相关论文: Goal Oriented Adaptive Finite Element Method for t…

This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…

We consider the finite element method on locally damaged meshes allowing for some distorted cells which are isolated from one another. In the case of the Poisson equation and piecewise linear Lagrange finite elements, we show that the usual…

The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…

We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…

This paper provides an orientation angle optimization method for the design of fiber-reinforced composite materials using topology optimization. The orientation angle optimization is based on a topological derivative, which measures the…

This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated…

We propose several adaptive algorithmic methods for problems of non-smooth convex optimization. The first of them is based on a special artificial inexactness. Namely, the concept of inexact ($ \delta, \Delta, L$)-model of objective…

This work surveys an r-adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the…

Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…

Large-scale homogeneous detectors with optical readouts are widely used in particle detection, with Cherenkov and scintillator neutrino detectors as prominent examples. Analyses in experimental physics rely on high-fidelity simulators to…

The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…

We consider a two-stage numerical procedure for imaging of objects buried in dry sand using time-dependent backscattering experimental radar measurements. These measurements are generated by a single point source of electric pulses and are…

In this paper we introduce a method for creating a transparent computational boundary for the simulation of unidirectional propagation of optical beams and pulses using leaky modes. The key element of the method is the introduction of an…

In this paper, we propose a novel adaptive finite element method for an elliptic equation with line Dirac delta functions as a source term. We first study the well-posedness and global regularity of the solution in the whole domain. Instead…

In the present article we investigate optical near fields in semiconductor lasers. We perform finite element simulations for two different laser types, namely a super large optical waveguide (SLOW) laser, which is an edge emitter, and a…

We introduce an adaptive superconvergent finite element method for a class of mixed formulations to solve partial differential equations involving a diffusion term. It combines a superconvergent postprocessing technique for the primal…

For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the…

Finite element model updating of a structure made of linear elastic materials is based on the solution of a minimization problem. The goal is to find some unknown parameters of the finite element model (elastic moduli, mass densities,…

This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…

We present a differentiable weak-form learning approach for accelerating finite element simulations. Rather than introducing black-box source terms in the strong form of the governing equations, we augment the momentum equation directly in…