LAUSR

For pixel-based microstructure representations we propose two different variants of adaptive, quadtree-based mesh coarsening algorithms that serve the purpose of a preprocessor for finite element analyses in the context of numerical homogenization. High resolution is preserved at interfaces for accuracy, coarse-graining in the defect-free interior of phases for efficiency. Error analysis is carried out on the micro scale by error estimation which itself is assessed by true error computation. Modified stress recovery schemes for an error indicator are proposed which overcome the deficits of the standard superconvergent recovery scheme for nodal stress computation in cases of interfaces with stiffness jump. By virtue of error analysis the improved efficiency by the reduction of unknowns is put into relation to the increase of the discretization error and thereby sets a rational basis for decisions on favorable meshes having the best trade-off between accuracy and efficiency as underpinned by various examples.