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Project

Finite element preconditioners for algebraic problems as arising in modelling of multiphase microstr

Research Area: Theoretical and computational mechanics
Project Members:
Do-Quang, M.
Neytcheva, M.
Sponsor: VR 

Project Description

We 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.

Publications related to the project

YearTitle
2010Element-by-Element Schur Complement Approximations for General Nonsymmetric Matrices of Two-by-Two Block Form
Lecture Notes in Computer Science 5910 108 (Published)

Internal Reports related to the project

YearTitleDocument Type
2011Solution methods for the Cahn–Hilliard equation discretized by conforming and non-conforming finite elements Technical report