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We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the…
Micro-Electro-Mechanical Systems (MEMS) normally have fixed or moving structures (plates or array of thin beams) with cross-sections of the order of microns and lengths of the order of tens or hundreds of microns. Electrostatic forces play…
The adoption of detailed mechanisms for chemical kinetics often poses two types of severe challenges: First, the number of degrees of freedom is large; and second, the dynamics is characterized by widely disparate time scales. As a result,…
This work concerns the numerical analysis of the linear elasticity problem with a Robin boundary condition on a smooth domain. A finite element discretization is presented using high-order curved meshes in order to accurately discretize the…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty…
Coarse-graining or model reduction is a term describing a range of approaches used to extend the time-scale of molecular simulations by reducing the number of degrees of freedom. In the context of molecular simulation, standard…
This document attempts to clarify potential confusion regarding electrostatics calculations, specifically in the context of biomolecular structure and specifically as regards the units typically used to contour/visualize isopotential…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
Experimental limits on supersymmetry and similar theories are difficult to set because of the enormous available parameter space and difficult to generalize because of the complexity of single points. Therefore, more phenomenological,…
We consider a set of electrostatic problems relevant for determining the real-space structure and the ground-state energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are…
An efficient and easy-to-implement method is proposed to regularize integral equations in the 3D boundary element method (BEM). The method takes advantage of an assumed three-noded triangle discretization of the boundary surfaces. The…
We consider elliptic variational inequalities generated by obstacle type problems with thin obstacles. For this class of problems, we deduce estimates of the distance (measured in terms of the natural energy norm) between the exact solution…
We show that a certain error estimate for a fully discrete finite element approximation of the solution of the heat equation which is defined in a two-dimensional Euclidean domain carries over to the case of a general linear parabolic…
This paper reviews the method of surface Laplacian differentiation to study EEG. We focus on topics that are helpful for a clear understanding of the underlying concepts and its efficient implementation, which is especially important for…
It is well known that popular optimization techniques can lead to overfitting or even a lack of convergence altogether; thus, practitioners often utilize ad hoc regularization terms added to the energy functional. When carefully crafted,…
This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart distribution, which enables us to capture the correlation…
We derive a mixed-dimensional 3D-1D formulation of the electrostatic equation in two domains with different dielectric constants to compute, with an affordable computational cost, the electric field and potential in the relevant case of…
A new model description for the numerical simulation of elastic stents is proposed. Based on the new formulation an inf-sup inequality for the finite element discretization is proved and the proof of the inf-sup inequality for the…
An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing…