RKEM Analysis-Suitable Geometry
The Reproducing Kernel Element Method (RKEM) provides a way to
represent smooth geometries on a mesh in a manner suitable for
analysis, i.e. analysis-suitable geometry representation. This
represesentation is derived from a discrete point set, and therefore
is suitable for traditional engineering applications, but also for the
increasingly important area of the life sciences. The life sciences
typically obtain the geometry of an object of interest through a
diagnostic technique, such as CT or MRI imaging.
What is analysis-suitable geometry?
The precise definition depends
on the type of analysis. Thus, analysis-suitable geometry is a
geometry representation that is suitable for use in a particular type
of analysis. For example, a discrete point set is certainly a
representation of geometry, but is not suitable for a finite element
analysis. On the other hand, a mesh consisting of linear triangles
representing a circle is not appropriate for analyzing a pressure
plate. So the definition, and consequently the goal, of
analysis-suitable geometry is to provide a geometric description
that is satisfactory for the problem of interest.
Current research in this area can be broken into three main categories:
RKEM Representation of geometry
Modification of RKEM mesh-based geometry (deformed geometry)
Isogeometric analysis on deformed and un-deformed geometry