Related papers: Energy-based comparison between the Fourier--Galer…
Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are computational methods for partial differential equations that are…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
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…
An FFT framework which preserves a good numerical performance in the case of domains with large regions of empty space is proposed and analyzed for its application to lattice based materials. Two spectral solvers specially suited to resolve…
Guaranteed upper-lower bounds on homogenized coefficients, arising from the periodic cell problem, are calculated in a scalar elliptic setting. Our approach builds on the recent variational reformulation of the Moulinec-Suquet (1994) Fast…
Moulinec and Suquet introduced FFT-based homogenization in 1994, and twenty years later, their approach is still effective for evaluating the homogenized properties arising from the periodic cell problem. This paper builds on the author's…
We propose a matrix-free finite element (FE) homogenization scheme that is considerably more efficient than generic FE implementations. The efficiency of our scheme follows from a preconditioned well-scaled reformulation allowing for the…
We introduce a family of Galerkin finite element methods which are constructed via recovery operators over element-wise discontinuous approximation spaces. This new family, termed collectively as recovered finite element methods (R-FEM) has…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
Computational micromechanics and homogenization require the solution of the mechanical equilibrium of a periodic cell that comprises a (generally complex) microstructure. Techniques that apply the Fast Fourier Transform have attracted much…
The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…
The paper addresses a numerical method for solving second order elliptic partial differential equations that describe fields inside heterogeneous media. The scope is general and treats the case of rough coefficients, i.e. coefficients with…
In this article, an efficient transient electricalthermal co-simulation method based on the finite element method (FEM) and the discontinuous Galerkin time-domain (DGTD) method is developed for electrical-thermal coupling analysis of…
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…
In this paper, we study a time-fractional initial-boundary value problem of Kirchhoff type involving memory term for non-homogeneous materials. The energy argument is applied to derive the a priori bounds on the solution of the considered…
This study presents a meshfree two-dimensional fractional-order Element-Free Galerkin (2D f-EFG) method as a viable alternative to conventional mesh-based FEM for a numerical solution of (spatial) fractional-order differential equations…
Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…
Finite element methods have been shown to achieve high accuracies in numerically solving the EEG forward problem and they enable the realistic modeling of complex geometries and important conductive features such as anisotropic…
In this paper, we propose a linearized finite element method (FEM) for solving the cubic nonlinear Schr\"{o}dinger equation with wave operator. In this method, a modified leap-frog scheme is applied for time discretization and a Galerkin…