UID:
kobvindex_HPB1066184466
Umfang:
1 online resource (152 pages)
ISBN:
9783319524627
,
3319524623
,
9783319524610
,
3319524615
Serie:
Simula SpringerBriefs on Computing Ser. ; v. 3
Inhalt:
Computer science; algorithms; visualization; software; programming.
Anmerkung:
5.1.1 A more general solver function.
,
Intro; Foreword; Contents; Preface; 1 Preliminaries; 1.1 The FEniCS Project; 1.2 What you will learn; 1.3 Working with this tutorial; 1.4 Obtaining the software; 1.4.1 Installation using Docker containers; 1.4.2 Installation using Ubuntu packages; 1.4.3 Testing your installation; 1.5 Obtaining the tutorial examples; 1.6 Background knowledge; 1.6.1 Programming in Python; 1.6.2 The finite element method; 2 Fundamentals: Solving the Poisson equation; 2.1 Mathematical problem formulation; 2.1.1 Finite element variational formulation; 2.1.2 Abstract finite element variational formulation.
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2.1.3 Choosing a test problem2.2 FEniCS implementation; 2.2.1 The complete program; 2.2.2 Running the program; 2.3 Dissection of the program; 2.3.1 The important first line; 2.3.2 Generating simple meshes; 2.3.3 Defining the finite element function space; 2.3.4 Defining the trial and test functions; 2.3.5 Defining the boundary conditions; 2.3.6 Defining the source term; 2.3.7 Defining the variational problem; 2.3.8 Forming and solving the linear system; 2.3.9 Plotting the solution using the plot command; 2.3.10 Plotting the solution using ParaView; 2.3.11 Computing the error.
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2.3.12 Examining degrees of freedom and vertex values2.4 Deflection of a membrane; 2.4.1 Scaling the equation; 2.4.2 Defining the mesh; 2.4.3 Defining the load; 2.4.4 Defining the variational problem; 2.4.5 Plotting the solution; 2.4.6 Making curve plots through the domain; 3 A Gallery of finite element solvers; 3.1 The heat equation; 3.1.1 PDE problem; 3.1.2 Variational formulation; 3.1.3 FEniCS implementation; 3.2 A nonlinear Poisson equation; 3.2.1 PDE problem; 3.2.2 Variational formulation; 3.2.3 FEniCS implementation; 3.3 The equations of linear elasticity; 3.3.1 PDE problem.
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3.3.2 Variational formulation3.3.3 FEniCS implementation; 3.4 The Navier-Stokes equations; 3.4.1 PDE problem; 3.4.2 Variational formulation; 3.4.3 FEniCS implementation; 3.5 A system of advection-diffusion-reaction equations; 3.5.1 PDE problem; 3.5.2 Variational formulation; 3.5.3 FEniCS implementation; 4 Subdomains and boundary conditions; 4.1 Combining Dirichlet and Neumann conditions; 4.1.1 PDE problem; 4.1.2 Variational formulation; 4.1.3 FEniCS implementation; 4.2 Setting multiple Dirichlet conditions; 4.3 Defining subdomains for different materials.
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4.3.1 Using expressions to define subdomains4.3.2 Using mesh functions to define subdomains; 4.3.3 Using C++ code snippets to define subdomains; 4.4 Setting multiple Dirichlet, Neumann, and Robin conditions; 4.4.1 Three types of boundary conditions; 4.4.2 PDE problem; 4.4.3 Variational formulation; 4.4.4 FEniCS implementation; 4.4.5 Test problem; 4.4.6 Debugging boundary conditions; 4.5 Generating meshes with subdomains; 4.5.1 PDE problem; 4.5.2 Variational formulation; 4.5.3 FEniCS implementation; 5 Extensions: Improving the Poisson solver; 5.1 Refactoring the Poisson solver.
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English.
Weitere Ausg.:
Print version: Langtangen, Hans Petter. Solving PDEs in Python : The FEniCS Tutorial I. Cham : Springer, ©2017 ISBN 9783319524610
Sprache:
Englisch
DOI:
10.1007/978-3-319-52462-7
URL:
ProQuest Ebook Central
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OAPEN
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