Automated Solution of Differential Equations by the Finite Element Method

Table of Contents

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   Book Overview
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   Chapter 1 Automated Solution of Differential Equations by the Finite Element Method
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   Chapter 2 The finite element method
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   Chapter 3 Common and unusual finite elements
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   Chapter 4 Constructing general reference finite elements
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   Chapter 5 Finite element variational forms
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   Chapter 6 Finite element assembly
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   Chapter 7 Quadrature representation of finite element variational forms
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   Chapter 8 Tensor representation of finite element variational forms
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    Chapter 9 Discrete optimization of finite element matrix evaluation
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    Chapter 10 DOLFIN: a C++/Python finite element library
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    Chapter 11 FFC: the FEniCS form compiler
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    Chapter 12 FErari: an optimizing compiler for variational forms
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    Chapter 13 FIAT: numerical construction of finite element basis functions
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    Chapter 14 Instant: just-in-time compilation of C/C++ in Python
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    Chapter 15 SyFi and SFC: symbolic finite elements and form compilation
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    Chapter 16 UFC: a finite element code generation interface
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    Chapter 17 UFL: a finite element form language
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    Chapter 18 Unicorn: a unified continuum mechanics solver
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    Chapter 19 Lessons learned in mixed language programming
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    Chapter 20 Finite elements for incompressible fluids
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    Chapter 21 A comparison of finite element schemes for the incompressible Navier–Stokes equations
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    Chapter 22 Simulation of transitional flows
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    Chapter 23 Computational hemodynamics
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    Chapter 24 Cerebrospinal fluid flow
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    Chapter 25 Improved Boussinesq equations for surface water waves
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    Chapter 26 Applications in solid mechanics
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    Chapter 27 A computational framework for nonlinear elasticity
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    Chapter 28 Turbulent flow and fluid–structure interaction
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    Chapter 29 An adaptive finite element solver for fluid–structure interaction problems
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    Chapter 30 Modeling evolving discontinuities
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    Chapter 31 Dynamic simulations of convection in the Earth’s mantle
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    Chapter 32 Automatic calibration of depositional models
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    Chapter 33 A coupled stochastic and deterministic model of Ca2+ dynamics in the dyadic cleft
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    Chapter 34 Electromagnetic waveguide analysis
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    Chapter 35 Block preconditioning of systems of PDEs
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    Chapter 36 Automated testing of saddle point stability conditions