Related papers: Matrix-free algorithms for fast ab initio calculat…

A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-uniform meshes. It is based on the utilization of hierarchical…

Matrix factorization (MF) is employed by many popular algorithms, e.g., collaborative filtering. The emerging GPU technology, with massively multicore and high intra-chip memory bandwidth but limited memory capacity, presents an opportunity…

Fully homomorphic encryption (FHE) has recently attracted significant attention as both a cryptographic primitive and a systems challenge. Given the latest advances in accelerated computing, FHE presents a promising opportunity for…

Sparse matrix-vector multiplication (SpMV) operations are commonly used in various scientific applications. The performance of the SpMV operation often depends on exploiting regularity patterns in the matrix. Various representations have…

The real-space density-functional perturbation theory (DFPT) for the computations of the response properties with respect to the atomic displacement and homogeneous electric field perturbation has been recently developed and implemented…

The $N$-point discrete Fourier transform (DFT) is a cornerstone for several signal processing applications. Many of these applications operate in real-time, making the computational complexity of the DFT a critical performance indicator to…

A linear-scaling algorithm is presented for computing the Hartree-Fock (HF) exchange matrix using concentric atomic density fitting. The algorithm utilizes the stronger distance dependence of the three-center electron repulsion integrals…

We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…

This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This…

We present an efficient real space formalism for hybrid exchange-correlation functionals in generalized Kohn-Sham density functional theory (DFT). In particular, we develop an efficient representation for any function of the real space…

Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…

Coreset selection compresses large datasets into compact, representative subsets, reducing the energy and computational burden of training deep neural networks. Existing methods are either: (i) DNN-based, which are tied to model-specific…

A simple method for improving cache efficiency of serial and parallel explicit finite procedure with application to casting solidification simulation over three-dimensional complex geometries is presented. The method is based on division of…

In this paper, we discuss the solution of certain matrix-valued partial differential equations. Such PDEs arise, for example, when constructing a Riemannian contraction metric for a dynamical system given by an autonomous ODE. We develop…

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the…

We introduce a new finite element (FE) discretization framework applicable for covariant split equations. The introduction of additional differential forms (DF) that form pairs with the original ones permits the splitting of the equations…

Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…

We introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. These methods can be applied to a broad class of kernels, from the Green's functions for classical partial differential…

All-electron calculations play an important role in density functional theory, in which improving computational efficiency is one of the most needed and challenging tasks. In the model formulations, both nonlinear eigenvalue problem and…