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Department of Information Technology

Multiscale problems and uncertainty quantification


Engineering applications that involves several different scales, multiscale problems (MS), and as well as uncertainty in the data, uncertainty quantification (UQ), are very computationally challenging. Because of the numerical difficulties in solving this kind of problems special numerical methods and algorithms has to be developed.



Multiscale problems are some of the greatest challenges in computational mathematics today. In all branches of the engineering sciences we encounter problems with features on several different scales. A typical example is simulations in a heterogenous media where material data such as module of elasticity, conductivity or permeability, varies in space over several different scales. In order to solve these problems efficiently we propose an adaptive multiscale method where the critical parameters of the method are chosen automatically through an adaptive algorithm.


Uncertainty quantification

In engineering applications it is very common that the data is given by experimental measurements. It is therefore associated with measurement errors. It is natural to model these errors using a probabilistic representation of the data. We develop efficient methods for forward sensitvity analysis of partial differential equations with uncertainty in the data. We present error estimates taking into account both the numerical and the statistical error e.g. when approximating the cumulative distribution function of a quantity of interest using numerical techniques.


Selected publications related to the project.

Updated  2017-02-04 12:16:05 by Kurt Otto.