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This paper presents a novel exact finite element formulation of quasi-3D beam for high-fidelity analysis of functionally graded sandwich beams. Unlike conventional displacement-based elements that rely on approximate interpolation functions…

Numerical Analysis · Mathematics 2026-01-21 Wenxiong Li , Suiyin Chen

We consider the calculation of the band structure of frequency dependent photonic crystals. The associated eigenvalue problem is nonlinear and it is challenging to develop effective convergent numerical methods. In this paper, the band…

Numerical Analysis · Mathematics 2020-07-23 Wenqiang Xiao , Bo Gong , Jiguang Sun , Zhimin Zhang

We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly-correlated materials where the one-electron description breaks down.…

Strongly Correlated Electrons · Physics 2009-11-11 G. Kotliar , S. Y. Savrasov , K. Haule , V. S. Oudovenko , O. Parcollet , C. A. Marianetti

This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…

Computational Engineering, Finance, and Science · Computer Science 2019-10-30 Yangfan Zhang , Pengfei Wang , Wenping Li , Shunchuan Yang

Electronic structure codes usually allow to calculate the work function as a part of the theoretical description of surfaces and processes such as adsorption thereon. This requires a proper calculation of the electrostatic potential in all…

Materials Science · Physics 2009-11-11 K. Doll

In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis…

Quantum Physics · Physics 2025-11-17 Fabian Langkabel , Stefan Knecht , Jakob S. Kottmann

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic…

Numerical Analysis · Mathematics 2016-04-27 Andrew Gillette , Alexander Rand , Chandrajit Bajaj

We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local bases for them using Bernstein-B\'ezier techniques, prove…

Numerical Analysis · Mathematics 2016-02-18 Oleg Davydov , Georgii Kostin , Abid Saeed

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…

Numerical Analysis · Mathematics 2013-08-15 Axel Malqvist , Daniel Peterseim

Calculations of electronic and optical properties of solids at finite temperature including electron-phonon interactions and quantum zero-point renormalization have enjoyed considerable progress during the past few years. Among the emerging…

Materials Science · Physics 2020-04-01 Marios Zacharias , Feliciano Giustino

We present a spectral finite-element formulation of the optimized effective potential (OEP) method for atomic structure calculations in the random phase approximation (RPA). In particular, we develop a finite-element framework that employs…

Computational Physics · Physics 2026-01-28 Shubhang Krishnakant Trivedi , Phanish Suryanarayana

An efficient method for calculating the electronic structure of systems that need a very fine sampling of the Brillouin zone is presented. The method is based on the variational optimization of a "single" (i.e. common to all points in the…

Materials Science · Physics 2009-10-31 Sandro Scandolo , Jorge Kohanoff

To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…

Logic in Computer Science · Computer Science 2024-10-03 François Clément , Vincent Martin

Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…

Materials Science · Physics 2007-05-23 Nimal Wijesekera , Guogang Feng , Thomas L. Beck

In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…

Optics · Physics 2024-09-12 Jingwei Wang , Lida Liu , Yuhao Jing , Zhongfei Xiong , Yuntian Chen

We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal…

Chemical Physics · Physics 2019-02-20 Steven R. White , E. Miles Stoudenmire

We develop a cut finite element method for a second order elliptic coupled bulk-surface model problem. We prove a priori estimates for the energy and $L^2$ norms of the error. Using stabilization terms we show that the resulting algebraic…

Numerical Analysis · Mathematics 2014-03-27 Erik Burman , Peter Hansbo , Mats G. Larson , Sara Zahedi

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an…

Computational Physics · Physics 2015-06-05 Phani Motamarri , Michael R Nowak , Kenneth Leiter , Jaroslaw Knap , Vikram Gavini

In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…

One of the goals in the development of large scale electronic structure methods is to perform calculations explicitly for a localised region of a system, while still taking into account the rest of the system outside of this region. An…

Materials Science · Physics 2009-10-01 J. R. Trail , D. M. Bird