The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the...
The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining cha...
This proceedings volume collects review articles that summarize research conducted at the Munich Centre of Advanced Computing (MAC) from 2008 to 2012. The articles address the increasing gap between what should be possible in Computational Science and Engineering due to recent advances in algorithms, hardware, and networks, and what can actually be achieved in practice; they also examine novel computing architectures, where computation itself is a multifaceted process, with hardware awareness or ubiquitous parallelism due to many-core systems being just two of the challenges faced. Topics...
This proceedings volume collects review articles that summarize research conducted at the Munich Centre of Advanced Computing (MAC) from 2008 to 2012....
The scope ofthis book is to discuss recent numerical and algorithmic tools for the solution of certain flow problems arising in Computational Fluid Dynam ics (CFD). Here, we mainly restrict ourselves to the case ofthe incompressible Navier-Stokes equations, Ut - v u + U . V'u+ V'p = f, V'.u = o. (1) These basic equations already play an important role in CFD, both for math ematicians as well as for more practical scientists: Physically important facts with "real life" character can be described by them, including also economical aspects in industrial applications. On the other hand, the...
The scope ofthis book is to discuss recent numerical and algorithmic tools for the solution of certain flow problems arising in Computational Fluid Dy...
Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse grids make it possible to overcome the "curse" of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparse grids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present...
Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical ...
Warm Dense Matter (WDM) occupies a loosely defined region of phase space intermediate between solid, liquid, gas, and plasma, and typically shares characteristics of two or more of these phases. WDM is generally associated with the combination of strongly coupled ions and moderately degenerate electrons, and careful attention to quantum physics and electronic structure is essential. The lack of a small perturbation parameter greatly limits approximate attempts at its accurate description. Since WDM resides at the intersection of solid state and high energy density physics, many high energy...
Warm Dense Matter (WDM) occupies a loosely defined region of phase space intermediate between solid, liquid, gas, and plasma, and typically shares cha...
Thisis the proceedings of a conference held near Bordeauxin spring 2013. The main topic is high order methods for compressible fluid dynamics. This is a quite hot topic these days as seen from the number of publications in journals, conferences but also mini symposium organised in international conferences. A selection of the papers will be includedin the proceedings. The topic ranges from Discontinuous Galerin, finite element methods, Lagrangian hydrodynamics, finite difference methods andapplications to uncertainty quantification."
Thisis the proceedings of a conference held near Bordeauxin spring 2013. The main topic is high order methods for compressible fluid dynamics. This is...
This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method.
This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numer...
The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling...
The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attendin...
This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The...
This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control an...
In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 "Mathematical Methods for Extracting Quantifiable Information from Complex Systems." This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also...
In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 "Mathematical Methods for Extracting Quantifiable Informat...
