Fast multipole boundary element method: theory and applications in engineering
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XVII, 235 S. Ill., graph. Darst. |
| ISBN: | 9780521116596 |
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| 245 | 1 | 0 | |a Fast multipole boundary element method |b theory and applications in engineering |c Yijun Liu |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XVII, 235 S. |b Ill., graph. Darst. | ||
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Contents
Preface
page
xi
Acknowledgments
xv
Acronyms Used in This Book
xvii
1
Introduction
.1
1.1
What Is the Boundary Element Method?
1
1.2
Why the Boundary Element Method?
1
1.3
A Comparison of the Finite Element Method and the
Boundary Element Method
2
1.4
A Brief History of the Boundary Element Method and
Other References
3
1.5
Fast Multipole Method
3
1.6
Applications of the Boundary Element Method in
Engineering
4
1.7
An Example
-
Bending of a Beam
5
1.8
Some Mathematical Preliminaries
9
1.8.1
Integral Equations
9
1.8.2
Indiciai
Notation
10
1.8.3
Gauss Theorem
11
1.8.4
The Green's Identities
12
1.8.5
Dirac
S
Function
12
1.8.6
Fundamental Solutions
12
1.8.7
Singular Integrals
13
1.9
Summary
15
Problems
15
2
Conventional Boundary Element Method for Potential
Problems
.
I7
2.1
The Boundary-Value Problem
17
vi
Contents
2.2 Fundamental
Solution
for Potential Problems
18
2.3
Boundary Integral Equation Formulations
19
2.4
Weakly Singular Forms of the Boundary Integral Equations
23
2.5
Discretization of the Boundary Integral Equations for 2D
Problems Using Constant Elements
24
2.6
Using Higher-Order Elements
26
2.6.1
Linear Elements
26
2.6.2
Quadratic Elements
29
2.7
Discretization of the Boundary Integral Equations for
3D
Problems
30
2.8
Multidomain Problems
34
2.9
Treatment of the Domain Integrals
35
2.9.1
Numerical Integration Using Internal Cells
35
2.9.2
Transformation to Boundary Integrals
35
2.9.3
Use of Particular Solutions
36
2.10
Indirect Boundary Integral Equation Formulations
36
2.11
Programming for the Conventional Boundary Element
Method
38
2.12
Numerical Examples
39
2.12.1
An Annular Region
39
2.12.2
Electrostatic Fields Outside Two Conducting Beams
40
2.12.3
Potential Field in a Cube
43
2.12.4
Electrostatic Field Outside a Conducting Sphere
43
2.13
Summary
45
Problems
45
3
Fast Multipole Boundary Element Method for Potential
Problems
.47
3.1
Basic Ideas in the Fast Multipole Method
48
3.2
Fast Multipole Boundary Element Method for 2D Potential
Problems
50
3.2.1
Multipole Expansion (Moments)
51
3.2.2
Error Estimate for the Multipole Expansion
53
3.2.3
Moment-to-Moment Translation
54
3.2.4
Local Expansion and Moment-to-Local Translation
54
3.2.5
Local-to-Local Translation
56
3.2.6
Expansions for the Integral with the
F
Kernel
56
3.2.7
Multipole Expansions for the Hypersingular
Boundary Integral Equation
57
3.2.8
Fast Multipole Boundary Element Method
Algorithms and Procedures
58
3.2.9
Preconditioning
64
3.2.10
Estimate of the Computational Complexity
65
Contents
vii
3.3 Programming
for the Fast Multipole Boundary Element
Method
65
3.3.1
Subroutine fmmmain
67
3.3.2
Subroutine tree
67
3.3.3
Subroutine fmmbvector
69
3.3.4
Subroutine dgmres
70
3.3.5
Subroutine upward
70
3.3.6
Subroutine dwnwrd
70
3.4
Fast Multipole Formulation for
3D
Potential Problems
71
3.5
Numerical Examples
74
3.5.1
An Annular Region
74
3.5.2
Electrostatic Fields Outside Conducting Beams
75
3.5.3
Potential Field in a Cube
78
3.5.4
Electrostatic Field Outside Multiple Conducting
Spheres
78
3.5.5
A Fuel Cell Model
79
3.5.6
Image-Based Boundary Element Method Models and
Analysis
80
3.6
Summary
83
Problems
83
4
Elastostatic Problems
.85
4.1
The Boundary-Value Problem
86
4.2
