This chapter highlights recent developments concerning adaptive wavelet methods for time dependent and stationary problems. The first problem class focusses on hyperbolic conservation laws where wavelet concepts exploit sparse representations of the conserved variables. Regarding the second problem class, we begin with matrix compression in the context of boundary integral equations where the k...

In this report we will discuss some numerical techniques for approximating the Shallow Water equations. In particular we will discuss finite difference schemes, adaptations of Roe’s approximate Riemann solver and the Q-Schemes of Bermudez & Vazquez with the objective of accurately approximating the solution of the Shallow Water equations. We consider four different test problems for the Shallow...

Many optimization techniques have been proposed since the inception of engineering optimization in 1960s. Traditional mathematical modeling-based approaches are incompetent to solve the engineering optimization problems, as these problems have complex system that involves large number of design variables as well as equality or inequality constraints. In order to overcome the various difficultie...

Exploiting the dependence of the refractive index on carrier concentration and temperature, various infrared laser probing techniques enable the experimental analysis of the carrier and heat flow distributions in the interior of semiconductor devices. In this work we present a complete numerical simulation sequence for the whole measurement process. It includes the electrothermal device simulat...

Article history: Received 14 January 2014 Received in revised form 14 August 2014 Accepted 23 August 2014 Available online 27 August 2014