Research in computational mechanics and physics is quite application oriented. All the central research topics originate from industry or from research laboratories. The most important areas are problems related to paper and papermaking, free boundary problems, heat radiation and electromagnetism. A significant part of the research funding comes from outside the university.
The goal of the project is to construct simulation models for some key parts of a paper machine, as well as to study the properties of paper. A so-called former section of a paper machine (where fluidlike suspension of water and fibres gradually solidifies to a porous fibre net) is one of the key interests. Mathematical model and numerical methods for the flow of fiber suspension are developed.
Also the modelling of the copying behaviour of paper is considered. The research focuses on modelling the heat and moisture transfer in paper during hot roll nip actions which are common in copying and laser printing machines. Experimental tests have also been carried out in order to obtain verification data for the developed model.
Free boundary problems form one of the main research fields of the laboratory. In the past, the work on free boundary problems and related control problems has initiated the research in nonsmooth optimization and in state constrained control problems. Currently, the laboratory takes part in the ESF programme ``Mathematical Treatment of Free Boundary Problems''.
The theoretical work on free boundary problems concentrates now on modelling the evaporation process. The goal is to find adequate free boundary conditions for a coupled system of Navier-Stokes and Stefan equations, as well as to develop suitable techniques for mathematical analysis and numerical solution of such problems.
Another main line in the research is the use of techniques developed for shape optimization in solving free boundary problems and analysing the solution methods. Often, free boundary conditions can be formulated as optimality conditions of a shape optimization problem. The methods are developed for applications in naval hydrodynamics in co-operation with the Maritime Institute of Finland.
There is also work going on in numerical simulation of industrial processes involving solidification. A numerical model for production of silicon crystals has been constructed which takes into account all the major mechanisms of heat transfer including solidification and heat radiation. For simulation of the continuous casting of steel new linearization algorithms are being developed. The aim is to construct a real time simulation for 3D casting process.
In this project, thermodynamical models for heat radiation are analysed from the mathematical point of view. The models lead to nonlinear integro-differential equations. Currently, the work concentrates on the problems related to diffuse and gray radiation on opaque surfaces and in semi-transparent materials.
The goal has been to introduce efficient and reliable methods for the synthesis of magnetic and electric fields. The results have been documented in a monograph ``Inverse Problems and Optimal Design in Electricity and Magnetism''.