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عدد المساهمات : 18928 التقييم : 35294 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
![كتاب Partial Differential Equations and the Finite Element Method Empty](https://2img.net/i/fa/empty.gif) | موضوع: كتاب Partial Differential Equations and the Finite Element Method الأحد 03 يونيو 2012, 4:40 am | |
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أخوانى فى الله أحضرت لكم كتاب
Partial Differential Equations and the Finite Element Method P Solin
ويتناول الموضوعات الأتية :
Partial Differential Equations Selected general properties Classification and examples Hadamard’s well-posedness Exercises General existence and uniqueness results Second-order elliptic problems Weak formulation of a model problem Bilinear forms, energy norm, and energetic inner product The Lax-Milgram lemma Unique solvability of the model problem Nonhomogeneous Dirichlet boundary conditions Neumann boundary conditions Newton (Robin) boundary conditions Combining essential and natural boundary conditions Energy of elliptic problems Maximum principles and well-posedness Exercises Second-order parabolic problems Initial and boundary conditions Weak formulation Exercises Existence and uniqueness of solution Second-order hyperbolic problems Initial and boundary conditions The wave equation I Exercises Weak formulation and unique solvability First-order hyperbolic problems Conservation laws S Characteristics S Riemann problem S Exercises Exact solution to linear first-order systems Nonlinear flux and shock formation Continuous Elements for D Problems The general framework I Exercises The Galerkin method Orthogonality of error and CCa’s lemma Convergence of the Cialerkin method Ritz method for symmetric problems Lowest-order elements Model problem Piecewise-affine basis functions Element-by-element assembling procedure Refinement and convergence Exercises Finite-dimensional subspace V,, C v The system of linear algebraic equations Higher-order numerical quadrature Gaussian quadrature rules Selected quadrature constants Adaptive quadrature Exercises Higher-order elements Motivation problem Affine concept: reference domain and reference maps Transformation of weak forms to the reference domain Higher-order Lagrange nodal shape functions Chebyshev and Gauss-Lobatto nodal points Higher-order Lobatto hierarchic shape functions Constructing basis of the space Vh,p Data structures Assembling algorithm Exercises The sparse stiffness matrix Condition number Conditioning of shape functions Exercises Compressed sparse row (CSR) data format Stiffness matrix for the Lobatto shape functions Implementing nonhomogeneous boundary conditions Dirichlet boundary conditions Exercises Combination of essential and natural conditions Interpolation on finite elements The Hilbert space setting Best interpolant Projection-based interpolant Nodal interpolant Exercises General Concept of Nodal Elements The nodal finite element Unisolvency and nodal basis Checking unisolvency Example: lowest-order Q' - and PI-elements Q-element P-element Invertibility of the quadrilateral reference map z~ Interpolation on nodal elements Local nodal interpolant Global interpolant and conformity Conformity to the Sobolev space H' Equivalence of nodal elements Exercises Continuous Elements for D Problems Lowest-order elements Approximations and variational crimes Connectivity arrays Assembling algorithm for Q'/P'-elements Lagrange interpolation on Q'/P'-meshes Exercises Higher-order numerical quadrature in D Gaussian quadrature on quads Gaussian quadrature on triangles Product Gauss-Lobatto points Lagrange-Gauss-Lobatto Qp,'-elements The Fekete points Lagrange-Fekete PP-elements Data structures Connectivity arrays Assembling algorithm for QPIPp-elements Lagrange interpolation on Qp/Pp-meshes Exercises Model problem and its weak formulation Basis of the space Vh,p Transformation of weak forms to the reference domain Simplified evaluation of stiffness integrals Higher-order nodal elements Lagrange interpolation and the Lebesgue constant Basis of the space v,Tl Transient Problems and ODE Solvers Method of lines Model problem Weak formulation The ODE system Construction of the initial vector Autonomous systems and phase flow One-step methods, consistency and convergence Explicit and implicit Euler methods Selected time integration schemes Stiffness Explicit higher-order RK schemes General (implicit) RK schemes Embedded RK methods and adaptivity Introduction to stability Autonomization of RK methods A-stability and L-stability Collocation methods Solution of nonlinear systems Stability of linear autonomous systems Stability functions and stability domains Stability functions for general RK methods