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Inside Finite Elements.
All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises a complete...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin/Boston :
De Gruyter,
2016.
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| Colección: | De Gruyter textbook.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface ; 1. Finite Element Fundamentals ; 1.1 Stationary Heat Equation ; 1.2 Boundary Conditions ; 1.3 Weak Formulation ; 1.4 Galerkin Discretization ; 1.5 Finite Elements ; Exercises ; 2. Grids and Finite Elements ; 2.1 Cells and Vertices.
- 2.2 Shape and Ansatz Functions 2.3 Grid Generation and Visualization ; 2.3.1 Preprocessing ; 2.3.2 Postprocessing ; 2.4 Edges and Boundaries ; Exercises ; 3. Assembly ; 3.1 System Matrices ; 3.1.1 Elemental Stiffness Matrices ; 3.1.2 Scattering ; 3.1.3 Elemental Mass Matrices.
- 3.2 Boundary Conditions 3.2.1 Robin Boundary Conditions ; 3.2.2 Dirichlet Boundary Conditions ; 3.3 Right Hand Sides ; 3.4 Examples ; 3.5 Sparse Matrix Storage Formats ; 3.5.1 Triplet Format ; 3.5.2 Compressed Row Storage ; 3.5.3 Computational Efficiency ; Exercises ; 4. Solvers.
- 4.1 Direct Solvers 4.2 Iterative Solvers ; 4.2.1 Stationary Iterations ; 4.2.2 Gradient Descent ; 4.2.3 Conjugate Gradient Method ; 4.3 Examples ; Exercises ; 5. Error Estimation ; 5.1 Hierarchical Error Estimation ; 5.2 DLY simplification ; 5.3 Assembly.
- 5.3.1 Elemental Matrices 5.3.2 Elemental Right Hand Sides ; 5.3.3 Quadrature Rules ; 5.4 Examples ; Exercises ; 6. Mesh Refinement ; 6.1 Marking Strategies ; 6.2 Refinement ; 6.2.1 Bisection ; 6.2.2 Triangle splitting ; 6.3 Grid Hierarchy ; 6.4 Examples ; Exercises.