Multiscale extended finite element method for deformable fractured porous media

Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within computational mechanics community for accurate modeling of deformation, its application natural geoscientific applications is not straightforward. This mainly due to fact that subsurface formations are heterogeneous and span large length scales with fractures at different scales. In this work, we propose a novel multiscale formulation XFEM, based on locally computed basis functions. The local functions capture heterogeneity discontinuities introduced by fractures. Local boundary conditions set follow reduced-dimensional system, order preserve accuracy Using these bases, coarse-scale system then governed algebraically solved, which no enrichment exist. Such allows significant cost reduction, same time, it preserves discrete displacement vector space. solution finally interpolated back fine scale using proposed XFEM (MS-XFEM) also integrated two-stage algebraic iterative solver, through error reduction any desired level can be achieved. Several proof-of-concept numerical tests presented assess performance method. It shown MS-XFEM accurate, when compared fine-scale reference solutions. At significantly more efficient than resolution. As such, develops first scalable method large-scale heavily media.