BDDC for mixed-hybrid formulation of flow in porous media with combined mesh dimensions

We extend the Balancing Domain Decomposition by Constraints (BDDC) method to mixed-hybrid finite element discretization of flow in porous media with combined mesh dimensions. It is assumed that the modeler desires to incorporate into the finite element model a detailed description of the reservoir geometry, including a possibly complex structure of vugs, cavities and fractures with various topology and sizes. Use of the mixed-hybrid formulation is motivated by an effort to modify the saddle-point problem into the one which is symmetric, positive definite, so that conjugate gradients with the BDDC preconditioner can be used. The preconditioner then takes an advantage of the special structure of the global finite element matrix. We apply our solver to several academic and real world problems, and the numerical experiments indicate that our approach allows for an efficient and scalable iterative solution of the resulting large systems of equations. MSC: 65F08, 65F10, 65M55, 65N55, 65Y05