Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
Anders Logg, Kent-Andre Mardal, Garth Wells
Springer Science & Business Media, Feb 24, 2012 - Computers - 731 pages
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
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algorithm arguments assemble Automated basis functions bilinear form boundary conditions Brezzi C++ code CBC.Twist cell Chapter coefficients components computed const convection corresponding defined degrees of freedom derivatives Differential Equations dimension Dirichlet boundary conditions discontinuous discrete DOLFIN domain eigenvalue error evaluation example expression facets FEniCS Figure finite element method finite element space flow fluid form compiler formulation function space global grad implementation integration iteration Lagrange elements linear system Logg mapping matrix mesh module multilinear form Nédélec nonlinear NumPy NumPy arrays object operator optimization parameters piecewise polynomials preconditioner pressure Python code Python interface quadrature reference representation scalar scheme Simula Research Laboratory simulation solution solve solver specified stability subdomain SWIG tensor contraction triangle typemap values variable variational forms variational problem vector velocity vertex vertices wave zero