2nd Edition

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

By Robert E. White Copyright 2016
    500 Pages 97 B/W Illustrations
    by Chapman & Hall

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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.

    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
    SOR and MPI
    Parallel ADI Schemes

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