Admin مدير المنتدى
عدد المساهمات : 19002 التقييم : 35506 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب An Introduction to Scientific Computing - Twelve Computational Projects Solved with MATLAB الأربعاء 19 يونيو 2024, 1:51 pm | |
|
أخواني في الله أحضرت لكم كتاب An Introduction to Scientific Computing - Twelve Computational Projects Solved with MATLAB Ionut Danaila, Pascal Joly, Sidi Mahmoud Kaber, Marie Postel
و المحتوى كما يلي :
Contents 1 Numerical Approximation of Model Partial Differential Equations 1 1.1 Discrete Integration Methods for Ordinary Differential Equations 1 1.1.1 Construction of Numerical Integration Schemes . 2 1.1.2 General Form of Numerical Schemes . 6 1.1.3 Application to the Absorption Equation 8 1.1.4 Stability of a Numerical Scheme . 9 1.2 Model Partial Differential Equations . 11 1.2.1 The Convection Equation 11 1.2.2 The Wave Equation . 14 1.2.3 The Heat Equation 17 1.3 Solutions and Programs 19 Chapter References . 30 2 Nonlinear Differential Equations: Application to Chemical Kinetics . 33 2.1 Physical Problem and Mathematical Modeling 33 2.2 Stability of the System . 34 2.3 Model for the Maintained Reaction 36 2.3.1 Existence of a Critical Point and Stability 36 2.3.2 Numerical Solution 37 2.4 Model of Reaction with a Delay Term 37 2.5 Solutions and Programs 41 Chapter References . 48 3 Polynomial Approximation 49 3.1 Introduction 49 3.2 Polynomial Interpolation . 50 3.2.1 Lagrange Interpolation . 51 3.2.2 Hermite Interpolation 57XII Contents 3.3 Best Polynomial Approximation . 59 3.3.1 Best Uniform Approximation . 59 3.3.2 Best Hilbertian Approximation 61 3.3.3 Discrete Least Squares Approximation . 64 3.4 Piecewise Polynomial Approximation 65 3.4.1 Piecewise Constant Approximation 66 3.4.2 Piecewise Affine Approximation . 67 3.4.3 Piecewise Cubic Approximation . 68 3.5 Further Reading . 69 3.6 Solutions and Programs 70 Chapter References . 83 4 Solving an Advection–Diffusion Equation by a Finite Element Method . 85 4.1 Variational Formulation of the Problem 85 4.2 A P1 Finite Element Method . 87 4.3 A P2 Finite Element Method . 90 4.4 A Stabilization Method 93 4.4.1 Computation of the Solution at the Endpoints of the Intervals . 93 4.4.2 Analysis of the Stabilized Method . 95 4.5 The Case of a Variable Source Term . 97 4.6 Solutions and Programs 97 Chapter References . 108 5 Solving a Differential Equation by a Spectral Method 111 5.1 Some Properties of the Legendre Polynomials . 112 5.2 Gauss–Legendre Quadrature 113 5.3 Legendre Expansions . 115 5.4 A Spectral Discretization . 117 5.5 Possible Extensions 119 5.6 Solutions and Programs 120 Chapter References . 125 6 Signal Processing: Multiresolution Analysis 127 6.1 Introduction 127 6.2 Approximation of a Function: Theoretical Aspect 127 6.2.1 Piecewise Constant Functions . 127 6.2.2 Decomposition of the Space VJ 129 6.2.3 Decomposition and Reconstruction Algorithms 132 6.2.4 Importance of Multiresolution Analysis . 133 6.3 Multiresolution Analysis: Practical Aspect 134 6.4 Multiresolution Analysis: Implementation . 135 6.5 Introduction to Wavelet Theory . 137 6.5.1 Scaling Functions and Wavelets . 137Contents XIII 6.5.2 The Schauder Wavelet . 139 6.5.3 Implementation of the Schauder Wavelet . 141 6.5.4 The Daubechies Wavelet . 142 6.5.5 Implementation of the Daubechies Wavelet D4 144 6.6 Generalization: Image Processing 146 6.6.1 Image Processing: Implementation . 