L Ridgway Scott / L. Ridgway Scott
Librería 7artes
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Librería Elías (Asturias)
Librería Kolima (Madrid)
Librería Proteo (Málaga)
Introduction to Automated Modeling with FEniCS exploressolution of partial differential equations via the finiteelement method. It illustrates the use of automated softwaregeneration via the FEniCS Project systems. The book reviewsmost common types of partial differential equations arisingin technical simulation. It is ideal for engineers and forcomputational and applied mathematicians.PDEs are used pervasively in science, engineering, and technologyto model phenomena of interest. The most widely used techniqueto convert a PDE into a computable form is the finite element method.This book is primarily about PDEs as they are used in models. Ouremphasis is on the diversity of PDEs that occur in practice, theirfeatures and their foibles. Our intent is to enable explorationof new models and to show how easily this can be done. However,this approach is not without caveats. We describe pitfalls in variousaspects of the use of PDE models. We show how to be sure that a PDEmodel is well posed in many cases. In particular, we use this theoryto understand appropriate boundary conditions.Secondarily, the book introduces basic concepts of numerical methodsfor approximating the solutions of PDEs. This is done so that thelanguage used by software from the FEniCS Project can be properlyunderstood. We limit the discussion of numerical methods as much aspossible, except when it is essential to avoid catastrophes.A tertiary objective is to present some examples of the modelingprocess. One important type of model is derived by specializing amore general model. An important example of this is the plate modelin structural mechanics. We show how the plate model is derived fromthe general elasticity model and indicate some issues that ariserelated to it. When relevant, we explain other modeling approaches aswell. Ultimately, FEniCS can support an automated approach to modeling.
