| Research questions: Development of a mathematical/computational model, involving a vector Stefan problem, for particle segregation and dissolution in homogenization of aluminium. The challenge is to devise efficient computing methods for three-dimensional configurations. Development of a fundamental model and an efficient computing method for bubbly multifluid flow, such that mass is conserved and interfaces are predicted accurately. We will also contribute to financial mathematics. To include jumps in stock prices, recently a new model for option pricing has been developed involving partial integro-differential equations. For computing the best exercise time for American-style options, one has to solve a free boundary problem. For this, novel accurate and efficient computing methods are needed. We expect to make progress by a clever combination of moving grid techniques, phase field and level set methods. |
