Related papers: Numerical analysis of several FFT-based schemes fo…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
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…
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…
In this paper, we consider an approximation method, and a novel general analysis, for second-order elliptic differential equations with heterogeneous multiscale coefficients. We obtain convergence of the Generalized Multi-scale Finite…
Micromechanical homogenization is often carried out with Fourier-accelerated methods that are prone to ringing artifacts. We here generalize the compatibility projection introduced by Vond\v{r}ejc, Zeman & Marek [Comput. Math. Appl. 68, 156…
In this paper, we assess the performance of four iterative algorithms for solving non-symmetric rank-deficient linear systems arising in the FFT-based homogenization of heterogeneous materials defined by digital images. Our framework is…
Homogenization is a fundamental technique for estimating the macroscopic properties of materials with microscale heterogeneity. Among Homogenization methods, the FFT-based Homogenization algorithm has become widely used due to its…
Generalized or extended finite element methods (GFEM/XFEM) are in general badly conditioned and have numerous additional degrees of freedom (DOF) compared with the FEM because of introduction of enriched functions. In this paper, we develop…
We analyze the random fluctuations of several multi-scale algorithms such as the multi-scale finite element method (MsFEM) and the finite element heterogeneous multiscale method (HMM), that have been developed to solve partial differential…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
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…
An approximation of a system coupling the cross-diffusion of chemical species within a solvent, subjected to an electric field, is obtained through a control volume finite element (CVFE) scheme on general simplicial meshes in two or three…
In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically studied. The local spaces are built from selected eigenvectors…
Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…
In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type…
Searches for signals at low signal-to-noise ratios frequently involve the Fast Fourier Transform (FFT). For high-throughput searches, we here consider FFT on the homogeneous mesh of Processing Elements (PEs) of a wafer-scale engine (WSE).…
Electrical machines commonly consist of moving and stationary parts. The field simulation of such devices can be very demanding if the underlying numerical scheme is solely based on a domain discretization, such as in case of the Finite…
Time discretization along with space discretization is important in the numerical simulation of subsurface flow applications for long run. In this paper, we derive theoretical convergence error estimates in discrete-time setting for…
We present and analyze three distinct semi-discrete schemes for solving nonlocal geometric flows incorporating perimeter terms. These schemes are based on the finite difference method, the finite element method, and the finite element…