Numerical Analysis of Multiscale Problems
Description
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.
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Content
- Intro
- Numerical Analysis of Multiscale Problems
- Preface
- Contents
- Multiscale Modelling and Inverse Problems
- Transported Probability and Mass Density Function (PDF/MDF) Methods for Uncertainty Assessment and Multi-Scale Problems
- A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods
- Coarse-Grid Multiscale Model Reduction Techniques for Flows in Heterogeneous Media and Applications
- Fast Algorithms for High Frequency Wave Propagation
- Uncertainty Quantification for Subsurface Flow Problems Using Coarse-Scale Models
- Sparse Tensor Approximation of Parametric Eigenvalue Problems
- Mixed Multiscale Methods for Heterogeneous Elliptic Problems
- On Stability of Discretizations of the Helmholtz Equation
- Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods
