I'm getting more technical books! It may be strange that I got fed up with shopping and fled the store today rather than buy an extra package of socks, but still have the wherewithal to pitch in to a mass book-order that my office is making to SIAM; but so it goes.
- Mechanics:
- Numerical simulation in fluid dynamics: a practical introduction. -- Why? Because, despite the fact that I took a year sequence in fluid mechanics and have a fair amount of experience in parallel computation and numerical solution of certain classes of PDEs, I've only a foggy notion of a lot of computational fluid mechanics.
- Augmented Lagrangian and operator splitting methods in nonlinear mechanics -- I've borrowed this book before, actually. It has a lot of useful stuff in it, both from the numerical side and from the mechanics side.
- Iterative methods
- Iterative methods for solving linear and nonlinear equations -- I want this book for the treatment of Newton-Krylov methods and analysis of inexact Newton methods, mostly. I have a bunch of papers that talk about results in this area, but no unified treatments. Newton-Krylov methods are particularly useful when taking analytical Jacobians becomes painful -- which happens a lot for interesting problems (including problems involving electrostatic-mechanical coupling that I find interesting).
- Iterative methods for solving linear systems -- All sorts of useful analysis that's hard to find elsewhere. I've checked out this book before, too.
- Structured methods
- Spectral methods in MATLAB -- There are three main methods for discretization of partial differential equations: finite elements, finite differences, and spectral elements. Well, okay, there are finite volume methods, too. Still, I know a lot more about the first two than about the third. Considering how much I prefer to get compact models that fit onto a single machine, it sould behoove me to learn more about spectral methods, I think. Besides, Trefethen is an outstanding writer.
- Fast reliable algorithms for matrices with structure -- This deals more with linear systems than with eigensystems (where I've done work on similar methods). Still, I don't have any books on this topic, and the methods are still sufficiently poorly unified that the talks tend to either be high-level or incomprehensible, and the papers all use different notations. Having one book reference on the topic, at least, will be a nice change.
- Other
- The SIAM 100-digit challenge: a study in high-accuracy numerical computing -- In 2002, Nick Trefethen posted a contest in SIAM News: find the first hundred digits of the answers to 10 numerical problems. This book describes how the winning team did it.
Time to stop gloating and go get food.