147 6.7 Solutions and Programs 148 Chapter References . 150 7 Elasticity: Elastic Deformation of a Thin Plate 151 7.1 Introduction 151 7.2 Modeling Elastic Deformations (Linear Problem) 152 7.3 Modeling Electrostatic Forces (Nonlinear Problem) 153 7.4 Numerical Discretization of the Problem 154 7.5 Programming Tips . 157 7.5.1 Modular Programming . 157 7.5.2 Program Validation 158 7.6 Solving the Linear Problem . 159 7.7 Solving the Nonlinear Problem 159 7.7.1 A Fixed-Point Algorithm . 159 7.7.2 Numerical Solution 160 7.8 Solutions and Programs 162 7.8.1 Further Comments 162 Chapter References . 164 8 Domain Decomposition Using a Schwarz Method 165 8.1 Principle and Application Field of Domain Decomposition 165 8.2 One-Dimensional Finite Difference Solution . 166 8.3 Schwarz Method in One Dimension 167 8.3.1 Discretization . 168 8.4 Extension to the Two-Dimensional Case 171 8.4.1 Finite Difference Solution 171 8.4.2 Domain Decomposition in the Two-Dimensional Case 175 8.4.3 Implementation of Realistic Boundary Conditions . 178 8.4.4 Possible Extensions 180 8.5 Solutions and Programs 181 Chapter References . 190 9 Geometrical Design: B´ezier Curves and Surfaces . 193 9.1 Introduction 193 9.2 B´ezier Curves . 193 9.3 Basic Properties of B´ezier Curves 195 9.3.1 Convex Hull of the Control Points . 195 9.3.2 Multiple Control Points 196 9.3.3 Tangent Vector to a B´ezier Curve . 197XIV Contents 9.3.4 Junction of B´ezier Curves 197 9.3.5 Generation of the Point P(t) 198 9.4 Generation of B´ezier Curves 200 9.5 Splitting B´ezier Curves . 201 9.6 Intersection of B´ezier Curves 203 9.6.1 Implementation . 205 9.7 B´ezier Surfaces 206 9.8 Basic properties of B´ezier Surfaces . 206 9.8.1 Convex Hull 206 9.8.2 Tangent Vector . 207 9.8.3 Junction of B´ezier Patches 207 9.8.4 Construction of the Point P(t) 208 9.9 Construction of B´ezier Surfaces . 209 9.10 Solutions and Programs 210 Chapter References . 212 10 Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem . 213 10.1 Physical Description of the Shock Tube Problem 213 10.2 Euler Equations of Gas Dynamics . 215 10.2.1 Dimensionless Equations . 218 10.2.2 Exact Solution 218 10.3 Numerical Solution 222 10.3.1 Lax–Wendroff and MacCormack Centered Schemes 222 10.3.2 Upwind Schemes (Roe’s Approximate Solver) . 227 10.4 Solutions and Programs 232 Chapter References . 233 11 Thermal Engineering: Optimization of an Industrial Furnace 235 11.1 Introduction 235 11.2 Formulation of the Problem . 236 11.3 Finite Element Discretization . 237 11.4 Implementation . 239 11.5 Boundary Conditions 241 11.5.1 Modular Implementation . 242 11.5.2 Numerical Solution of the Problem 242 11.6 Inverse Problem Formulation 244 11.7 Implementation of the Inverse Problem . 245 11.8 Solutions and Programs 248 11.8.1 Further Comments 249 Chapter References . 250Contents XV 12 Fluid Dynamics: Solving the Two-Dimensional Navier–Stokes Equations 251 12.1 Introduction 251 12.2 The Incompressible Navier–Stokes Equations 252 12.3 Numerical Algorithm 253 12.4 Computational Domain, Staggered Grids, and Boundary Conditions 255 12.5 Finite Difference Discretization 256 12.6 Flow Visualization . 264 12.7 Initial Condition 265 12.8 Step-by-Step Implementation . 268 12.8.1 Solving a Linear System with Tridiagonal, Periodic Matrix . 268 12.8.2 Solving the Unsteady Heat Equation . 