Target-matrix Construction Algorithms

A gap in the series of reports describing the Target-matrix paradigm for mesh optimization is filled by describing a method for automatic construction of Target-matrices, so that diverse applications such as shape improvement, geometric-adaptivity, solutionadaptivity, mesh alignment, and anisotropic smoothing can be served while using only a limited set of local quality metrics. The method makes use of the Jacobian matrices at sample points in the initial mesh. A QR-factorization is applied to the Jacobian matrix to isolate different initial mesh properties such as Size, Shape, and Orientation. To construct a Target-matrix, each factor can be retained if the goal is to preserve the property of the initial mesh, or it can be replaced by a new factor based on application or other data if the goal is to improve the initial property. By this method, one can rapidly implement custom-made mesh optimization algorithms in response to requests from application groups desiring improved meshes in order to perform more accurate and efficient simulations. An example from a Cubit application is given.