Adaptive Numerical Solution Of Pdes DOWNLOAD HERE
1;Preface;5 2;Outline;13 3;1 Elementary Partial Differential Equations;17 3.1;1.1 Laplace and Poisson Equation;17 3.1.1;1.1.1 Boundary Value Problems;18 3.1.2;1.1.2 Initial Value Problem;22 3.1.3;1.1.3 Eigenvalue Problem;24 3.2;1.2 Diffusion Equation;27 3.3;1.3 Wave Equation;30 3.4;1.4 Schrdinger Equation;35 3.5;1.5 Helmholtz Equation;38 3.5.1;1.5.1 Boundary Value Problems;38 3.5.2;1.5.2 Time-harmonic Differential Equations;39 3.6;1.6 Classification;41 3.7;1.7 Exercises;43 4;2 Partial Differential Equations in Science and Technology;46 4.1;2.1 Electrodynamics;46 4.1.1;2.1.1 Maxwell Equations;46 4.1.2;2.1.2 Optical Model Hierarchy;49 4.2;2.2 Fluid Dynamics;52 4.2.1;2.2.1 Euler Equations;53 4.2.2;2.2.2 Navier-Stokes Equations;56 4.2.3;2.2.3 Prandtl s Boundary Layer;61 4.2.4;2.2.4 Porous Media Equation;63 4.3;2.3 Elastomechanics;64 4.3.1;2.3.1 Basic Concepts of Nonlinear Elastomechanics;64 4.3.2;2.3.2 Linear Elastomechanics;68 4.4;2.4 Exercises;71 5;3 Finite Difference Methods for Poisson Problems;74 5.1;3.1 Discretization of Standard Problem;74 5.1.1;3.1.1 Discrete Boundary Value Problems;75 5.1.2;3.1.2 Discrete Eigenvalue Problem;80 5.2;3.2 Approximation Theory on Uniform Grids;83 5.2.1;3.2.1 Discretization Error in L2;85 5.2.2;3.2.2 Discretization Error in L8;88 5.3;3.3 Discretization on Nonuniform Grids;90 5.3.1;3.3.1 One-dimensional Special Case;90 5.3.2;3.3.2 Curved Boundaries;92 5.4;3.4 Exercises;95 6;4 Galerkin Methods;98 6.1;4.1 General Scheme;98 6.1.1;4.1.1 Weak Solutions;98 6.1.2;4.1.2 Ritz Minimization for Boundary Value Problems;101 6.1.3;4.1.3 Rayleigh-Ritz Minimization for Eigenvalue Problems;105 6.2;4.2 Spectral Methods;107 6.2.1;4.2.1 Realization by Orthogonal Systems;108 6.2.2;4.2.2 Approximation Theory;112 6.2.3;4.2.3 Adaptive Spectral Methods;115 6.3;4.3 Finite Element Methods;120 6.3.1;4.3.1 Meshes and Finite Element Spaces;120 6.3.2;4.3.2 Elementary Finite Elements;123 6.3.3;4.3.3 Realization of Finite Elements;133 6.4;4.4 Approximation Theory for Finite Elements;140 6.4.1;4.4.1 Boundary Value Problems;140 6.4.2;4.4.2 Eigenvalue Problems;143 6.4.3;4.4.3 Angle Condition for Nonuniform Meshes;148 6.5;4.5 Exercises;151 7;5 Numerical Solution of Linear Elliptic Grid Equations;155 7.1;5.1 Direct Elimination Methods;156 7.1.1;5.1.1 Symbolic Factorization;157 7.1.2;5.1.2 Frontal Solvers;159 7.2;5.2 Matrix Decomposition Methods;162 7.2.1;5.2.1 Jacobi Method;164 7.2.2;5.2.2 Gauss-Seidel Method;166 7.3;5.3
Conjugate Gradient Method;168 7.3.1;5.3.1 CG-Method as Galerkin Method;168 7.3.2;5.3.2 Preconditioning;171 7.3.3;5.3.3 Adaptive PCG-method;175 7.3.4;5.3.4 A CG-variant for Eigenvalue Problems;177 7.4;5.4 Smoothing Property of Iterative Solvers;182 7.4.1;5.4.1 Illustration for the Poisson Model Problem;182 7.4.2;5.4.2 Spectral Analysis for Jacobi Method;186 7.4.3;5.4.3 Smoothing Theorems;187 7.5;5.5 Iterative Hierarchical Solvers;192 7.5.1;5.5.1 Classical Multigrid Methods;194 7.5.2;5.5.2 Hierarchical-basis Method;202 7.5.3;5.5.3 Comparison with Direct Hierarchical Solvers;205 7.6;5.6 Power Optimization of a Darrieus Wind Generator;206 7.7;5.7 Exercises;212 8;6 Construction of Adaptive Hierarchical Meshes;215 8.1;6.1 A Posteriori Error Estimators;215 8.1.1;6.1.1 Residual Based Error Estimator;218 8.1.2;6.1.2 Triangle Oriented Error Estimators;223 8.1.3;6.1.3 Gradient Recovery;227 8.1.4;6.1.4 Hierarchical Error Estimators;231 8.1.5;6.1.5 Goal-oriented Error Estimation;234 8.2;6.2 Adaptive Mesh Refinement;235 8.2.1;6.2.1 Equilibration of Local Discretization Errors;236 8.2.2;6.2.2 Refinement Strategies;241 8.2.3;6.2.3 Choice of Solvers on Adaptive Hierarchical Meshes;245 8.3;6.3 Convergence on Adaptive Meshes;245 8.3.1;6.3.1 A Convergence Proof;246 8.3.2;6.3.2 An Example with a Reentrant Corner;248 8.4;6.4 Design of a Plasmon-Polariton Waveguide;252 8.5;6.5 Exercises;256 9;7 Adaptive Multigrid Methods for Linear Elliptic Pr EAN/ISBN : 9783110283112 Publisher(s): De Gruyter Format: ePub/PDF Author(s): Deuflhard, Peter - Weiser, Martin
DOWNLOAD HERE
Similar manuals: Adaptive Numerical Solution Of PDEs