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Inside Finite Elements.

By: Material type: TextTextSeries: De Gruyter Textbook SeriesPublisher: Berlin/Boston : Walter de Gruyter GmbH, 2016Copyright date: ©2016Edition: 1st edDescription: 1 online resource (158 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110373202
Subject(s): Genre/Form: Additional physical formats: Print version:: Inside Finite ElementsLOC classification:
  • QC20.7.F56 -- .W45 2016eb
Online resources:
Contents:
Intro -- Contents -- 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 -- 7. Multigrid -- 7.1 Smoothers -- 7.2 Coarse Grid Correction -- 7.3 Multigrid Solver -- 7.4 Additive Multilevel Preconditioners -- 7.5 Examples -- Exercises -- 8. Elastomechanics -- 8.1 Linear Elastomechanics -- 8.2 Vectorial Finite Elements -- 8.3 Time-harmonic Dynamics -- 8.3.1 Eigenfunctions -- 8.4 Examples -- 8.4.1 Stationary Problems -- 8.4.2 Oscillatory Problems -- Exercises -- 9. Fluid Mechanics -- 9.1 Stokes Equation -- 9.2 Uzawa's Method.
9.3 Examples -- 9.3.1 Discretization -- 9.3.2 Iterative Solution -- Exercises -- A. Grid Data Structure -- B. Function Reference -- Bibliography -- Index.
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Intro -- Contents -- 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 -- 7. Multigrid -- 7.1 Smoothers -- 7.2 Coarse Grid Correction -- 7.3 Multigrid Solver -- 7.4 Additive Multilevel Preconditioners -- 7.5 Examples -- Exercises -- 8. Elastomechanics -- 8.1 Linear Elastomechanics -- 8.2 Vectorial Finite Elements -- 8.3 Time-harmonic Dynamics -- 8.3.1 Eigenfunctions -- 8.4 Examples -- 8.4.1 Stationary Problems -- 8.4.2 Oscillatory Problems -- Exercises -- 9. Fluid Mechanics -- 9.1 Stokes Equation -- 9.2 Uzawa's Method.

9.3 Examples -- 9.3.1 Discretization -- 9.3.2 Iterative Solution -- Exercises -- A. Grid Data Structure -- B. Function Reference -- Bibliography -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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