Dual field structure-preserving discretization of a Cosserat rod

MSc assignment

Real-world phenomena are often described through mathematics by differential equations. These differential equations describe phenomena in a time-continuous manner. However, when a computer simulation is desired for systems described by these differential equations, it is needed to discretize these equations in order for a computer to understand.

Over the years a variety of discretization methods were developed to be able to produce simulations. Some discretization methods preserve certain time-continuous aspects of differential equations better than other methods. It is also sometimes more computationally efficient to choose one method over the other. For example in order to work with a
coarser mesh and still get usable simulation results for mesh-based methods.

Through the use of exterior calculus, the dual-field method reformulates the differential equation in two equivalent ways on the time-continuous level but differs on a discrete level. This thesis will focus on the use of the dual-field representation of a Cosserat rod model described by differential equations and explores the structure-preserving properties and efficiencies of the discretized versions of the primal and dual version of the model.