Fundamental Solution for Elastostatic Problems
87
4.3
Boundary Integral Equation Formulations
88
4.4
Weakly Singular Forms of the Boundary Integral
Equations
91
4.5
Discretization of the Boundary Integral Equations
92
4.6
Recovery of the Full Stress Field on the Boundary
93
4.7
Fast Multipole Boundary Element Method for 2D
Elastostatic Problems
95
4.7.1
Multipole Expansion for the
U
Kernel Integral
97
4.7.2
Moment-to-Moment Translation
98
4.7.3
Local Expansion and Moment-to-Local
Translation
98
4.7.4
Local-to-Local Translation
99
4.7.5
Expansions for the
Γ
Kernel Integral
99
4.7.6
Expansions for the Hypersingular Boundary Integral
Equation
100
4.8
Fast Multipole Boundary Element Method for
3D
Elastostatic Problems
101
4.9
Fast Multipole Boundary Element Method for Multidomain
Elasticity Problems
104
viii Contents
4.10
Numerical Examples
108
4.10.1
A Cylinder with Pressure Loads
108
4.10.2
A Square Plate with a Circular Hole
110
4.10.3
Multiple Inclusion Problems 111
4.10.4
Modeling of Functionally Graded Materials
113
4.10.5
Large-Scale Modeling of Fiber-Reinforced
Composites
115
4.11
Summary
117
Problems
118
5
Stokes Flow Problems
.119
5.1
The Boundary-Value Problem
120
5.2
Fundamental Solution for Stokes Flow Problems
120
5.3
Boundary Integral Equation Formulations
121
5.4
Fast Multipole Boundary Element Method for 2D Stokes
Flow Problems
124
5.4.1
Multipole Expansion (Moments) for the
U
Kernel
Integral
126
5.4.2
Moment-to-Moment Translation
127
5.4.3
Local Expansion and Moment-to-Local Translation
127
5.4.4
Local-to-Local Translation
128
5.4.5
Expansions for the
Τ
Kernel Integral
128
5.4.6
Expansions for the Hypersingular Boundary Integral
Equation
129
5.5
Fast Multipole Boundary Element Method for
3D
Stokes
Flow Problems
130
5.6
Numerical Examples
133
5.6.1
Flow That Is Due to a Rotating Cylinder
133
5.6.2
Shear Flow Between Two Parallel Plates
135
5.6.3
Flow Through a Channel with Many Cylinders
138
5.6.4
A Translating Sphere
141
5.6.5
Large-Scale Modeling of Multiple Particles
142
5.7
Summary
144
Problems
145
6
Acoustic Wave Problems
.146
6.1
Basic Equations in Acoustics
147
6.2
Fundamental Solution for Acoustic Wave Problems
150
6.3
Boundary Integral Equation Formulations
152
6.4
Weakly Singular Forms of the Boundary Integral
Equations
154
6.5
Discretization of the Boundary Integral Equations
156
Contents ix
6.6 Fast Multipole
Boundary
Element
Method for 2D Acoustic
Wave Problems
157
6.7
Fast Multipole Boundary Element Method for
3D
Acoustic
Wave Problems
159
6.8
Numerical Examples
163
6.8.1
Scattering from Cylinders in a 2D Medium
163
6.8.2
Radiation from a Pulsating Sphere
164
6.8.3
Scattering from Multiple Scatterers
165
6.8.4
Performance Study of the
3D
Fast Multipole
Boundary Element Method Code
166
6.8.5
An Engine-Block Model
167
6.8.6
A Submarine Model
169
6.8.7
An Airbus A320 Model
170
6.8.8
A Human-Head Model
170
6.8.9
Analysis of Sound Barriers
-
A Half-Space Acoustic
Wave Problem
172
6.9
Summary
174
Problems
174
APPENDIX A: Analytical Integration of the Kernels
.177
A.I 2D Potential Boundary Integral Equations
177
A.2 2D Elastostatic Boundary Integral Equations
178
A.3 2D Stokes Flow Boundary Integral Equations
181
APPENDIX
В
:
Sample Computer Programs
.184
B.I A Fortran Code of the Conventional Boundary Element
Method for 2D Potential Problems
184
B.2 A Fortran Code of the Fast Multipole Boundary Element
Method for 2D Potential Problems
192
B.3 Sample Input File and Parameter File
220
References
223
Index
233
The fast
multi
pole method is one of the most important algorithms in computing
developed in the 20th century. Along with the fast
multi
pole method, the boundary
element method
(BEM)
has also emerged as a powerful method for modeling
large-scale problems.
