This research monograph addresses recent developments of wavelet concepts in the context of large scale numerical simulation. It offers a systematic attempt to exploit the sophistication of wavelets as a numerical tool by adapting wavelet bases to the problem at hand. This includes both the construction of wavelets on fairly general domains and the adaptation of wavelet bases to the particular structure of function spaces governing certain variational problems. Those key features of wavelets that make them a powerful tool in numerical analysis and simulation are clearly pointed out. The...
This research monograph addresses recent developments of wavelet concepts in the context of large scale numerical simulation. It offers a systematic a...
This book contains lecture notes of current development 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, fast multipole methods and wavelets. The text includes well designed exercises and project reports on different...
This book contains lecture notes of current development in multiscale modeling, computations and applications. It covers fundamental mathematical t...
This is an overview of the development of adaptive techniques for atmospheric modeling. Written in an educational style, it functions as a starting point for readers interested in adaptive modeling, in atmospheric sciences and beyond. Coverage includes paradigms of adaptive techniques, such as error estimation and adaptation criteria. Mesh generation methods are presented for triangular/tetrahedral and quadrilateral/hexahedral meshes, with a special section on initial meshes for the sphere.
This is an overview of the development of adaptive techniques for atmospheric modeling. Written in an educational style, it functions as a starting...
In the last few years there has been a growing interest in the development of numerical techniques appropriate for the approximation of differential model problems presenting multiscale solutions. This is the case, for instance, with functions displaying a smooth behavior, except in certain regions where sudden and sharp variations are localized. Typical examples are internal or boundary layers. When the number of degrees of freedom in the discretization process is not sufficient to ensure a fine resolution of the layers, some stabilization procedures are needed to avoid unpleasant...
In the last few years there has been a growing interest in the development of numerical techniques appropriate for the approximation of differential m...
The book concerns theoretical and numerical aspects of systems of conservation laws, which can be considered as a mathematical model for the flows of inviscid compressible fluids. Five leading specialists in this area give an overview of the recent results, which include: kinetic methods, non-classical shock waves, viscosity and relaxation methods, a-posteriori error estimates, numerical schemes of higher order on unstructured grids in 3-D, preconditioning and symmetrization of the Euler and Navier-Stokes equations. This book will prove to be very useful for scientists working in...
The book concerns theoretical and numerical aspects of systems of conservation laws, which can be considered as a mathematical model for the flows of ...
The Third International Workshop on Numerical Analysis and Lattice QCD tookplaceattheUniversityofEdinburgh fromJune30th toJuly4th,2003. It continued a sequence which started in 1995 at the University of Kentucky and continuedin1999withaworkshopattheUniversityofWuppertal.Theaimof these workshops is to bring together applied mathematicians and theoretical physicists to stimulate the exchange of ideas between leading experts in the ?elds of lattice QCD and numerical analysis. Indeed, the last ten years have seen quite a substantial increase in cooperation between the two scienti?c communities,...
The Third International Workshop on Numerical Analysis and Lattice QCD tookplaceattheUniversityofEdinburgh fromJune30th toJuly4th,2003. It continued a...
Multiscale problems naturally pose severe challenges for computational science and engineering. The smaller scales must be well resolved over the range of the larger scales. Challenging multiscale problems are very common and are found in e.g. materials science, fluid mechanics, electrical and mechanical engineering. Homogenization, subgrid modelling, heterogeneous multiscale methods, multigrid, multipole, and adaptive algorithms are examples of methods to tackle these problems. This volume is an overview of current mathematical and computational methods for problems with multiple scales with...
Multiscale problems naturally pose severe challenges for computational science and engineering. The smaller scales must be well resolved over the rang...
The first international symposium on mathematical foundations of the finite element method was held at the University of Maryland in 1973. During the last three decades there has been great progress in the theory and practice of solving partial differential equations, and research has extended in various directions. Full-scale nonlinear problems have come within the range of nu merical simulation. The importance of mathematical modeling and analysis in science and engineering is steadily increasing. In addition, new possibili ties of analysing the reliability of computations have appeared....
The first international symposium on mathematical foundations of the finite element method was held at the University of Maryland in 1973. During the ...
In Douglas Adams' book 'Hitchhiker's Guide to the Galaxy', hyper-intelligent beings reached a point in their existence where they wanted to understand the purpose of their own existence and the universe. They built a supercomputer, called Deep Thought, and upon completion, they asked it for the answer to the ultimate question of life, the universe and everything else. The computer worked for several millennia on the answers to all these questions. When the day arrived for hyper-intelligent beings the to receive the answer, they were stunned, shocked and disappointed to hear that the answer...
In Douglas Adams' book 'Hitchhiker's Guide to the Galaxy', hyper-intelligent beings reached a point in their existence where they wanted to understand...
Meshfree methods for the numerical solution of partial differential equations are becoming more and more mainstream in many areas of applications. This volume represents the state-of-the-art in meshfree methods. It consists of articles which address the different meshfree techniques, their mathematical properties and their application in applied mathematics, physics and engineering.
Meshfree methods for the numerical solution of partial differential equations are becoming more and more mainstream in many areas of applications. ...
