Related papers: Numerical Homogenization of Fractal Interface Prob…
The work is motivated by the Faraday cage effect. We consider the Helmholtz equation over a 3D-domain containing a thin heterogeneous interface of thickness $\delta \ll 1$. The layer has a $\delta-$periodic structure in the in-plane…
Homogenization of a scalar elliptic equation in a bounded domain with Neuman boundary condition is studied. Coefficients of the operator are oscillating over two different groups of variables with different small periods $\varepsilon$ and…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
In this paper, we study the homogenization of elliptic equations that combine a local part, given by the Laplacian with Neumann boundary conditions, and its nonlocal version, defined through an integral operator with a smooth kernel. These…
This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with $\alpha$-order. Solutions for these equations with constant coefficients are…
This paper is concerned with space-time homogenization problems for damped wave equations with spatially periodic oscillating elliptic coefficients and temporally (arithmetic) quasi-periodic oscillating viscosity coefficients. Main results…
In this article we introduce a procedure, which allows to recover the potentially very good approximation properties of tensor-based model reduction procedures for the solution of partial differential equations in the presence of interfaces…
We present a new numerical method for solving the elliptic homogenization problem. The main idea is that the missing effective matrix is reconstructed by solving the local least-squares in an offline stage, which shall be served as the…
In this study, we propose a class of total variation diminishing (TVD) schemes for solving pseudo-monotone variational inequality arises in elasto-hydrodynamic lubrication point contact problem. A limiter based stable hybrid line splittings…
This paper presents a general convergence theory of penalty based numerical methods for elliptic constrained inequality problems, including variational inequalities, hemivariational inequalities, and variational-hemivariational…
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…
We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for time-harmonic scattering problems of Helmholtz type with high wavenumber $\kappa$. On a coarse mesh of width $H$, the proposed method identifies local…
In this paper, we introduce the foundation of a fractal topological space constructed via a family of nested topological spaces endowed with subspace topologies, where the number of topological spaces involved in this family is related to…
Fractal functions that produce smooth and non-smooth approximants constitute an advancement to classical nonrecursive methods of approximation. In both classical and fractal approximation methods emphasis is given for investigation of…
To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
If an elliptic differential operator associated with an $\mathbf{H}(\mathrm{curl})$-problem involves rough (rapidly varying) coefficients, then solutions to the corresponding $\mathbf{H}(\mathrm{curl})$-problem admit typically very low…
The improved city clustering algorithm can be used to identify urban boundaries on a digital map, and the results are a set of isolines. The relationships between the urban measurements within the variable boundaries follow allometric…
In this paper, we discuss the second-order finite element method (FEM) and finite difference method (FDM) for numerically solving elliptic cross-interface problems characterized by vertical and horizontal straight lines, piecewise constant…
Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…