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Uncertainty quantification for random fields estimated from effective moduli of elasticity (2018)
Conference Proceeding
Pierce-Brown, J., Neves, L. C., & Brown, D. L. (2018). Uncertainty quantification for random fields estimated from effective moduli of elasticity. In Proceedings of the 8th International Workshop on Reliable Computing "Computing with Confidence", 16-18 July 2018, University of Liverpool, Liverpool, UK, 51-62

The stochastic finite element method is a useful tool to calculate the response of systems subject to uncertain parameters and has been applied extensively to analyse structures composed of randomly heterogeneous materials. The methodology to estimat... Read More

A hierarchical finite element Monte Carlo method for stochastic two-scale elliptic equations (2017)
Journal Article
stochastic two-scale elliptic equations. Journal of Computational and Applied Mathematics, 323, doi:10.1016/j.cam.2017.04.004. ISSN 0377-0427

We consider two-scale elliptic equations whose coefficients are random. In particular, we study two cases: in the first case, the coefficients are obtained from an ergodic dynamical system acting on a probability space, and in the second the case, th... Read More

Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations (2017)
Journal Article
Brown, D., Gallistl, D., & Peterseim, D. (in press). Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations. Lecture Notes in Computational Science and Engineering, 115, doi:10.1007/978-3-319-51954-8_6. ISSN 1439-7358

This paper presents a multiscale Petrov-Galerkin finite element method for time-harmonic acoustic scattering problems with heterogeneous coefficients in the high-frequency regime. We show that the method is pollution free also in the case of heteroge... Read More

Effective equations governing an active poroelastic medium (2017)
Journal Article
Collis, J., Brown, D., Hubbard, M. E., & O'Dea, R. D. (2017). Effective equations governing an active poroelastic medium. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2198), doi:10.1098/rspa.2016.0755. ISSN 1364-5021

In this work we consider the spatial homogenization of a coupled transport and fluid-structure interaction model, to the end of deriving a system of effective equations describing the flow, elastic deformation, and transport in an active poroelastic... Read More

An energy-stable time-integrator for phase-field models (2016)
Journal Article
Vignal, P., Collier, N., Dalcin, L., Brown, D., & Calo, V. (2017). An energy-stable time-integrator for phase-field models. Computer Methods in Applied Mechanics and Engineering, 316, doi:10.1016/j.cma.2016.12.017. ISSN 0045-7825

We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of th... Read More

A Generalized Multiscale Finite Element Method for poroelasticity problems II: nonlinear coupling (2015)
Journal Article
Brown, D., & Vasilyeva, M. (2015). A Generalized Multiscale Finite Element Method for poroelasticity problems II: nonlinear coupling. Journal of Computational and Applied Mathematics, 297, doi:10.1016/j.cam.2015.11.007. ISSN 0377-0427

In this paper, we consider the numerical solution of some nonlinear poroelasticity problems that are of Biot type and develop a general algorithm for solving nonlinear coupled systems. We discuss the difficulties associated with flow and mechanics in... Read More