Meshfree simulation of deforming domains

Spatial discretization of the domain and/or boundary conditions prevents application of many numerical techniques to physical problems with time-varying geometry and boundary conditions. By contrast, the R-functions method (RFM) for solving boundary and initial value problems discretizes not the domain but the underlying functional space, while the prescribed boundary conditions are satisfied exactly. The clean and modular separation of geometric information from the numerical procedures results in a solution technique that is essentially meshfree and allows an almost effortless modification of geometrical shapes, boundary conditions, and the governing equations. We show that these properties of the RFM make it highly suitable for automated modeling and simulation of nonstationary physical problems with time-varying geometries and boundary conditions.