Related papers: An O(N) Method for Rapidly Computing Periodic Pote…
A fast method of an arbitrary high order for approximating volume potentials is proposed, which is effective also in high dimensional cases. Basis functions introduced in the theory of approximate approximations are used. Results of…
An accelerated polynomial expansion scheme to construct the density matrix in quantum mechanical molecular dynamics simulations is proposed. The scheme is based on recursive density matrix expansions, e.g. [Phys. Rev. B. 66 (2002), p.…
Numerical Simulation is an essential part of the design and optimisation of astronomical adaptive optics systems. Simulations of adaptive optics are computationally expensive and the problem scales rapidly with telescope aperture size, as…
The atomic cluster expansion (ACE) (Drautz, 2019) yields a highly efficient and intepretable parameterisation of symmetric polynomials that has achieved great success in modelling properties of many-particle systems. In the present work we…
We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $[E-\epsilon, E+\epsilon]$. In order to reduce the spectral weight of all other eigenvectors by…
A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the…
The large sparse linear systems arising from the finite element or finite difference discretization of elliptic PDEs can be solved directly via, e.g., nested dissection or multifrontal methods. Such techniques reorder the nodes in the grid…
We study the evaluation of layer potentials close to the domain boundary. Accurate evaluation of layer potentials near boundaries is needed in many applications, including fluid-structure interactions and near-field scattering in…
Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These…
We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…
The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code \verb+PACE+ that is suitable for use in large scale…
A unified treatment for fast and spectrally accurate evaluation of electrostatic potentials subject to periodic boundary conditions in any or none of the three spatial dimensions is presented. Ewald decomposition is used to split the…
We study the convergence of a linear atomic cluster expansion (ACE) potential with respect to its basis functions, in terms of the effective two-body interactions of elemental Carbon and Silicon systems. We build ACE potentials with…
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…
An Ewald decomposition of the two-dimensional Yukawa potential and its derivative is presented for both the periodic and the free-space case. These modified Bessel functions of the second kind of zeroth and first degrees are used e.g. when…
The accurate and efficient evaluation of potentials is of great importance for the numerical solution of partial differential equations. When the integration domain of the potential is irregular and is discretized by an unstructured mesh,…
This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poisson and Helmholtz equations in two dimensions. Following the…
We extend the piecewise orthogonal collocation method to computing periodic solutions of coupled renewal and delay differential equations. Through a rigorous error analysis, we prove convergence of the relevant finite-element method and…
In an ever-increasing interest for Machine Learning (ML) and a favorable data development context, we here propose an original methodology for data-based prediction of two-dimensional physical fields. Polynomial Chaos Expansion (PCE),…
It is tacitly accepted that, for practical basis sets consisting of N functions, solution of the two-electron Coulomb problem in quantum mechanics requires storage of O(N^4) integrals in the small N limit. For localized functions, in the…