相关论文: Multigrid Methods in Electronic Structure Calculat…

Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively…

With tens of petaflops supercomputers already in operation and exaflops machines expected to appear within the next 10 years, efficient parallel computational methods are required to take advantage of such extreme-scale machines. In this…

One well adopted power grid simulation methodology is to factorize matrix once and perform only backward forward substitution with a deliberately chosen step size along the simulation. Since the required simulation time is usually long for…

Block Floating Point (BFP) arithmetic is currently seeing a resurgence in interest because it requires less power, less chip area, and is less complicated to implement in hardware than standard floating point arithmetic. This paper explores…

We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…

Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…

Considerable information about the early-stage dynamics of heavy-ion collisions is encoded in the rapidity dependence of measurements. To leverage the large amount of experimental data, we perform a systematic analysis using…

We present evidence that multigrid (MG) works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder. We introduce a "neural computations" point of view into large scale…

We present a high-accuracy procedure for electronic structure calculations of strongly correlated materials. To address limitations in current electronic structure methods, we employ density functional theory in combination with the…

A multigrid scheme is proposed for the pressure equation of the incompressible unsteady fluid flow equations, allowing efficient implementation on clusters of modern CPUs, many integrated core devices (MICs), and graphics processing units…

The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. Here, a novel, implicit, particle-in-cell based…

To resolve the rising temperatures in 3.5D-ICs, a thermal-aware design flow becomes increasingly crucial, necessitating an accurate and efficient thermal simulation tool. However, previous tools struggle to handle the unique heterogeneous…

As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised…

From AlexNet to Inception, autoencoders to diffusion models, the development of novel and powerful deep learning models and learning algorithms has proceeded at breakneck speeds. In part, we believe that rapid iteration of model…

Multigrid algorithms are among the fastest iterative methods known today for solving large linear and some non-linear systems of equations. Greatly optimized for serial operation, they still have a great potential for parallelism not fully…

An efficient nonlinear multigrid method for a mixed finite element method of the Darcy-Forchheimer model is constructed in this paper. A Peaceman-Rachford type iteration is used as a smoother to decouple the nonlinearity from the divergence…

A mixed basis approach based on density functional theory is extended to one-dimensional(1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the…

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…

We present a multigrid scheme for the solution of finite-element Hartree-Fock equations for diatomic molecules. It is shown to be fast and accurate, the time effort depending linearly on the number of variables. Results are given for the…