271 12.8.3 Solving the Steady Heat Equation Using FFTs 275 12.8.4 Solving the 2D Navier–Stokes Equations . 275 12.9 Solutions and Programs 277 Chapter References . 284 Bibliography . 285 Index 289 Index of Programs . 293 Index absorption equation, 8 Adams–Bashforth scheme, 7, 252, 253, 273 Adams–Moulton scheme, 7 ADI method, 259, 260, 273 algorithm de Casteljau, 200 divided differences, 54 Remez, 60 Thomas, 252, 268 approximation best Hilbertian, 62 uniform, 60 piecewise affine, 67 constant, 66 cubic, 68 basis canonical, 52 Haar, 131 Hilbertian, 62 Lagrange, 52 Legendre, 112 Bernstein polynomial, 194 best Hilbertian approximation, 62 best uniform approximation, 60 bilaplacian, 155 boundary condition, 120, 241 Dirichlet, 14, 17, 171, 236 Fourier, 179, 183, 236 homogeneous, 14 inhomogeneous, 171 Neumann, 179, 183, 236 periodic, 16, 26, 251, 257 boundary layer, 98 boundary value problem, 85 Brusselator, 33 B´ezier curve, 193 patch, 206 surface, 206 CAGD, 193 CFL condition, 13, 15, 23, 224, 264, 272 characteristic curve, 12, 15, 22, 217, 219 characteristic equation, 38 Chebyshev expansion, 79 points, 55 polynomial, 55 compressible fluid, 215 condensation, 95 condition number, 52 consistency, 9 contact discontinuity, 214, 220 convection equation, 11, 21, 216, 217, 224 phenomenon, 30 convection-diffusion equation, 265 convergence, 9, 57, 187 fast, 116 slow, 116 Crank–Nicolson scheme, 7, 252, 253, 273 critical point, 34, 37 data compression, 133 Daubechies wavelet, 142 de Casteljau algorithm, 200 delayed differential equation, 37 density, 215 differences (divided –), 54 differential equation, 33, 111, 165 diffusion, 17, 18, 226, 254 numerical, 27 phenomenon, 29 diffusivity (thermal –), 29 Dirichlet boundary condition, 14, 17, 153, 171, 236 discontinuity, 116290 Index contact, 214, 220 dissipation, 25 artificial, 226 divergence, 45, 252 divided differences, 53, 54 domain decomposition, 166 domain of dependence, 15 elasticity, 152 energy (total –), 215 enthalpy, 215 equioscillatory, 59 erf (error function), 18 Euler explicit modified scheme, 6, 7 explicit scheme, 5, 7, 20, 39, 46, 272 implicit scheme, 5, 7 system of equations, 215 expansion Chebyshev, 79 fan, 220 Fourier, 16 Legendre, 62 wave, 214 extrapolation, 49 FEM, 87, 237 FFT, 70, 252, 262 finite difference, 125, 155, 167, 171 backward, 3, 224, 226 centered, 3, 4, 224, 257 forward, 3, 224, 226 finite element, 86, 87, 90, 237 P1, 87 P2, 90 fluid compressible, 215 incompressible, 251 flux, 215, 229 splitting, 228 formulation (variational –), 86 Fourier boundary condition, 179, 183, 236 expansion, 16 FFT, 70, 252, 262 series, 261 Galerkin approximation, 117 Gauss quadrature, 113 Gibbs phenomenon, 116 Godunov scheme, 228 gradient, 252 Green formula, 237 grid (computational –), 172, 182, 256 Haar basis, 131 wavelet, 137 heat coefficient, 215, 217 equation, 17, 29, 226, 271, 275 steady equation, 171 Helmholtz equation, 252, 255, 258 Hermite, 119 interpolation, 57 polynomial, 58 Heun scheme, 7 Hopf bifurcation, 42 hyperbolic system, 216 ill-conditioned, 56 incompressible fluid, 251, 252 interpolation, 49, 51 Hermite, 57, 58 Lagrange, 51, 57 stability, 56 inverse problem, 244 isentropic flow, 217 isocontours, 274 Jacobian matrix, 35, 38, 216 jet flow, 266 junction of curves, 197 of patches, 207 Kelvin–Helmholtz instability, 252, 265Index 291 Lagrange basis, 52 interpolation, 51 polynomial, 51, 52 Laplacian, 152, 