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 the implementation of the numerical schemes.
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Software Development of Finite-Element Code

Development of the finite element framework AMDiS and the numerical 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 size (deformable) spherical particles immersed in a fluid. In addition, multiphase flow through porous and granular media is studied with applications in printing processes.
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Interacting Cells

We have formulated a model for the (steric) interaction of many cells 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, such as rods or plates, and have an order of orientation and translation. They can be characterized in one sense as a liquid and in another as a solid. Forcing the molecules to locate at a liquid-liquid interface and to orient themselves tangentially to that surface results in interesting crystal arrangements.
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Phase-Field Crystal Model

The phase-field crystal model describes the evolution of a particle density of spherical colloidal particles in an overdamped limit.
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