Tetrahedral Mesh Optimisation and Adaptivity for Steady-state and Transient ®nite Element Calculations

A method for optimising a pre-existing mesh of tetrahedral ®nite elements is described. It is based on a series of mesh connectivity and node position searches of the landscape de®ning mesh quality. A Riemannian metric, re¯ecting the a posteriori error measure, is used to calculate element size and shape. A functional is de®ned which embodies both shape and size quality of an element with respect to the metric, and is used to gauge mesh quality. A heuristic-based local search strategy is adopted ± local in the sense that it has no hill-climbing abilities. The paper presents applications of the method to complex, steady-state and time-dependent problems which highlight its anisotropic, feature-capturing abilities. Numerical evidence is provided which suggests that the computational complexity (time) of the proposed algorithm varies linearly with the number of elements or nodes of the ®nite element mesh.