  A novel and efficient approach which is based on the framework of
isogeometric analysis for elliptic homogenization problems is proposed. These
problems possess highly oscillating coefficients leading to extremely high
computational expenses while using traditional finite element methods. The
isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in
this paper is regarded as an alternative approach to the standard Finite
Element Heterogeneous Multiscale Method (FE-HMM) which is currently an
effective framework to solve these problems. The method utilizes non-uniform
rational B-splines (NURBS) in both macro and micro levels instead of standard
Lagrange basis. Beside the ability to describe exactly the geometry, it
tremendously facilitates high-order macroscopic/microscopic discretizations
thanks to the flexibility of refinement and degree elevation with an arbitrary
continuity level provided by NURBS basis functions. A priori error estimates of
the discretization error coming from macro and micro meshes and optimal micro
refinement strategies for macro/micro NURBS basis functions of arbitrary orders
are derived. Numerical results show the excellent performance of the proposed
method.
