Generation of curvilinear coordinates on multiply connected regions with boundary singularities

A new algorithm to generate smooth two-dimensional boundary conforming coordinates, with grid lines control, on multiply connected regions including boundary singularities, is devised. The technique fits into the category of elliptic grid generators, since it is based on the numerical solution of Poisson equations. The physical domain D is transformed into a topologically equivalent connected rectangular domain D ′ by defining a branch cut inside D . Control of the grid line spacing over the multiply connected regions is established by appropriately distributing nodal points on the branch cut, and on other boundary curves. Simple and computationally convenient expressions for the control functions, present in the Poisson system, are obtained from this initial distribution of points. Thus, a natural link between clustering properties and the control functions is created. Fixing the nodal points on the branch cut causes the convergence of the numerical method about the singular boundary points. An iterative smoothing process relocating the branch cut is described. As a result, smooth grids are obtained. Grid quality analysis shows that coordinate line orthogonality in the new meshes is superior than in similar grids obtained from a well-known commercial software. The algorithm is successfully tested over a variety of multiply connected domains. The computational advantage of this novel grids is revealed by using them to numerically model the vibrations of complexly shaped annular membranes.