Related papers: Constraint energy minimizing generalized multiscal…
Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference…
We begin by addressing the time-domain full-waveform inversion using the adjoint method. Next, we derive the scaled boundary semi-weak form of the scalar wave equation in heterogeneous media through the Galerkin method. Unlike conventional…
This note constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…
Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly-varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
We devise a stabilized method to weakly enforce bound constraints in the discrete solution of advection-dominated diffusion problems. This method combines a nonlinear penalty formulation with a discontinuous Galerkin-based residual…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
We propose a finite volume method on general meshes for the discretization of a degenerate parabolic convection-reaction-diffusion equation. Equations of this type arise in many contexts, such as the modeling of contaminant transport in…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
An energy-based discontinuous Galerkin method for the advective wave equation is proposed and analyzed. Energy-conserving or energy-dissipating methods follow from simple, mesh-independent choices of the inter-element fluxes, and both…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
On Bakhvalov-type mesh, uniform convergence analysis of finite element method for a 2-D singularly perturbed convection-diffusion problem with exponential layers is still an open problem. Previous attempts have been unsuccessful. The…
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
We have obtained an exact expression for the phase-space volume corresponding to a microcanonical ensemble of systems under center of mass, total linear and angular momenta conservation constraints, and arbitrary constraints on the…
This paper is devoted to the construction and analysis of the finite element approximations for the $H(D)$ convection-diffusion problems, where $D$ can be chosen as ${\rm grad}$, ${\rm curl}$ or ${\rm div}$ in 3D case. An essential feature…
Current state-of-the-art discrete optimization methods struggle behind when it comes to challenging contrast-enhancing discrete energies (i.e., favoring different labels for neighboring variables). This work suggests a multiscale approach…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…