Related papers: Numerical Homogenization of Fractal Interface Prob…
Linear elastic fracture mechanics admit analytic solutions that have low regularity at crack tips. Current numerical methods for partial differential equations (PDEs) of this type suffer from the constraint of such low regularity, and fail…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves a fractional power of an elliptic operator of second order. Finite element approximation in space is…
There is mounting evidence indicating that relaxation dynamics in liquids approaching their glass transition not only becomes increasingly cooperative (1,2) but the relaxing regions also become more compact in shape(3-7). While the surface…
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the solution, classical superconvergence phenomenon for finite…
A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and…
This contribution describes relationship between fractions, projective representation, duality, linear algebra and geometry. Many problems lead to a system of linear equations. This paper presents equivalence of the Cross-product operation…
In this note we treat the equations of fractional elasticity. After establishing well-posedness, we show a compactness result related to the theory of homogenization. For this, a previous result in (abstract) homogenization theory of…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
We discuss a numerical method for convection-diffusion-reaction problems with a free boundary in 1D. The method is based on the numerical modelling of the interface evolution, the transformation to a fixed domain problem and the…
A multiscale method is proposed for a parabolic stochastic partial differential equation with additive noise and highly oscillatory diffusion. The framework is based on the localized orthogonal decomposition (LOD) method and computes a…
Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions…
Although FFT-based methods are renowned for their numerical efficiency and stability, traditional discretizations fail to capture material interfaces that are not aligned with the grid, resulting in suboptimal accuracy. To address this…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
Multiscale modeling and analysis of multiphysics coupling processes in highly heterogeneous media present significant challenges. In this paper, we propose a novel multiphysics embedding localized orthogonal decomposition (ME-LOD) method…
Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…
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…
A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with…
In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…