Related papers: Real-Space Mesh Techniques in Density Functional T…
A new iterative solver is proposed to efficiently calculate the ground state electronic structure in Density Functional Theory calculations. This algorithm is particularly useful for simulating physical systems considered difficult to…
In this paper, we present a novel parallel augmented subspace method and build a package Parallel Augmented Subspace Eigensolver (PASE) for solving large scale eigenvalue problems by the massively parallel finite element discretization.…
We show that classical molecular density functional theory (MDFT), here in the homogeneous reference fluid approximation in which the functional is inferred from the properties of the bulk solvent, is a powerful new tool to study, at a…
We propose a reduced-space elasto-dynamic solver that is well suited for augmenting rigged character animations with secondary motion. At the core of our method is a novel deformation subspace based on Linear Blend Skinning that overcomes…
Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…
Reciprocal space methods for solving Poisson's equation for finite charge distributions are investigated. Improvements to previous proposals are presented, and their performance is compared in the context of a real-space density functional…
As the second component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for extended…
In this paper, we propose and analyze a mixed virtual element method for the approximation of the eigenvalues and eigenfunctions of the two-dimensional elasticity eigenvalue problem. Under standard assumptions on polygonal meshes, we prove…
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods…
Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on…
The advancements in additive manufacturing (AM) technology have allowed for the production of geometrically complex parts with customizable designs. This versatility benefits large-scale space-frame structures, as the individual design of…
We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here the unit cell) with advanced electronic-structure methods, that are computationally too expensive for periodic…
Quantum mechanical calculations for material modelling using Kohn-Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for $N$ smallest eigenvector-eigenvalue pairs with $N$ proportional to the number…
We introduce meshfree finite difference methods for approximating nonlinear elliptic operators that depend on second directional derivatives or the eigenvalues of the Hessian. Approximations are defined on unstructured point clouds, which…
We propose a method for efficiently coupling the finite element method with atomistic simulations, while using molecular dynamics or kinetic Monte Carlo techniques. Our method can dynamically build an optimized unstructured mesh that…
We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…
In this paper a numerical multiscale method for discrete networks is presented. The method gives an accurate coarse scale representation of the full network by solving sub-network problems. The method is used to solve problems with highly…
A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…
An efficient parallelization approach to simulate optical properties of ensembles of quantum emitters in realistic electromagnetic environments is considered. It relies on balancing computing load of utilized processors and is built into…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…