Selected Projects

Surface Vector and Tensor Fields

Discretization of vector and tensor valued surface partial differential equations. This includes the development of higher-order methods and implementing the numerical schemes.
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Software Development of Finite-Element Code

Development of the finite-element framework AMDiS and the numerics environment DUNE, study of discretization methods for distributed solvers, boundary conditions and multi-mesh approaches.
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Discrete Exterior Calculus

Discrete Exterior Calculus is a grid-based geometric discretization technique for differential/integral forms and exterior derivatives. We study the application of the method to various partiatial differential equations on surfaces. A toolbox that can handle the discrete exterior calculus discretization is developed.
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Flow of Complex Fluids

We have studied the influence of finite sized (deformable) spherical particles immersed in a fluid. Additionally, the multiphase flow through porouse and granular matter is studied, with applications in printing processes.
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Interacting Cells

We have formulated a model for the (steric) interaction of many cell (membranes) that is based on a phase-field description for each cell.
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Liquid Crystals on Curved Manifolds

Liquid crystals are composed of anisometric molecules, like rods or plate-lets, and have orientational and translation order. They can be characterized in some sense as a liquid and in another sense as a solid. Forcing the molecules to locate at a fluid-fluid interface and align tagentially to this surface gives rise to interesting arrangements of the crystals.
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Phase-Field Crystal Model

The Phase-Field Crystal model describes the evolution of a particle density of spherical collodal particles in an overdamped limit.
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