دانلود کتاب Inside Finite Elements

فهرست مطالب :

Contents\nPreface\n1. Finite Element Fundamentals\n 1.1 Stationary Heat Equation\n 1.2 Boundary Conditions\n 1.3 Weak Formulation\n 1.4 Galerkin Discretization\n 1.5 Finite Elements\n Exercises\n2. Grids and Finite Elements\n 2.1 Cells and Vertices\n 2.2 Shape and Ansatz Functions\n 2.3 Grid Generation and Visualization\n 2.3.1 Preprocessing\n 2.3.2 Postprocessing\n 2.4 Edges and Boundaries\n Exercises\n3. Assembly\n 3.1 System Matrices\n 3.1.1 Elemental Stiffness Matrices\n 3.1.2 Scattering\n 3.1.3 Elemental Mass Matrices\n 3.2 Boundary Conditions\n 3.2.1 Robin Boundary Conditions\n 3.2.2 Dirichlet Boundary Conditions\n 3.3 Right Hand Sides\n 3.4 Examples\n 3.5 Sparse Matrix Storage Formats\n 3.5.1 Triplet Format\n 3.5.2 Compressed Row Storage\n 3.5.3 Computational Efficiency\n Exercises\n4. Solvers\n 4.1 Direct Solvers\n 4.2 Iterative Solvers\n 4.2.1 Stationary Iterations\n 4.2.2 Gradient Descent\n 4.2.3 Conjugate Gradient Method\n 4.3 Examples\n Exercises\n5. Error Estimation\n 5.1 Hierarchical Error Estimation\n 5.2 DLY simplification\n 5.3 Assembly\n 5.3.1 Elemental Matrices\n 5.3.2 Elemental Right Hand Sides\n 5.3.3 Quadrature Rules\n 5.4 Examples\n Exercises\n6. Mesh Refinement\n 6.1 Marking Strategies\n 6.2 Refinement\n 6.2.1 Bisection\n 6.2.2 Triangle splitting\n 6.3 Grid Hierarchy\n 6.4 Examples\n Exercises\n7. Multigrid\n 7.1 Smoothers\n 7.2 Coarse Grid Correction\n 7.3 Multigrid Solver\n 7.4 Additive Multilevel Preconditioners\n 7.5 Examples\n Exercises\n8. Elastomechanics\n 8.1 Linear Elastomechanics\n 8.2 Vectorial Finite Elements\n 8.3 Time-harmonic Dynamics\n 8.3.1 Eigenfunctions\n 8.4 Examples\n 8.4.1 Stationary Problems\n 8.4.2 Oscillatory Problems\n Exercises\n9. Fluid Mechanics\n 9.1 Stokes Equation\n 9.2 Uzawa’s Method\n 9.3 Examples\n 9.3.1 Discretization\n 9.3.2 Iterative Solution\n Exercises\nA. Grid Data Structure\nB. Function Reference\nBibliography\nIndex