Computational Mathematics : Models, Methods, and Analysis with MATLAB® and MPI, Second Edition book cover
2nd Edition

Computational Mathematics
Models, Methods, and Analysis with MATLAB® and MPI, Second Edition

ISBN 9781482235159
Published November 17, 2015 by Chapman and Hall/CRC
500 Pages 97 B/W Illustrations

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Book Description

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.

Table of Contents

Discrete Time–Space Models
Newton Cooling Models
Heat Diffusion in a Wire
Diffusion in a Wire with Little Insulation
Flow and Decay of a Pollutant in a Stream
Heat and Mass Transfer in Two Directions
Convergence Analysis

Steady-State Discrete Models
Steady-State and Triangular Solves
Heat Diffusion and Gauss Elimination
Cooling Fin and Tridiagonal Matrices
Schur Complement
Convergence to Steady-State
Convergence to Continuous Model

Poisson Equation Models
Steady-State and Iterative Methods
Heat Transfer in 2D Fin and SOR
Fluid Flow in a 2D Porous Medium
Ideal Fluid Flow
Deformed Membrane and Steepest Descent
Conjugate Gradient Method

Nonlinear and 3D Models
Nonlinear Problems in One Variable
Nonlinear Heat Transfer in a Wire
Nonlinear Heat Transfer in 2D
Steady-State 3D Heat Diffusion
Time-Dependent 3D Diffusion
High-Performance Computations in 3D

FEM and Fluid Flows
FEM and Linear Shape Functions
FEM with Heat and Fluid Flow
Lax–Wendroff Methods
Shallow Water Wave Model
Navier–Stokes Equations
Discrete Navier–Stokes Equations

Epidemics, Images, and Money
Epidemics and Dispersion
Epidemic Dispersion in 2D
Image Restoration
Restoration in 2D
Option Contract Models
Black—Scholes Model for Two Assets

High-Performance Computing
CPUs and Vector Pipes
Multiprocessor and Multicore Computers
Parallel MATLAB
Parallel MATLAB and SPMD
Introduction to MPI
MPI and Matrix Products

Message Passing Interface
Collective Subroutines
Grouped Datatypes
Fox Algorithm for AB
Shared Memory and OpenMP
Hybrid MPI/OpenMP

Classical Methods for Ax = d
Gauss Elimination
Symmetric Positive Definite Matrices
Domain Decomposition and MPI
SOR and P-Regular Splittings
Parallel ADI Schemes

Krylov Methods for Ax = d
Conjugate Gradient Method
Least Squares
GMRES(m) and MPI

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