Project
Finite element preconditioners for algebraic problems as arising in modelling of multiphase microstr
Project DescriptionWe consider numerical simulations of mathematical models to simulate morphological pattern formation and interface motion of multiphase microstructures, an in particular multiphase flow. The aim of this project is to enable fast and reliable numerical solution of the large scale problems as arising from finite element discretizations of the above models. To this end we will consider the construction, analysis and implementation of a fully robust preconditioned iterative solution method based on local features of the Finite Element method (FEM) discretization techniques. The preconditining method will targed non-selfadjoint algebraic systems of equations as arising in dynamical multiphase microstructure simulations but will be applicable to a broader class of problems, arising from partial differential equations (PDEs), discretized by FEM. In the construction of preconditioner, particular emphasize will be given to the utilization of adaptive FEM (AFEM to ensure as low as possible overall computational cost.
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