Related papers: An improved integration scheme for Mode-coupling-t…
Due to the high computational load of modern numerical simulation, there is a demand for approaches that would reduce the size of discrete problems while keeping the accuracy reasonable. In this work, we present an original algorithm to…
Finite difference approximation, in addition to Taylor truncation errors, introduces numerical dispersion-and-dissipation errors into numerical solutions of partial differential equations. We analyze a class of finite difference schemes…
We present a general framework to design Godunov-type schemes for multidimensional ideal magnetohydrodynamic (MHD) systems, having the divergence-free relation and the related properties of the magnetic field B as built-in conditions. Our…
This paper presents a method for achieving equilibrium in the ISING Hamiltonian when confronted with unevenly distributed charges on an irregular grid. Employing (Multi-Edge) QC-LDPC codes and the Boltzmann machine, our approach involves…
This paper presents nonlinear iterative methods for the fundamental thermal radiative transfer (TRT) model defined by the time-dependent multifrequency radiative transfer (RT) equation and the material energy balance (MEB) equation. The…
Minimizing the Euclidean distance to a set arises frequently in applications. When the set is algebraic, a measure of complexity of this optimization problem is its number of critical points. In this paper we provide a general framework to…
We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a…
This paper considers the problem of decentralized optimization on compact submanifolds, where a finite sum of smooth (possibly non-convex) local functions is minimized by $n$ agents forming an undirected and connected graph. However, the…
We present a numerical method for calculating piecewise smooth spectral functions of correlated quantum systems in the thermodynamic limit from the spectra of finite systems computed using the dynamical or correction-vector density-matrix…
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…
The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a robust and efficient solution method for a wide range of block-separable convex minimization problems, typically stemming from discretizations of nonlinear and nonsmooth partial…
Perturbative schemes utilizing a spectral moment expansion are well known and extensively used for investigating the physics of model Hamiltonians and real material systems. The advantages they offer, in terms of being computationally…
Accurate and fast treatment of electron-electron interactions remains a central challenge in electronic structure theory because post-Hartree-Fock methods often suffered from the computational cost for 4-index electron repulsion integrals…
Gradient schemes is a framework which enables the unified convergence analysis of many different methods -- such as finite elements (conforming, non-conforming and mixed) and finite volumes methods -- for $2^{\rm nd}$ order diffusion…
Partial Differential Equations (PDEs) are fundamental for modeling physical systems, yet solving them in a generic and efficient manner using machine learning-based approaches remains challenging due to limited multi-input and multi-scale…
Marginal emissions rates -- the sensitivity of carbon emissions to electricity demand -- are important for evaluating the impact of emissions mitigation measures. Like locational marginal prices, locational marginal emissions rates (LMEs)…
We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the…
A nonhydrostatic dynamical core has been developed by using the multi-moment finite volume method that ensures the rigorous numerical conservation. To represent the spherical geometry free of polar problems, the cubed-sphere grid is…
This paper presents a novel Riemannian conjugate gradient method for the Kohn-Sham energy minimization problem in density functional theory (DFT), with a focus on non-metallic crystal systems. We introduce an energy-adaptive metric that…
Many problems in science and engineering require an efficient numerical approximation of integrals or solutions to differential equations. For systems with rapidly changing dynamics, an equidistant discretization is often inadvisable as it…