Adaptive unstructured volume remeshing - I: The method

The remeshing algorithm is versatile and can be applied to a number of physical and biological problems, where the local length scales are dictated by the specific problem. In Part II [X. Zheng, J. Lowengrub, A. Anderson, V. Cristini, Adaptive unstructured volume remeshing - II: application to two- and three-dimensional level-set simulations of multiphase flow, J. Comp. Phys., in press], we illustrate the performance of an implementation of the algorithm in finite-element/level-set simulations of deformable droplet and fluid-fluid interface interactions, breakup and coalescence in multiphase flows.