In the GeNuIn project we consider simulation and modelling of multi-body dynamics, and
problems arising in biomedical imaging. Our main scientific goal is to achieve more accurate and
reliable computer simulations of the considered physical phenomena by exploiting the qualitative
properties of the underlying models.
In the first PhD project we are interested in the correct and
accurate simulation of the pipe-laying process from
ships on the bottom of the sea. The problem comprises the modelling of two interacting structures:
a long and thin pipe (modelled as a rod) and a vessel (modelled as a rigid body). The system is
subject to environmental forces (such as sea and wind effects). The control parameters for this
problem are the vessel position and velocity, the pay-out speed and the pipe tension while the
control objectives consist in determining the touchdown position of the pipe as well as ensuring the
integrity of the pipe and to avoid critical deformations.
We have considered numerical methods for the solution of these equations. With appropriate
techniques, called splitting methods, we transform the system into several simpler problems
which are solved in sequence. We use Jacobi elliptic functions and Lie group integrators to solve
each sub-problem. An important feature of the numerical methods is to preserve the dissipative
properties of the system of equations under numerical discretization.
One of the post doscs has worked on numerical methods for similar mechanical systems and
geometric methods for problems with holonomic and nonholonomic constraints.
In the second PhD project we have considered volume preserving integrators. These are
interesting in problems of image registration, shape matching and shape analysis. We have
derived explicit, volume-preserving methods for polynomial divergence-free vector fields of
arbitrary degree. The methods appear to be competitive with state of the art techniques. A different
class of volume preserving integrators has been also derived by considering generating forms and
functions for volume preserving mappings.
The second post doc has worked on different, but related problems in medical imaging.
In this project we will consider
simulation and modelling of multi-body dynamics, nonholonomic
systems, and problems arising in biomedical imaging.
Our main scientific goal is to achieve more accurate and reliable numerical
simulations of the considered physical
phenomena by exploiting the qualitative properties of the
underlying models.
Our starting point are models with an underlying geometric
structure.
Our research team
has been in the international forefront in the development of geometric integ ration algorithms over the last 16 years.
We
are convinced
that the exploitation of this knowledge in a more applied problem setting will lead to
significant advance in the considered applications and give new insight for the
design of
superior
numer ical strategies.