Computational mathematics: models, methods, and analysis with MATLAB and MPI
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton
CRC Press, Taylor & Francis Group
[2016]
|
| Edition: | Second edition |
| Series: | Textbooks in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | "A Chapman & Hall book.". - "This edition has a new chapter 5 with two sections on the finite element method, two sections on shallow water waves, and two sections on the driven cavity problem"...Preface. - Includes bibliographical references (pages 467-469) and index |
| Physical Description: | xxii, 476 pages Diagramme |
| ISBN: | 9781482235159 1482235153 |
Staff View
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Record in the Search Index
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| adam_text | Contents
fj
List of Figures xi
List of Tables xv
Preface to First Edition xvii
Preface to Second Edition xix
Introduction xxi
1 Discrete Time—Space Models 1
1.1 Newton Cooling Models...................................... 1
1.2 Heat Diffusion in a Wire................................. 9
1.3 Diffusion in a Wire with Little Insulation............... 18
1.4 Flow and Decay of a Pollutant in a Stream............... . 26
1.5 Heat and Mass Transfer in Two Directions................ 34
1.6 Convergence Analysis ..................................... 45
2 Steady-State Discrete Models 55
2.1 Steady-State and Triangular Solves........................ 55
2.2 Heat Diffusion and Gauss Elimination...................... 63
2.3 Cooling Fin and Tridiagonal Matrices ..................... 74
2.4 Schur Complement.......................................... 83
2.5 Convergence to Steady-State Solution...................... 92
2.6 Convergence to Continuous Model......................... . 99
3 Poisson Equation Models 107
3.1 Steady-State and Iterative Methods ...................... 107
3.2 Heat Transfer in 2D Fin and SOR.......................... 117
3.3 Fluid Flow in a 2D Porous Medium......................... 125
3.4 Ideal Fluid Flow......................................... 132
3.5 Deformed Membrane and Steepest Descent................... 141
3.6 Conjugate Gradient Method................................ 150
Vll
viii CONTENTS
4 Nonlinear and 3D Models 161
4.1 Nonlinear Problems in One Variable........................ 161
4.2 Nonlinear Heat Transfer in a Wire......................... 169
4.3 Nonlinear Heat Transfer in 2D ............................ 177
4.4 Steady-State 3D Heat Diffusion............................ 183
4.5 Time-Dependent 3D Diffusion .............................. 189
4.6 High-Performance Computations in 3D....................... 197
5 FEM and Fluid Flows 209
5.1 FEM and Linear Shape Functions ........................... 209
5.2 FEM with Heat and Fluid Flow.............................. 218
5.3 Lax-Wendroff Methods ..................................... 226
5.4 Shallow Water Wave Model.................................. 232
5.5 Navier-Stokes Equations................................... 237
5.6 Discrete Navier-Stokes Equations.......................... 240
6 Epidemics, Images, and Money 247
6.1 Epidemics and Dispersion.................................. 247
6.2 Epidemic Dispersion in 2D................................. 255
6.3 Image Restoration......................................... 262
6.4 Restoration in 2D......................................... 271
6.5 Option Contract Models.................................... 277
6.6 Biack-Scholes Model for Two Assets........................ 286
7 High-Performance Computing 295
7.1 CPUs and Vector Pipes..................................... 295
7.2 Multiprocessor and Multicore Computers ................. . 307
7.3 Parallel MATLAB®.......................................... 316
7.4 Parallel MATLAB and SPMD.................................. 326
7.5 Introduction to MPI....................................... 334
7.6 MPI and Matrix Products................................... 343
8 Message Passing Interface 355
8.1 Collective Subroutines.................................... 355
8.2 Grouped Datatypes......................................... 367
8.3 Communicators............................................. 374
8.4 Fox Algorithm for AB...................................... 380
8.5 Shared Memory and OpenMP.................................. 386
8.6 Hybrid MPI/OpenMP......................................... 392
9 Classical Methods for Ax = d 399
9.1 Gauss Elimination......................................... 399
9.2 Symmetric Positive Definite Matrices...................... 404
9.3 Domain Decomposition and MPI.............................. 410
9.4 SOR and P-Regular Splittings.............................. 415
9.5 SOR and MPI............................................... 420
CONTENTS ix
9.6 Parallel ADI Schemes ............................. 426
10 Krylov Methods for Ax = d 431
10.1 Conjugate Gradient Method......................... 431
10.2 Preconditioners................................... 436
10.3 PCG and MPI ...................................... 442
10.4 Least Squares..................................... 446
10.5 GMRES............................................. 453
10.6 GMRES(m) and MPI ................................. 460
Bibliography 467
Index 471
Mathematics
TEXTBOOKS in MATHEMATICS
Computational Mathematics: Models, Methods, and Analysis
with MATLAB® and MPI is a unique book covering the concepts and
techniques at the core of computational science. The author delivers
a hands-on introduction to nonlinear, 2D, and 3D models; nonrect-
angular domains; systems of partial differential equations; and large
algebraic problems requiring high-performance computing. The book
shows how to apply a model, select a numerical method, implement
computer simulations, and assess the ensuing results.
