|
The R-functions method (RFM) is a meshfree method
that allows all prescribed boundary conditions to be satisfied
exactly on all boundary points. The original idea underlying
RFM is due to Kantorovich (1958). He proposed that the homogeneous
Dirichlet conditions may be satisfied exactly by representing
the solution as the product of two functions: (1) an real-valued
function that takes on zero values on the boundary points;
and (2) an unknown function that allows to satisfy (exactly
or approximately) the differential equation of the problem.
Rvachev generalized this idea to any and all types of boundary
value problems using the concept of RFM solution structure.
A solution structure combines in one data structure portions
of a geometrical model described by implicit functions, given
boundary conditions and preferred system of basis functions.
The solution structures for many boundary conditions are known
and cataloged. |
| [1] V. Shapiro and I. Tsukanov, Meshfree Simulation of Deforming
Domains, Computer-Aided Design , Vol. 31, No. 7, 1999, pp.
459-471
[2] V. L. Rvachev,
T.I.Sheiko, V.Shapiro and I.Tsukanov, On Completeness of RFM
Solution Structures, Computational Mechanics, special issue
on meshfree methods, Vol. 25, 2000, pp. 305-316
[3] V. L.
Rvachev, T.I. Sheiko, V. Shapiro, I. Tsukanov, Transfinite
Interpolation Over Implicitly Defined Sets, Computer Aided
Geometric Design, Vol. 18, No. 4, 2001, pp.195-220 |
