DE-604 Muntean, Adrian Sonstige (DE-588)131777459 oth COE lecture note 34 (DE-604)BV039750795 34 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024598264&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Homogenization method and multiscale modeling COE lecture note Mehrskalenmodell (DE-588)7600619-0 gnd Homogenisierungsmethode (DE-588)4257770-6 gnd |
| subject_GND | (DE-588)7600619-0 (DE-588)4257770-6 |
| title | Homogenization method and multiscale modeling |
| title_auth | Homogenization method and multiscale modeling |
| title_exact_search | Homogenization method and multiscale modeling |
| title_full | Homogenization method and multiscale modeling [Ed.:] Adrian Muntean ... |
| title_fullStr | Homogenization method and multiscale modeling [Ed.:] Adrian Muntean ... |
| title_full_unstemmed | Homogenization method and multiscale modeling [Ed.:] Adrian Muntean ... |
| title_short | Homogenization method and multiscale modeling |
| title_sort | homogenization method and multiscale modeling |
| topic | Mehrskalenmodell (DE-588)7600619-0 gnd Homogenisierungsmethode (DE-588)4257770-6 gnd |
| topic_facet | Mehrskalenmodell Homogenisierungsmethode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024598264&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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