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|a 9783319524627
|q (electronic bk.)
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|z 9783319524610
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|a (MiAaPQ)EBC5588874
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|a (OCoLC)1066184466
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|a MiAaPQ
|b eng
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|c MiAaPQ
|d MiAaPQ
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|a QA71-90
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|a Langtangen, Hans Petter.
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|a Solving PDEs in Python :
|b The FEniCS Tutorial I.
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| 250 |
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|a 1st ed.
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| 264 |
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|a Cham :
|b Springer International Publishing AG,
|c 2017.
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|c Ã2016.
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|a 1 online resource (152 pages)
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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| 490 |
1 |
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|a Simula SpringerBriefs on Computing Series ;
|v v.3
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| 505 |
0 |
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|a 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 -- 2.1.3 Choosing a test problem -- 2.2 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 -- 2.3.12 Examining degrees of freedom and vertex values -- 2.4 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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|a 3.3.2 Variational formulation -- 3.3.3 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 -- 4.3.1 Using expressions to define subdomains -- 4.3.2 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 -- 5.1.1 A more general solver function -- 5.1.2 Writing the solver as a Python module -- 5.1.3 Verification and unit tests -- 5.1.4 Parameterizing the number of space dimensions -- 5.2 Working with linear solvers -- 5.2.1 Choosing a linear solver and preconditioner -- 5.2.2 Choosing a linear algebra backend -- 5.2.3 Setting solver parameters -- 5.2.4 An extended solver function -- 5.2.5 A remark regarding unit tests -- 5.2.6 List of linear solver methods and preconditioners -- 5.3 High-level and low-level solver interfaces -- 5.3.1 Linear variational problem and solver objects -- 5.3.2 Explicit assembly and solve -- 5.3.3 Examining matrix and vector values.
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|a 5.4 Degrees of freedom and function evaluation -- 5.4.1 Examining the degrees of freedom -- 5.4.2 Setting the degrees of freedom -- 5.4.3 Function evaluation -- 5.5 Postprocessing computations -- 5.5.1 Test problem -- 5.5.2 Flux computations -- 5.5.3 Computing functionals -- 5.5.4 Computing convergence rates -- 5.5.5 Taking advantage of structured mesh data -- 5.6 Taking the next step -- References -- Index.
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| 588 |
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|a Description based on publisher supplied metadata and other sources.
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| 590 |
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|a Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2023. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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4 |
|a Electronic books.
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| 700 |
1 |
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|a Logg, Anders.
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| 776 |
0 |
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|i Print version:
|a Langtangen, Hans Petter
|t Solving PDEs in Python
|d Cham : Springer International Publishing AG,c2017
|z 9783319524610
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| 797 |
2 |
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|a ProQuest (Firm)
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| 830 |
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|a Simula SpringerBriefs on Computing Series
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| 856 |
4 |
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|u https://ebookcentral.proquest.com/lib/matrademy/detail.action?docID=5588874
|z Click to View
|
