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

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 ModelsNewton Cooling ModelsHeat Diffusion in a WireDiffusion in a Wire with Little InsulationFlow and Decay of a Pollutant in a StreamHeat and Mass Transfer in Two DirectionsConvergence Analysis Steady-State Discrete ModelsSteady-State and Triangular SolvesHeat Diffusion and Gauss EliminationCooling Fin and Tridiagonal MatricesSchur ComplementConvergence to Steady-StateConvergence to Continuous Model Poisson Equation ModelsSteady-State and Iterative MethodsHeat Transfer in 2D Fin and SORFluid Flow in a 2D Porous MediumIdeal Fluid FlowDeformed Membrane and Steepest DescentConjugate Gradient Method Nonlinear and 3D ModelsNonlinear Problems in One VariableNonlinear Heat Transfer in a WireNonlinear Heat Transfer in 2DSteady-State 3D Heat DiffusionTime-Dependent 3D DiffusionHigh-Performance Computations in 3D FEM and Fluid FlowsFEM and Linear Shape FunctionsFEM with Heat and Fluid FlowLax–Wendroff MethodsShallow Water Wave ModelNavier–Stokes EquationsDiscrete Navier–Stokes Equations Epidemics, Images, and MoneyEpidemics and DispersionEpidemic Dispersion in 2DImage RestorationRestoration in 2DOption Contract ModelsBlack—Scholes Model for Two Assets High-Performance ComputingCPUs and Vector PipesMultiprocessor and Multicore ComputersParallel MATLABParallel MATLAB and SPMDIntroduction to MPIMPI and Matrix Products Message Passing InterfaceCollective SubroutinesGrouped DatatypesCommunicatorsFox Algorithm for ABShared Memory and OpenMPHybrid MPI/OpenMP Classical Methods for Ax = dGauss EliminationSymmetric Positive Definite MatricesDomain Decomposition and MPISOR and P-Regular SplittingsSOR and MPIParallel ADI Schemes Krylov Methods for Ax = dConjugate Gradient MethodPreconditionersPCG and MPILeast SquaresGMRESGMRES(m) and MPI