Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

Description

Эта книга представляет собой учебник, написанный исследователями и разработчиками проектов FEniCS о подходах к разработке математического программного обеспечения. Книга начинается со вступительного раздела для начинающих. 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. Front Matter....Pages I-XIII A FEniCS tutorial....Pages 1-73 Front Matter....Pages 75-75 The finite element method....Pages 77-94 Common and unusual finite elements....Pages 95-119 Constructing general reference finite elements....Pages 121-132 Finite element variational forms....Pages 133-140 Finite element assembly....Pages 141-146 Quadrature representation of finite element variational forms....Pages 147-158 Tensor representation of finite element variational forms....Pages 159-162 Discrete optimization of finite element matrix evaluation....Pages 163-169 Front Matter....Pages 171-171 DOLFIN: a C++/Python finite element library....Pages 173-225 FFC: the FEniCS form compiler....Pages 227-238 FErari: an optimizing compiler for variational forms....Pages 239-246 FIAT: numerical construction of finite element basis functions....Pages 247-255 Instant: just-in-time compilation of C/C++ in Python....Pages 257-272 SyFi and SFC: symbolic finite elements and form compilation....Pages 273-282 UFC: a finite element code generation interface....Pages 283-302 UFL: a finite element form language....Pages 303-338 Unicorn: a unified continuum mechanics solver....Pages 339-361 Lessons learned in mixed language programming....Pages 363-381 Front Matter....Pages 383-383 Finite elements for incompressible fluids....Pages 385-397 Front Matter....Pages 383-383 A comparison of finite element schemes for the incompressible Navier–Stokes equations....Pages 399-420 Simulation of transitional flows....Pages 421-440 Computational hemodynamics....Pages 441-454 Cerebrospinal fluid flow....Pages 455-470 Improved Boussinesq equations for surface water waves....Pages 471-504 Applications in solid mechanics....Pages 505-524 A computational framework for nonlinear elasticity....Pages 525-541 Turbulent flow and fluid–structure interaction....Pages 543-552 An adaptive finite element solver for fluid–structure interaction problems....Pages 553-569 Modeling evolving discontinuities....Pages 571-583 Dynamic simulations of convection in the Earth’s mantle....Pages 585-600 Automatic calibration of depositional models....Pages 601-609 A coupled stochastic and deterministic model of Ca 2+ dynamics in the dyadic cleft....Pages 611-627 Electromagnetic waveguide analysis....Pages 629-642 Block preconditioning of systems of PDEs....Pages 643-655 Automated testing of saddle point stability conditions....Pages 657-671 Back Matter....Pages 673-723