155, 166, 172, 252 Lax–Wendroff scheme, 223 leapfrog scheme, 5, 7 Lebesgue constant, 56 Legendre basis, 112 coefficients, 63 expansion, 62, 115 polynomials, 62, 111 series, 62 MacCormack scheme, 223 Mach number, 215 Mallat transform, 141 matrix exponential, 35 inverse, 233 Jacobian, 216 tridiagonal, 268 tridiagonal periodic, 260, 268, 269, 277 Vandermonde, 64, 70 mesh, 238 mother wavelet, 138 multiresolution analysis, 133 multiscale analysis, 133 Navier–Stokes equations, 252 fractional-step method, 253 projection method, 253 Neumann boundary condition, 153, 179, 183, 236 normal equations, 65 numerical integration, 113 ODE, 1, 33, 111 orthogonal projection, 63 overlap, 166 P1 finite element, 87 P2 finite element, 90 parametric curve, 36, 43 PDE, 1, 111, 165 Peclet number, 90, 265 periodic boundary condition, 16, 26, 251, 257 trajectory, 42, 46 phenomenon Gibbs, 116 Runge, 57 Poisson equation, 252, 255, 261 polygon (control –), 196 polynomial Bernstein, 194 Hermite, 119 Lagrange, 51, 52 Legendre, 62, 111 of best Hilbertian approximation, 62 of best uniform approximation, 60 projection (orthogonal), 63 quadrature, 50, 86 Gauss, 113 rule, 113 Simpson, 87 trapezoidal, 86 Rankine–Hugoniot, 219 rarefaction wave, 214 regression line, 64 Remez algorithm, 60 Reynolds number, 253 Riemann problem, 217 Roe approximate solver, 229 average, 230 Runge–Kutta scheme, 7, 20, 37, 40 Runge phenomenon, 57 scaling function, 137 Schauder wavelet, 139, 141 scheme 13-point, 156292 Index 5-point, 155, 172 Adams–Bashforth, 7, 253, 273 Adams–Moulton, 7 centered, 19, 222 conservative, 230 Crank–Nicolson, 7, 253, 273 Euler explicit , 7 Euler implicit , 7 explicit, 5, 6, 224, 272 Godunov, 228 Heun, 7 implicit, 5, 6, 273 Lax–Wendroff, 223 leapfrog, 7 MacCormack, 223 Roe, 229 Runge–Kutta, 7 upwind, 13, 23, 25, 224, 227 Schwarz method, 166 series Chebyshev, 79 Legendre, 62 Taylor, 3 shock tube, 213 wave, 214, 219 Simpson quadrature, 87 smooth function, 116 Sod shock tube, 221 spectral method, 117 spline, 66 stability, 9, 34, 56 amplification function, 10 CFL condition, 13, 15, 23, 224, 264, 272 region, 10, 20, 26 steady solution, 34 stopping criterion, 169 stream-function, 267 string (vibrating –), 16 Taylor expansion, 3, 35, 172, 224 formula, 35 thermal diffusivity, 179 shock, 171 Thomas algorithm, 252, 268, 269 tracer (passive –), 265 trajectory, 42 periodic, 42, 46 trapezoidal quadrature, 86 triangulation, 238 tridiagonal matrix, 167, 173 two-scale relation, 128, 139, 142 upwind scheme, 13, 23, 25, 224, 227 Vandermonde matrix, 64, 70 variational formulation, 86, 237 viscosity artificial, 226 kinematic, 253 vortex, 264, 267 dipole, 252, 267 vorticity, 264 wave characteristic, 217, 224 elementary, 16 equation, 14 expansion, 214 number, 16, 262 rarefaction, 214 shock, 214 wavelength, 279 wavelet, 137 Daubechies, 142 Haar, 137 Schauder, 139Index of Programs APP ApproxScript1.m, 70 APP ApproxScript2.m, 71 APP ApproxScript3.m, 72 APP ApproxScript4.m, 73 APP ApproxScript5.m, 73 APP ApproxScript8.m, 77 APP condVanderMonde.m, 71 APP condVanderMondeBis.m, 71 APP dd.m, 72 APP ddHermite.m, 76 APP equiosc.m, 79 APP interpol.m, 73 APP Interpolation.m, 76 APP Lebesgue.m, 73 APP ls.m, 80 APP Remez.m, 79 APP Runge.m, 76 APP scriptHermite.m, 77 APP spline0.m, 81 APP spline1.m, 82 APP spline3.m, 82 CAGD casteljau.m, 210 CAGD cbezier.m, 210 CAGD coox.m, 211 CAGD ex1.m, 210 CAGD