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E-raamat: Computational Mathematics: Models, Methods, and Analysis with MATLAB, and MPI, Second Edition

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(North Carolina State University, Raleigh, USA)
  • Formaat: 500 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 11-Nov-2015
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781482235166
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Computational Mathematics: Models, Methods, and Analysis with MATLAB, and MPI, Second EditionSuurem pilt
  • Formaat: 500 pages
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 11-Nov-2015
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781482235166
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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; nonrectangular 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.
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(54)
1.1 Newton Cooling Models
1(8)
1.2 Heat Diffusion in a Wire
9(9)
1.3 Diffusion in a Wire with Little Insulation
18(8)
1.4 Flow and Decay of a Pollutant in a Stream
26(8)
1.5 Heat and Mass Transfer in Two Directions
34(11)
1.6 Convergence Analysis
45(10)
2 Steady-State Discrete Models 55(52)
2.1 Steady-State and Triangular Solves
55(8)
2.2 Heat Diffusion and Gauss Elimination
63(11)
2.3 Cooling Fin and Tridiagonal Matrices
74(9)
2.4 Schur Complement
83(9)
2.5 Convergence to Steady-State Solution
92(7)
2.6 Convergence to Continuous Model
99(8)
3 Poisson Equation Models 107(54)
3.1 Steady-State and Iterative Methods
107(10)
3.2 Heat Transfer in 2D Fin and SOR
117(8)
3.3 Fluid Flow in a 2D Porous Medium
125(7)
3.4 Ideal Fluid Flow
132(9)
3.5 Deformed Membrane and Steepest Descent
141(9)
3.6 Conjugate Gradient Method
150(11)
4 Nonlinear and 3D Models 161(48)
4.1 Nonlinear Problems in One Variable
161(8)
4.2 Nonlinear Heat Transfer in a Wire
169(8)
4.3 Nonlinear Heat Transfer in 2D
177(6)
4.4 Steady-State 3D Heat Diffusion
183(6)
4.5 Time-Dependent 3D Diffusion
189(8)
4.6 High-Performance Computations in 3D
197(12)
5 FEM and Fluid Flows 209(38)
5.1 FEM and Linear Shape Functions
209(9)
5.2 FEM with Heat and Fluid Flow
218(8)
5.3 Lax-Wendroff Methods
226(6)
5.4 Shallow Water Wave Model
232(5)
5.5 Navier-Stokes Equations
237(3)
5.6 Discrete Navier-Stokes Equations
240(7)
6 Epidemics, Images, and Money 247(48)
6.1 Epidemics and Dispersion
247(8)
6.2 Epidemic Dispersion in 2D
255(7)
6.3 Image Restoration
262(9)
6.4 Restoration in 2D
271(6)
6.5 Option Contract Models
277(9)
6.6 Black-Scholes Model for Two Assets
286(9)
7 High-Performance Computing 295(60)
7.1 CPUs and Vector Pipes
295(12)
7.2 Multiprocessor and Multicore Computers
307(9)
7.3 Parallel MATLAB®
316(10)
7.4 Parallel MATLAB and SPMD
326(8)
7.5 Introduction to MPI
334(9)
7.6 MPI and Matrix Products
343(12)
8 Message Passing Interface 355(44)
8.1 Collective Subroutines
355(12)
8.2 Grouped Datatypes
367(7)
8.3 Communicators
374(6)
8.4 Fox Algorithm for AB
380(6)
8.5 Shared Memory and OpenMP
386(6)
8.6 Hybrid MPI/OpenMP
392(7)
9 Classical Methods for Ax = d 399(32)
9.1 Gauss Elimination
399(5)
9.2 Symmetric Positive Definite Matrices
404(6)
9.3 Domain Decomposition and MPI
410(5)
9.4 SOR and P-Regular Splittings
415(5)
9.5 SOR and MPI
420(6)
9.6 Parallel ADI Schemes
426(5)
10 Krylov Methods for Ax = d 431(36)
10.1 Conjugate Gradient Method
431(5)
10.2 Preconditioners
436(6)
10.3 PCG and MPI
442(4)
10.4 Least Squares
446(7)
10.5 GMRES
453(7)
10.6 GMRES(m) and MPI
460(7)
Bibliography 467(4)
Index 471
Robert E. White (North Carolina State University, Raleigh, USA)
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