Related papers: A three-dimensional domain decomposition method fo…
Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…
Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…
The theorems of density functional theory (DFT) and reduced density matrix functional theory (RDMFT) establish a bijective map between the external potential of a many-body system and its electron density or one-particle reduced density…
Density functional theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically…
Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…
The core structure of dislocations is critical to their mobility, cross slip, and other plastic behaviors. Atomistic simulation of the core structure is limited by the size of first-principles density functional theory (DFT) calculation and…
In this paper, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the…
Density functional theory (DFT) can run into serious difficulties with localized states in elements such as transition metals with occupied-d states and oxygen. In contrast, Hartree-Fock (HF) method can be a better approach for such…
A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…
This paper is concerned with the numerical solution of compressible fluid flow in a fractured porous medium. The fracture represents a fast pathway (i.e., with high permeability) and is modeled as a hypersurface embedded in the porous…
We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive…
In this paper, we propose and analyze an additive domain decomposition method (DDM) for solving the high-frequency Helmholtz equation with the Sommerfeld radiation condition. In the proposed method, the computational domain is partitioned…
The high cost associated with the evaluation of Hartree-Fock exchange (HFX) makes hybrid functionals computationally challenging for large systems. In this work, we present an efficient way to accelerate HFX calculations with numerical…
As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…
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…
Dispersion-free ultra-high order FFT-based Maxwell solvers have recently proven to be paramount to a large range of applications, including the high-fidelity modeling of high-intensity laser-matter interactions with Particle-In-Cell (PIC)…
State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted on account of the risk of `variational collapse' down to the…
A parallel direct solution approach based on domain decomposition method (DDM) and directed acyclic graph (DAG) scheduling is outlined. Computations are represented as a sequence of small tasks that operate on domains of DDM or dense matrix…
A massively parallel order-N electronic structure theory was constructed by an interdisciplinary research between physics, applied mathematics and computer science. (1) A high parallel efficiency with ten-million-atom nanomaterials was…
Electronic structure calculations based on density-functional theory (DFT) represent a significant part of today's HPC workloads and pose high demands on high-performance computing resources. To perform these quantum-mechanical DFT…