ex1b.m, 210 CAGD ex1c.m, 210 CAGD ex2.m, 211 CAGD pbzier.m, 210 CAGD tbezier.m, 210 DDM f1BB.m, 183 DDM f1CT, 183 DDM f1Exact.m, 183 DDM f2CT.m, 183 DDM f2Exact.m, 183 DDM FinDif2dDirichlet.m, 183 DDM FinDif2dFourier.m, 183 DDM FunSchwarz1d.m, 181 DDM g1BB.m, 183 DDM g1CT.m, 183 DDM g1Exact.m, 183 DDM g2Exact.m, 183 DDM LaplaceDirichlet.m, 183 DDM LaplaceFourier.m, 183 DDM Perf.m, 187 DDM rhs1d.m, 181 DDM rhs2dBB.m, 183 DDM rhs2dCT.m, 183 DDM rhs2dExact.m, 183 DDM RightHandSide2dDirichlet.m, 183 DDM RightHandSideFourier.m, 183 DDM Schwarz2dDirichlet.m, 187 DDM Schwarz2dFourier.m, 190 DDM TestFinDif2d.m, 183 DDM TestSchwarz2d.m, 184, 190 ELAS bilap matrix.m, 162 ELAS bilap rhs.m, 162 ELAS lap matrix.m, 162 ELAS lap rhs.m, 162 ELAS plate ex.m, 162 ELAS solution.m, 162 FEM ConvecDiffAP1.m, 101 FEM ConvecDiffAP2.m, 104 FEM ConvecDiffbP1.m, 101 FEM ConvecDiffbP2.m, 104 FEM ConvecDiffscript1.m, 101 FEM ConvecDiffscript2.m, 102 FEM ConvecDiffscript3.m, 102 FEM ConvecDiffscript4.m, 105 FEM ConvecDiffscript5.m, 106 FEM ConvecDiffSolExa.m, 98 HYP calc dt.m, 232 HYP flux roe.m, 233 HYP mach compat.m, 232 HYP plot graph.m, 232 HYP shock tube.m, 232 HYP shock tube exact.m, 232 HYP trans usol w.m, 232294 Index of Programs HYP trans w f.m, 232 HYP trans w usol.m, 232 MRA daube4.m, 149 MRA daube4 ex1.m, 149 MRA daube4 ex2.m, 149 MRA daube4 ex3.m, 149 MRA haar.m, 148 MRA haar ex1.m, 148 MRA haar ex2.m, 148 MRA haar ex3.m, 149 MRA schauder.m, 148 MRA schauder ex1.m, 149 MRA schauder ex2.m, 149 MRA schauder ex3.m, 149 NSE ADI init.m, 278 NSE ADI step.m, 278 NSE affiche div.m, 279 NSE calc hc.m, 278 NSE calc lap.m, 277 NSE fexact.m, 277 NSE fsource.m, 277 NSE fsource nonl.m, 278 NSE init KH.m, 278 NSE init vortex.m, 278 NSE norm L2.m, 277 NSE Phi init.m, 278 NSE Phi step.m, 278 NSE Q2fft lap.m, 278 NSE Qexp lap.m, 277 NSE Qfft lap.m, 278 NSE Qimp lap.m, 277 NSE Qimp lap nonl.m, 278 NSE QNS.m, 278 NSE test trid.m, 271, 277 NSE trid per c2D.m, 277 NSE visu isos.m, 277 NSE visu sca.m, 278 NSE visu vort.m, 278 ODE Chemistry2.m, 42 ODE Chemistry3.m, 44 ODE DelayEnzyme.m, 46 ODE Enzyme.m, 46 ODE EnzymeCondIni.m, 47 ODE ErrorEnzyme.m, 47 ODE EulerDelay.m, 46 ODE fun2.m, 42 ODE fun3.m, 44 ODE RungeKuttaDelay.m, 46 ODE stab2comp.m, 41 ODE stab3comp.m, 43 ODE StabDelay.m, 45 PDE absorption.m, 20 PDE absorption source.m, 20 PDE conv bound cond.m, 24 PDE conv exact sol.m, 23 PDE conv init cond.m, 24 PDE convection.m, 24 PDE EulerExp.m, 20 PDE heat.m, 29 PDE heat u0.m, 29 PDE heat uex.m, 29 PDE RKutta4.m, 20 PDE wave fstring.m, 28 PDE wave fstring exact.m, 28 PDE wave fstring in.m, 28 PDE wave infstring.m, 26 PDE wave infstring u0.m, 26 PDE wave infstring u1.m, 26 SPE AppLegExp.m, 122 SPE CalcLegExp, 122 SPE fbe.m, 122 SPE LegExpLoop.m, 122 SPE LegLinComb.m, 120 SPE PlotLegPol.m, 120 SPE special.m, 122 SPE SpecMeth.m, 123 SPE specsec.m, 122 SPE TestIntGauss.m, 121 SPE xwGauss.m, 121 THER matrix inv.m, 249 THER oven.m, 249 THER oven ex1.m, 248 THER oven ex2.m, 249 #ماتلاب,#متلاب,#Matlab,#مات_لاب,#مت_لاب,
كلمة سر فك الضغط : books-world.net The Unzip Password : books-world.net أتمنى أن تستفيدوا من محتوى الموضوع وأن ينال إعجابكم رابط من موقع عالم الكتب لتنزيل كتاب An Introduction to Scientific Computing - Twelve Computational Projects Solved with MATLAB رابط مباشر لتنزيل كتاب An Introduction to Scientific Computing - Twelve Computational Projects Solved with MATLAB
|
|