This book introduces transfinite interpolation as a generalization of interpolation of data prescribed at a finite number of points to data prescribed on a geometrically structured set, such as a piece of curve, surface, or submanifold. The time-independent theory is readily extended to a moving/deforming data set whose dynamics is specified in a Eulerian or Lagrangian framework. The resulting innovative tools cover a very broad spectrum of applications in fluid mechanics, geometric optimization, and imaging. The authors chose to focus on the dynamical mesh updating in fluid mechanics and the construction of velocity fields from the boundary expression of the shape derivative. Transfinite Interpolations and Eulerian/Lagrangian Dynamics is a self-contained graduate-level text that integrates theory, applications, numerical approximations, and computational techniques. It applies transfinite interpolation methods to finite element mesh adaptation and ALE fluid-structure interaction. Specialists in applied mathematics, physics, mechanics, computational sciences, imaging sciences, and engineering will find this book of interest.

This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.

Physics and Ecology in Fluids: Modeling and Numerical Experiments develops mathematical and numerical modeling methodologies for coupled biological-hydrodynamic problems with a focus on process studies. The modeling is presented in a way that discusses mathematical background but does not depend on a large body of mathematical pre-requisites or experience. Models are built up from simple, to complex. This includes discussion of approximations and shortcuts commonly made by large computational models for natural bodies of water. Computational approaches are presented using conceptual explanations and pseudo-code along with well-documented, open-source code. Over a dozen codes that run locally on the reader's laptop provide hands on experience with various aspects of the modeling process and its scientific results. One large-scale code for basin scale modeling based on the Discontinuous Galerkin methodology is presented, along with a self-contained discussion of theoretical background and implementation details. Physics and Ecology in Fluids is written for graduate students, academic researchers and government scientists. Professors can use the book as a stand-alone resource for a one term graduate course, or to supplement teaching of their own graduate courses. All readers may also use the book as background/user's guide for the software included with the book. - Presents accessible codes along with clear explanations of the mathematical modeling process that leads up to the code - Provides a consistent development of the mathematical models for hydrodynamic and biological modeling, which are rarely covered together - Includes an informal, discussion-style tone throughout, but with serious applied mathematics content, allowing a level of detail relevant for multiple reader types

The Encyclopedia of Computational Mechanics provides a comprehensive collection of knowledge about the theory and practice of computational mechanics.

This book presents the state-of-the-art in simulation on supercomputers. Leading researchers present results achieved on systems of the High Performance Computing Center Stuttgart (HLRS) for the year 2010. The reports cover all fields of computational science and engineering, ranging from CFD to computational physics and chemistry to computer science, with a special emphasis on industrially relevant applications. Presenting results for both vector systems and microprocessor-based systems, the book makes it possible to compare the performance levels and usability of various architectures. As HLRS operates the largest NEC SX-8 vector system in the world, this book gives an excellent insight into the potential of vector systems, covering the main methods in high performance computing. Its outstanding results in achieving the highest performance for production codes are of particular interest for both scientists and engineers. The book includes a wealth of color illustrations and tables.