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In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…
Linear poroelasticity models have a number of important applications in biology and geophysics. In particular, Biot's consolidation model is a well-known model that describes the coupled interaction between the linear response of a porous…
We present a mathematical framework and computational methods to optimally design a finite number of sequential experiments. We formulate this sequential optimal experimental design (sOED) problem as a finite-horizon partially observable…
In this work, we employ the Constraint Energy Minimizing Generalized Multiscale Finite Element Method (CEM-GMsFEM) to solve the problem of linear heterogeneous poroelasticity with coefficients of high contrast. The proposed method makes use…
In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational…
In this work we introduce and analyze a new multiscale method for strongly nonlinear monotone equations in the spirit of the Localized Orthogonal Decomposition. A problem-adapted multiscale space is constructed by solving linear local…
The growing use of composite materials in engineering applications has accelerated the demand for computational methods to accurately predict their complex behavior. Multiscale modeling based on computational homogenization is a potentially…
This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…
In this work, we introduce a novel algorithm for the Biot problem based on a Hybrid High-Order discretization of the mechanics and a Symmetric Weighted Interior Penalty discretization of the flow. The method has several assets, including,…
Sequential robot manipulation tasks require finding collision-free trajectories that satisfy geometric constraints across multiple object interactions in potentially high-dimensional configuration spaces. Solving these problems in real-time…
In this paper, we present a flow-based method for global optimization of continuous Sobolev functions, called Stein Boltzmann Sampling (SBS). SBS initializes uniformly a number of particles representing candidate solutions, then uses the…
In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…
The paper is devoted to the homogenization of porous piezoelectric materials saturated by electrically inert fluid. The solid part of a representative volume element consists of the piezoelectric skeleton with embedded conductors. The pore…
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we consider the mixed formulation of the flow problem and aim to solve…
In this work, we introduce a time memory formalism in poroelasticity model that couples the pressure and displacement. We assume this multiphysics process occurs in multicontinuum media. The mathematical model contains a coupled system of…
Modelling and understanding properties of materials from first principles require knowledge of the underlying atomistic structure. This entails knowing the individual identity and position of all involved atoms. Obtaining such information…
In order to optimally design materials, it is crucial to understand the structure-property relations in the material by analyzing the effect of microstructure parameters on the macroscopic properties. In computational homogenization, the…
In this paper, we combine concepts of the generalized multiscale finite element method and mode decomposition methods to construct a robust local-global approach for model reduction of flows in high-contrast porous media. This is achieved…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
Topology optimization (TopOpt) is a mathematical-driven design procedure to realize optimal material architectures. This procedure is often used to automate the design of devices involving flow through porous media, such as micro-fluidic…