Multiscale CutFEM for Mixed Dimensional Problems

We develop numerical methods for simulation of physical phenomena such as pressure driven flow, heat transfer, and elasticity in heterogenous materials, described by a mixed dimensional model consisting of a bulk domain intersected by embedded surfaces that in turn may intersect. The surfaces model thin structures that have strong effects on the overall solution, for instance fractures.

The methods are based on the Cut Finite Element Method, an unfitted finite element method that can handle complex geometry in a flexible way.

We develop: a geometric modeling system for complex arrangements of intersecting surfaces, multilevel solvers for efficient solution of the discrete equations, and multiscale methods for modeling of the effects of unresolved small fractures.The project team consists of the PI, the coPI, a PhD candidate, and a Post Doc.

The research involves development of numerical methods and theoretical study of their properties using mathematical techniques, implementation of methods in software, and numerical testing on problems ranging from model problems to realistic applications.Mixed dimensional problems enable powerful modeling of important phenomena including mechanics of lightweight materials and subsurface flow with applications in studies of storage of energy and CO2.

The project aims at setting a new standard for numerical modeling and simulation of such problems allowing studies of scenarios not tractable by experiments and theory.