2011: Multiscale Methods
The 2011 Winter School will take place from Sunday January 23rd to Friday January 28th at Dr. Holms Hotel, Geilo, Norway. The winter school is the eleventh in a series of fifteen winter schools organized by SINTEF.

Mathematical and numerical methods for multiscale problems

Almost all problems in science and engineering involve processes and mechanisms that act on multiple spatial and temporal scales. Physical and man-made systems can be described on many levels, from quantum mechanics and molecular dynamics, via the mesoscale or nano-level, to continuum and system-level descriptions. For a specific problem, it is common to refer to the particular scale one is interested in as the macroscale. Scales smaller than the macroscale are often referred to as microscale, and sometimes one also introduces intermediate scales that are referred to as mesoscales.

A multiscale problem can be defined as a problem where the macroscopic behaviour of a system is strongly affected by processes and properties from micro- and mesoscales. Solving the 'whole' problem at once is seldom possible as it would involve too many variables or too large scale differences to be computationally tractable, even on today's largest supercomputers. The traditional alternative has therefore been to compute effective parameters and usethese to communicate information between models on different scales. However, as the need for more accurate modelling increases, traditional homogenization and upscaling methods are becoming inadequate to answer advanced queries about multiscale problems. In some cases, effective properties may not be suffcient to properly describe complex interactions between macroscale and microscale processes; in other cases, one may not even know what are the correct properties to average.

In this winter school, we will focus on a few selected and challenging multiscale problem from material science and subsurface flow, and present mathematical and numerical methods suitable for these problems.


  Sunday Monday Tuesday Wednesday Thursday Friday
07:00 - 09:00   Breakfast
09:00 - 10:30   KR/FL JMN IL TR HvB
10:30 - 12:30   Break (lunch 12:30 - 14:00) JMN, TK
12:30 - 14:45   Lunch, End
15:00 - 16:30   KR/FL CT KAL TR  
16:30 - 17:00   Coffee  
17:00 - 18:30 TK KR/FL IL   HvB  


TK: Trond Kvamsdal: Overview of multiscale methods
Presentation (PDF)
KR/FL: Kenneth Runesson/ Fredrik Larsson: Computational homogenization
Presentation 1 (PDF)
Presentation 2 (PDF)
Presentation 3 (PDF)
JMN: Jan M. Nordbotten: Multiscale methods with applications to CO2 storage
Presentation (PDF)
CT: Christian Thaulow: Atomistic and multiscale material modelling
Presentation 1 (PDF)
Presentation 2 (PDF)
IL: Ivan Lunati: Multiscale finite-volume methods for subsurface flow
Presentation (PDF)
KAL: Knut-Andreas Lie: Multiscale mixed finite-element methods for subsurface flow
Presentation 1 (PDF)
TR: Talal Rahman: Multiscale domain decomposition and mortar methods
Presentation 1 (PDF)
Presentation 2 (PDF)
Presentation 3 (PDF)
Presentation 4 (PDF)
Presentation 5 (PDF)
Presentation 6 (PDF)
Presentation 7 (PDF)
Presentation 8 (PDF)
HvB: E.H. (Harald) van Brummelen: Multigrid methods
Presentation 1 (PDF)
Presentation 2 (PDF)

Scientific committee

Local organizers


The participants are expected to stay at Dr. Holms Hotel, where we have reserved a limited number of rooms. Please register early. NB! The registration is binding after the deadline.

Published October 13, 2010