Providing a wealth of MATLAB, Fortran, and C++ code online for
download, the Second Edition of this very popular text:
• Includes a new chapter with two sections on the finite element
method, two sections on shallow water waves, and two sections
on the driven cavity problem
• Introduces multiprocessor/multicore computers, parallel
MATLAB, and message passing interface (MPI) in the chapter on
high-performance computing
• Updates and adds code and documentation
Computational Mathematics: Models, Methods, and Analysis
with MATLAB® and MPI, Second Edition is an ideal textbook for an
undergraduate course taught to mathematics, computer science, and
engineering students. By using code in practical ways, students take
their first steps toward more sophisticated numerical modeling.
ISBN T7fl 1 MfiEP 3515 ^
|
| any_adam_object | 1 |
| author | White, Robert E. 1946- |
| author_GND | (DE-588)129384968 |
| author_facet | White, Robert E. 1946- |
| author_role | aut |
| author_sort | White, Robert E. 1946- |
| author_variant | r e w re rew |
| building | Verbundindex |
| bvnumber | BV043638349 |
| classification_rvk | SK 900 |
| ctrlnum | (OCoLC)968134838 (DE-599)BVBBV043638349 |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV043638349 |
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| indexdate | 2025-02-20T07:08:22Z |
| institution | BVB |
| isbn | 9781482235159 1482235153 |
| language | English |
| lccn | 016304815 |
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| owner_facet | DE-703 DE-862 DE-BY-FWS |
| physical | xxii, 476 pages Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | CRC Press, Taylor & Francis Group |
| record_format | marc |
| series2 | Textbooks in mathematics |
| spellingShingle | White, Robert E. 1946- Computational mathematics models, methods, and analysis with MATLAB and MPI MATLAB. MATLAB. fast (OCoLC)fst01365096 MATLAB. fast Computer interfaces fast Numerical analysis / Data processing fast Parallel programming (Computer science) fast Datenverarbeitung Numerical analysis Data processing Computer interfaces Parallel programming (Computer science) Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd Algorithmus (DE-588)4001183-5 gnd MPI Schnittstelle (DE-588)4456003-5 gnd |
| subject_GND | (OCoLC)fst01365096 (DE-588)4042805-9 (DE-588)4329066-8 (DE-588)4001183-5 (DE-588)4456003-5 |
| title | Computational mathematics models, methods, and analysis with MATLAB and MPI |
| title_auth | Computational mathematics models, methods, and analysis with MATLAB and MPI |
| title_exact_search | Computational mathematics models, methods, and analysis with MATLAB and MPI |
| title_full | Computational mathematics models, methods, and analysis with MATLAB and MPI Robert E. White, North Carolina State University, Raleigh, North Carolina, USA |
| title_fullStr | Computational mathematics models, methods, and analysis with MATLAB and MPI Robert E. White, North Carolina State University, Raleigh, North Carolina, USA |
| title_full_unstemmed | Computational mathematics models, methods, and analysis with MATLAB and MPI Robert E. White, North Carolina State University, Raleigh, North Carolina, USA |
| title_short | Computational mathematics |
| title_sort | computational mathematics models methods and analysis with matlab and mpi |
| title_sub | models, methods, and analysis with MATLAB and MPI |
| topic | MATLAB. MATLAB. fast (OCoLC)fst01365096 MATLAB. fast Computer interfaces fast Numerical analysis / Data processing fast Parallel programming (Computer science) fast Datenverarbeitung Numerical analysis Data processing Computer interfaces Parallel programming (Computer science) Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd Algorithmus (DE-588)4001183-5 gnd MPI Schnittstelle (DE-588)4456003-5 gnd |
| topic_facet | MATLAB. Computer interfaces Numerical analysis / Data processing Parallel programming (Computer science) Datenverarbeitung Numerical analysis Data processing Numerical analysis Numerische Mathematik MATLAB Algorithmus MPI Schnittstelle |
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