BEM
models with millions of unknowns on the boundary can
now be solved on desktop computers using the fast multipole
bem.
This is the first
book on the fast multipole
BEM.
which brings together the classical theories in
BEM
formulations and the recent development of the fast multipole method, two-and
three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems
are covered, supplemented with exercise problems and computer source codes.
Applications in modeling nanocomposite materials,
biomaterials,
fuel cells, acoustic
waves, and image-based simulations are demonstrated to show the potential of
the fast multipole
BEM.
This book will help students, researchers, and engineers to
learn the
BEM
and fast multipole method from a single source.
Dr. Yijun
üu
has more than
25
years of research experience on the
BEM
for subjects
including potential; elasticity; Stokes flow, and electromagnetic, elastic and acoustic
wave problems, and he has published extensively in research journals,
не
received
his Ph.D. in theoretical and applied mechanics from the university of Illinois and,
after a postdoctoral research appointment at Iowa state university, he joined the
Ford Motor Company as
a CAE
(computer-aided engineering) analyst He has been a
faculty member in the Department of Mechanical Engineering at the University of
Cincinnati since
1
996.
Dr. Liu is currently on the editorial board of the international
journals Engineering Analysis with Boundary Elements and the Electronic journal of
Boundary Elements. |
| any_adam_object | 1 |
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| indexdate | 2025-01-30T09:01:09Z |
| institution | BVB |
| isbn | 9780521116596 |
| language | English |
| lccn | 2009010912 |
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| physical | XVII, 235 S. Ill., graph. Darst. |
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| spelling | Liu, Yijun Verfasser aut Fast multipole boundary element method theory and applications in engineering Yijun Liu 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2009 XVII, 235 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Boundary element methods Randelemente-Methode (DE-588)4076508-8 gnd rswk-swf Randelemente-Methode (DE-588)4076508-8 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728676&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728676&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Liu, Yijun Fast multipole boundary element method theory and applications in engineering Boundary element methods Randelemente-Methode (DE-588)4076508-8 gnd |
| subject_GND | (DE-588)4076508-8 |
| title | Fast multipole boundary element method theory and applications in engineering |
| title_auth | Fast multipole boundary element method theory and applications in engineering |
| title_exact_search | Fast multipole boundary element method theory and applications in engineering |
| title_full | Fast multipole boundary element method theory and applications in engineering Yijun Liu |
| title_fullStr | Fast multipole boundary element method theory and applications in engineering Yijun Liu |
| title_full_unstemmed | Fast multipole boundary element method theory and applications in engineering Yijun Liu |
| title_short | Fast multipole boundary element method |
| title_sort | fast multipole boundary element method theory and applications in engineering |
| title_sub | theory and applications in engineering |
| topic | Boundary element methods Randelemente-Methode (DE-588)4076508-8 gnd |
| topic_facet | Boundary element methods Randelemente-Methode |
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