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This paper presents a mixed finite element framework for coupled hydro-mechanical-chemical processes in heterogeneous porous media. The framework combines two types of locally conservative discretization schemes: (1) an enriched Galerkin…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
We consider the systematic numerical approximation of Biot's quasistatic model for the consolidation of a poroelastic medium. Various discretization schemes have been analysed for this problem and inf-sup stable finite elements have been…
We consider Biot model with block preconditioners and generalized eigenvalue problems for scalability and robustness to parameters. A discontinuous Galerkin discretization is employed with the displacement and Darcy flow flux discretized as…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
In this paper we present a mixed projection- and density-based topology optimization approach. The aim is to combine the benefits of both parametrizations: the explicit geometric representation provides specific controls on certain design…
This paper concerns the convex optimal control problem governed by multiscale elliptic equations with arbitrarily rough $L^\infty$ coefficients, which has important applications in composite materials and geophysics. We use one of the…
Vugs are small to medium-sized cavities inside rock, which have significant effects on the fluid flow in rock. Moreover, the presence of vugs may have non-trivial impacts on the geomechanical behavior of rock. How to quantify and analyze…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
High-dimensional Bayesian optimization (BO) tasks such as molecular design often require 10,000 function evaluations before obtaining meaningful results. While methods like sparse variational Gaussian processes (SVGPs) reduce computational…
The complexity of performance-based building design stems from the evaluation of numerous candidate design options, driven by the plethora of variables, objectives, and constraints inherent in multi-disciplinary projects. This necessitates…
A key challenge in topology optimization (TopOpt) is that manufacturable structures, being inherently binary, are non-differentiable, creating a fundamental tension with gradient-based optimization. The subpixel-smoothed projection (SSP)…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
Gradient dominance property is a condition weaker than strong convexity, yet sufficiently ensures global convergence even in non-convex optimization. This property finds wide applications in machine learning, reinforcement learning (RL),…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
Stochastic microstructure reconstruction involves digital generation of microstructures that match key statistics and characteristics of a (set of) target microstructure(s). This process enables computational analyses on ensembles of…
Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…
Geometric model fitting is a fundamental research topic in computer vision and it aims to fit and segment multiple-structure data. In this paper, we propose a novel superpixel-guided two-view geometric model fitting method (called SDF),…
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…