ISBN: 1949133001 9781949133004

Category: Computers / General

Page count: 374

<p>Introduction to Automated Modeling with FEniCS explores<br> solution of partial differential equations via the finite<br> element method. It illustrates the use of automated software<br> generation via the FEniCS Project systems. The book reviews<br> most common types of partial differential equations arising<br> in technical simulation. It is ideal for engineers and for<br> computational and applied mathematicians.</p><p>PDEs are used pervasively in science, engineering, and technology<br> to model phenomena of interest. The most widely used technique<br> to convert a PDE into a computable form is the finite element method.<br> This book is primarily about PDEs as they are used in models. Our<br> emphasis is on the diversity of PDEs that occur in practice, their<br> features and their foibles. Our intent is to enable exploration<br> of new models and to show how easily this can be done. However, <br> this approach is not without caveats. We describe pitfalls in various<br> aspects of the use of PDE models. We show how to be sure that a PDE<br> model is well posed in many cases. In particular, we use this theory<br> to understand appropriate boundary conditions.</p><p>Secondarily, the book introduces basic concepts of numerical methods<br> for approximating the solutions of PDEs. This is done so that the<br> language used by software from the FEniCS Project can be properly<br> understood. We limit the discussion of numerical methods as much as<br> possible, except when it is essential to avoid catastrophes.</p><p>A tertiary objective is to present some examples of the modeling<br> process. One important type of model is derived by specializing a<br> more general model. An important example of this is the plate model<br> in structural mechanics. We show how the plate model is derived from<br> the general elasticity model and indicate some issues that arise<br> related to it. When relevant, we explain other modeling approaches as<br> well. Ultimately, FEniCS can support an automated approach to modeling.