| The term "meshfree" indicates that modeling and/or analysis technique
does not require that geometric model is represented by a conforming mesh
of elements. A background mesh may or may not be used for computations, but the
geometric representation neither depends on it nor conforms to it
(example).
Our meshfree approach interpolates
all boundary conditions directly from geometric model using normalized
functions. Such functions may be constructed automatically for
most types of geometric models using theory of R-functions.
The interpolated boundary conditions are combined with a set of basis functions,
typically on a uniform rectangular grid, into a solution
structure for the problem at hand that is assembled and solved
at run time. The solution procedure requires automatic
differentiation, adaptive numerical
integration, and visualization over meshfree domain.
The underlying mathematical method is based on the theory of R-functions
and is sometimes called RFM. It can be also viewed as partition
of unity method or generalized finite element method where enrichment functions
are constructed using R-functions. Method has been applied to virtually
all types of boundary value problems; example applications include
heat
transfer in time-varying domain, hydrodynamics,
torsion,
and geometric design (fairing). | 
