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The dynamical susceptibility of strongly correlated electronic systems can be calculated within the framework of the dynamical mean-field theory (DMFT). The required measurement of the four-point vertex of the auxiliary impurity model is…
Simulating charged many-body systems has been a computational demanding task due to the long-range nature of electrostatic interaction. For the multi-scale model of electrolytes which combines the strengths of atomistic/continuum…
In this paper, we will introduce a new heterogeneous fast multipole method (H-FMM) for 2-D Helmholtz equation in layered media. To illustrate the main algorithm ideas, we focus on the case of two and three layers in this work. The key…
The present work attempts to integrate the independent efforts in the fast N-body community to create the fastest N-body library for many-core and heterogenous architectures. Focus is placed on low accuracy optimizations, in response to the…
This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…
This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in two-dimensional space. The proposed algorithm remains highly accurate…
We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
The plane wave method is most widely used for solving the Kohn-Sham equations in first-principles materials science computations. In this procedure, the three-dimensional (3-dim) trial wave functions' fast Fourier transform (FFT) is a…
The efficiency of boundary element methods depends crucially on the time required for setting up the stiffness matrix. The far-field part of the matrix can be approximated by compression schemes like the fast multipole method or…
Series expansions have been a cornerstone of applied mathematics and engineering for centuries. In this paper, we revisit the Taylor series expansion from a modern Machine Learning perspective. Specifically, we introduce the Fast Continuous…
In micromagnetic simulations, the demagnetization field is by far the computationally most expensive field component and often a limiting factor in large multilayer systems. We present an exact method to calculate the demagnetization field…
Matrix multiplication (GEMM) is a core operation to numerous scientific applications. Traditional implementations of Strassen-like fast matrix multiplication (FMM) algorithms often do not perform well except for very large matrix sizes, due…
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…
Energy system optimization models are increasing in scope and resolution, yielding large and challenging linear programs. For a long time, the standard way to address such problems has relied on shared-memory interior-point methods (IPM),…
The convergence to the self-consistency in the dynamical-mean-field-theory (DMFT) calculations for models of correlated electron systems can be significantly accelerated by using an appropriate mixing of hybridization functions which are…
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
Adapting Foundation Models (FMs) for downstream tasks through Federated Learning (FL) emerges a promising strategy for protecting data privacy and valuable FMs. Existing methods fine-tune FM by allocating sub-FM to clients in FL, however,…
Large language models (LLMs) have been widely applied but face challenges in efficient inference. While quantization methods reduce computational demands, ultra-low bit quantization with arbitrary precision is hindered by limited GPU Tensor…