  The matrix formation associated to high-order discretizations is known to be
numerically demanding. Based on the existing procedure of interpolation and
lookup, we design a multiscale assembly procedure to reduce the exorbitant
assembly time in the context of isogeometric linear elasticity of complex
microstructured geometries modeled via spline compositions. The developed
isogeometric approach involves a polynomial approximation occurring at the
macro-scale and the use of lookup tables with pre-computed integrals
incorporating the micro-scale information. We provide theoretical insights and
numerical examples to investigate the performance of the procedure. The
strategy turns out to be of great interest not only to form finite element
operators but also to compute other quantities in a fast manner as for instance
sensitivity analyses commonly used in design optimization.