Maximum consistency order of IRK methods Higher-order IRK methods Gauss and Radau IRK methods Exercises Beam and Plate Bending Problems Bending of elastic beams I Euler-Bernoulli model Boundary conditions Weak formulation Lowest-order Hermite elements in D Model problem Cubic Hermite elements Higher-order Hermite elements in D Nodal higher-order elements Hierarchic higher-order elements Conditioning of shape functions Basis of the space Vh,p Transformation of weak forms to the reference domain Connectivity arrays Assembling algorithm Interpolation on Hermite elements Lowest-order elements Higher-order Hermite-Fekete elements Design of basis functions Reissner-Mindlin (thick) plate model Kirchhoff (thin) plate model Boundary conditions Existence and uniqueness of solution Hermite elements in D Global nodal interpolant and conformity Bending of elastic plates Weak formulation and unique solvability BabuSka’s paradox of thin plates xii CONTENTS Discretization by H-conforming elements Local interpolant, conformity Transformation to reference domains Design of basis functions Higher-order nodal Argyris-Fekete elements Lowest-order (quintic) Argyris element, unisolvency Nodal shape functions on the reference domain Exercises Equations of Electrornagnetics Electromagnetic field and its basic characteristics Integration along smooth curves Conductors and dielectrics Magnetic materials Conditions on interfaces Scalar electric potential Scalar magnetic potential Other wave equations Equations for the field vectors Interface and boundary conditions Time-harmonic Maxwell’s equations Helmholtz equation Normalization Model problem Weak formulation Maxwell’s equations in integral form Maxwell’s equations in differential form Constitutive relations and the equation of continuity Media and their characteristics Potentials Vector potential and gauge transformations Potential formulation of Maxwell’s equations Equation for the electric field Equation for the magnetic field Time-harmonic Maxwell’s equations Existence and uniqueness of solution Conformity requirements of the space H(cur) Lowest-order (Whitney) edge elements Higher-order edge elements of NCdClec Transformation of weak forms to the reference domain Interpolation on edge elements Edge elements Exercises Conformity of edge elements to the space H(cur) Appendix A: Basics of Functional Analysis A Linear spaces A Exercises Real and complex linear space Checking whether a set is a linear space Intersection and union of subspaces Linear combination and linear span Sum and direct sum of subspaces Linear independence, basis, and dimension Linear operator, null space, range Composed operators and change of basis Determinants, eigenvalues, and eigenvectors Hermitian, symmetric, and diagonalizable matrices Linear forms, dual space, and dual basis A Normed spaces A Norm and seminorm A Convergence and limit A Open and closed sets A Continuity of operators A Equivalence of norms A Banach spaces A Banach fixed point theorem A Lebesgue integral and LP-spaces A Basic inequalities in LP-spaces A Exercises Operator norm and C(U, V ) as a normed space Density of smooth functions in LP-spaces A Inner product spaces A Inner product A Hilbert spaces A Generalized angle and orthogonality A Generalized Fourier series A Projections and orthogonal projections A Representation of linear forms (Riesz) A Compactness, compact operators, and the Fredholm alternative A Weak convergence A Exercises A Sobolev spaces A Domain boundary and its regularity xiv CONTENTS Distributions and weak derivatives Spaces Wklp and Hk Discontinuity of HI-functions in R", d PoincarC-Friedrichs' inequality Embeddings of Sobolev spaces Traces of W"p-functions Generalized integration by parts formulae Exercises Appendix B: Software and Examples B Sparse Matrix Solvers B The sMatrix utility B An example application B Interfacing with PETSc B Interfacing with Trilinos B Interfacing with UMFPACK The High-Performance Modular Finite Element System HERMES B Modular structure of HERMES B The elliptic module B The Maxwell's module B Example : Insulator problem B Example : Sphere-cone problem B Example : Diffraction problem Example : L-shape domain problem Example : Electrostatic micromotor problem References
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Admin مدير المنتدى
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عدد المساهمات : 18928 التقييم : 35294 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
![كتاب Partial Differential Equations and the Finite Element Method Empty](https://2img.net/i/fa/empty.gif) | موضوع: رد: كتاب Partial Differential Equations and the Finite Element Method الأربعاء 07 نوفمبر 2012, 5:00 pm | |
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