Numerical Analysis of Multiscale Problems

✍ Scribed by James Nolen, Grigorios A. Pavliotis (auth.), Ivan G. Graham, Thomas Y. Hou, Omar Lakkis, Robert Scheichl (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2012
• Tongue: English
• Leaves: 381
• Series: Lecture Notes in Computational Science and Engineering 83
• Edition: 1
• Category: Library

✦ Synopsis

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 and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.

✦ Table of Contents

Front Matter....Pages i-x
Multiscale Modelling and Inverse Problems....Pages 1-34
Transported Probability and Mass Density Function (PDF/MDF) Methods for Uncertainty Assessment and Multi-Scale Problems....Pages 35-65
A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods....Pages 67-96
Coarse-Grid Multiscale Model Reduction Techniques for Flows in Heterogeneous Media and Applications....Pages 97-125
Fast Algorithms for High Frequency Wave Propagation....Pages 127-161
Uncertainty Quantification for Subsurface Flow Problems Using Coarse-Scale Models....Pages 163-202
Sparse Tensor Approximation of Parametric Eigenvalue Problems....Pages 203-241
Mixed Multiscale Methods for Heterogeneous Elliptic Problems....Pages 243-283
On Stability of Discretizations of the Helmholtz Equation....Pages 285-324
Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods....Pages 325-363
Back Matter....Pages 365-371

✦ Subjects

Computational Mathematics and Numerical Analysis;Computational Science and Engineering;Appl.Mathematics/Computational Methods of Engineering;Numerical and Computational Physics