"Artificial Boundary Method" systematically introduces the artificial boundary method for the numerical solutions of partial differential equations in unbounded domains. Detailed discussions treat different types of problems, including Laplace, Helmholtz, heat, Schrödinger, and Navier and Stokes equations. Both numerical methods and error analysis are discussed. The book is intended for resear…
These are the proceedings of the 20th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linearor nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel comp…
The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell’s equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from researchers across many disciplines. Thanks to enormou…
The book is the follow-up to its predecessor “Automation, Communication and Cybernetics in Science and Engineering 2009/2010” and includes a representative selection of all scientific publications published between 07/2011 and 06/2012 in various books, journals and conference proceedings by the researchers of the following institute cluster: IMA - Institute of Information Management in M…
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 2012. The reports cover all fields of computational science and engineering ranging from CFD via computational physics and chemistry to computer science with a special emphasis on industrially rele…
This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a mi…
The book presents the state of the art in high performance computing and simulation on modern supercomputer architectures. It covers trends in hardware and software development in general and specifically the future of high performance systems and heterogeneous architectures. The application contributions cover computational fluid dynamics, material science, medical applications and climate res…
In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach…
Computational biology, mathematical biology, biology and biomedicine are currently undergoing spectacular progresses due to a synergy between technological advances and inputs from physics, chemistry, mathematics, statistics and computer science. The goal of this book is to evidence this synergy by describing selected developments in the following fields: bioinformatics, biomedicine and neurosc…
This book presents the state of the art in high-performance computing and simulation on modern supercomputer architectures. It covers trends in hardware and software development in general and specifically the future of high-performance systems and heterogeneous architectures. The application contributions cover computational fluid dynamics, material science, medical applications and climate re…