Related papers: A numerical method for computing the overall respo…
We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform…
The contact of solids with rough surfaces plays a fundamental role in physical phenomena such as friction, wear, sealing, and thermal transfer. However, its simulation is a challenging problem due to surface asperities covering a wide range…
This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A Least-Squares functional is formulated and the corresponding…
We introduce a computational scheme for calculating the electronic structure of random alloys that includes electronic correlations within the framework of the combined density functional and dynamical mean-field theory. By making use of…
We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…
We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…
Analytical solutions to nonlinear differential equations -- where they exist at all -- can often be very difficult to find. For example, Duffing's equation for a system with cubic stiffness requires the use of elliptic functions in the…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
In this paper, we generalize results of Bruinier on automorphic Green functions on Hilbert modular surfaces to arbitrary ideals. For instance, we compute the Fourier expansion of the unregularized Green functions, use it to regularize them,…
The accurate and efficient computation of the electromagnetic response of objects made from artificial materials is crucial for designing photonic functionalities and interpreting experiments. Advanced fabrication techniques can nowadays…
A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes…
We propose a theoretical approach for calculating effective electric and magnetic properties of composites with field-dependent restructuring of the filler. The theory combines the Bruggeman-Landauer approximation extended to a…
The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
We introduce an integrated meshing and finite element method pipeline enabling black-box solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the…
The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests…
Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to…
Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic…
In this paper, we study a priori error estimates for the finite element approximation of the nonlinear Schr\"{o}dinger-Poisson model. The electron density is defined by an infinite series over all eigenvalues of the Hamiltonian operator. To…