Related papers: Fast calculation of the electrostatic potential in…
This paper is concerned with the extraction of the smallest eigenvalue and the corresponding eigenvector of a symmetric positive definite matrix pencil. We reveal implicit convexity of the eigenvalue problem in Euclidean space. A provable…
A formulation for the efficient calculation of the electromagnetic retarded potential generated by time-dependent electron density in the context of real-time time dependent density functional theory (RT-TDDFT) is presented. The electron…
Calculation of the effective quasistatic shear speed $c$ in 2D solid phononic crystals is analyzed. The plane-wave expansion (PWE) and the monodromy-matrix (MM) methods are considered. For each method, the stepwise sequence of upper and…
Large molecular dynamics simulations (millions of atoms, tens of microseconds, thousands of processors) hit the strong scalability wall: simulation on twice as many processors does not take half the time. Inspired by large N-body space…
Constant potential method molecular dynamics simulation (CPM MD) enables the accurate modelling of atomistic electrode charges when studying the electrode-electrolyte interface at the nanoscale. Here we extend the theoretical framework of…
We use a new configuration-based version of linear response theory to efficiently solve self-consistent mean field equations relating an effective single particle potential to the induced density. The versatility and accuracy of the method…
Computer simulations of model systems are widely used to explore striking phenomena in promising applications spanning from physics, chemistry, biology, to materials science and engineering. The long range electrostatic interactions between…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
We present a new approach to efficiently simulate electrolytes confined between infinite charged walls using a 3d Ewald summation method. The optimal performance is achieved by separating the electrostatic potential produced by the charged…
In this work, we provide the mathematical elements we think essential for a proper understanding of the calculus of the electrostatic energy of point-multipoles of arbitrary order under periodic boundary conditions. The emphasis is put on…
A melting transition for a system of hard spheres interacting by a repulsive Yukawa potential of DLVO form is studied. To find the location of the phase boundary, we propose a simple theory to calculate the free energies for the coexisting…
We develop a fast divided-and-conquer indirect collocation method for the homogeneous Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due to the impact of the space-dependent variable order, the…
The Immersed Interface Method is employed to solve the time-varying electric field equations around a three-dimensional vesicle. To achieve second-order accuracy the implicit jump conditions for the electric potential, up to the second…
We present and discuss a new computationally inexpensive method to study, within the single active electron approximation, the interaction of a complex system with an intense ultrashort laser pulse. As a first application, we consider the…
An inversion method is formulated for extracting entanglement-related information on two-particle interactions in a one-dimensional system from measurable one-particle position- and momentum-distribution functions. The method is based on a…
Achieving large-scale kinetic modelling is a crucial task for the development and optimization of modern plasma devices. With the trend of decreasing pressure in applications such as plasma etching, kinetic simulations are necessary to…
We consider the order of convergence for linear and nonlinear Monte Carlo approximation of compact embeddings from Sobolev spaces of dominating mixed smoothness defined on the torus $\mathbb{T}^d$ into the space $L_{\infty}(\mathbb{T}^d)$…
We show several results on convergence of the Monte Carlo method applied to consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Our method is based on combination of several new concepts. We…
The full-dimensional time-dependent Schrodinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange…
Frozen Density Embedding Theory (FDET) [Wesolowski {\it Phys. Rev. A} {\bf 77}, 012504 (2008)] provides the interpretation of the eigenvalue equations for an embedded $N'$-electron wavefunction, in which the embedding operator is…