DASMOD Summer School Lecture Series
Achi Brandt: "Multiscale Computing"
The Multiscale Computational Methodology
The multiscale computational methodology is a systematic approach to achieve efficient calculations of systems that include very many degrees of freedom (particle locations, discrete-function values, picture elements, etc.). It includes fast multigrid solvers for discretized partial-differential equations (PDEs) and for other large systems of local equations; fast summation of long-range (e.g., electrostatic) interactions and fast solvers of integral and inverse PDE problems; collective computation of many eigenfunctions; slowdown-free Monte Carlo simulators; multilevel methods of global optimization; and general procedures for "systematic upscaling".
Systematic Upscaling
Systematic upscaling means the methodical numerical derivation of equations (or statistical rules) that govern a given physical system at increasingly larger scales, starting at a microscopic scale where first-principle laws are known and advancing, scale after scale, to obtain suitable variables and operational rules for processing the system at
much larger scales.
Summary
The multiscale methods are key to surmounting computational bottlenecks in many areas of science and engineering, such as: elementary-particle physics; electronic structures of molecular systems; molecular dynamics of fluids, condensed matter, nano-structures and macromolecules; fluid dynamics; tomography (medical-imaging reconstruction); image segmentation and picture recognition; VLSI design; and various large-scale graph optimization, clustering and classification problems.
Lecture Notes: Multiscale Computational Methods (ppt)
Exercises: Multiscale Computational Methods
