Mesh association by projection along smoothed-normal-vector fields: Association of closed manifolds

The necessity to associate two geometrically distinct meshes arises in many engineering applications. Current mesh-association algorithms have generally been developed for piecewise-linear geometry approximations, and their extension to the high-order geometry representations corresponding to highorder finite element methods is nontrivial. In the present work, we therefore propose a mesh-association method for high-order geometry representations. The associative map defines the image of a point on a mesh as its projection along a so-called smoothed-normal-vector field onto the other mesh. The smoothednormal- vector field is defined by the solution of a modified Helmholtz equation with right-hand-side data corresponding to the normal-vector field. Classical regularity theory conveys that the smoothed-normalvector field is continuously differentiable, which renders it well suited for a projection-based association. Moreover, the regularity of the smoothed-normal-vector field increases with the regularity of the normalvector field and, hence, the smoothness of the association increases with the smoothness of the geometry representations. The proposed association method thus accommodates the higher regularity that can be provided by high-order geometry representations. Several important properties of smoothed-normalprojection association are established by analysis and by numerical experiments on closed manifolds. Copyright q 2007 John Wiley & Sons, Ltd