8 papers
Hierarchical Matrix Approximations of Hessians Arising in Inverse Problems Governed by PDEs
Ilona Ambartsumyan, Wajih Boukaram, Tan Bui-Thanh +5
Hessian operators arising in inverse problems governed by partial differential equations (PDEs) play a critical role in delivering efficient, dimension-independent convergence for…
A coupled multipoint stress -- multipoint flux mixed finite element method for the Biot system of poroelasticity
Ilona Ambartsumyan, Eldar Khattatov, Ivan Yotov
We present a mixed finite element method for a five-field formulation of the Biot system of poroelasticity that reduces to a cell-centered pressure-displacement system on simplicia…
A multipoint stress mixed finite element method for elasticity on quadrilateral grids
Ilona Ambartsumyan, Eldar Khattatov, Jan M. Nordbotten +1
We develop a multipoint stress mixed finite element method for linear elasticity with weak stress symmetry on quadrilateral grids, which can be reduced to a symmetric and positive…
A multipoint stress mixed finite element method for elasticity on simplicial grids
Ilona Ambartsumyan, Eldar Khattatov, Jan M. Nordbotten +1
We develop a new multipoint stress mixed finite element method for linear elasticity with weakly enforced stress symmetry on simplicial grids. Motivated by the multipoint flux mixe…
A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media
Ilona Ambartsumyan, Vincent J. Ervin, Truong Nguyen +1
We develop and analyze a model for the interaction of a quasi-Newtonian free fluid with a poroelastic medium. The flow in the fluid region is described by the nonlinear Stokes equa…
Stochastic multiscale flux basis for Stokes-Darcy flows
Ilona Ambartsumyan, Eldar Khattatov, ChangQing Wang +1
Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties…