Related papers: Massively Parallelized Interpolated Factored Green…
A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs) to perform mixed convolutions and correlations of the charge density with the Green function.…
The approximate minimum degree algorithm is widely used before numerical factorization to reduce fill-in for sparse matrices. While considerable attention has been given to the numerical factorization process, less focus has been placed on…
Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank representations of matrices and for predicting missing values and providing confidence intervals. Scaling up the posterior inference for massive-scale matrices is…
Iterative filtering methods were introduced around 2010 to improve definitions and measurements of structural features in signal processing. Like many applied techniques, they present considerable challenges for mathematicians to theorize…
In this paper we demonstrate the methodology for parallelizing the computation of large one-dimensional discrete fast Fourier transforms (DFFTs) on multi-core Intel Xeon processors. DFFTs based on the recursive Cooley-Tukey method have to…
We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
The Fast Fourier Transform (FFT) is a fundamental numerical technique with widespread application in a range of scientific problems. As scientific simulations attempt to exploit exascale systems, there has been a growing demand for…
Region proposal is critical for object detection while it usually poses a bottleneck in improving the computation efficiency on traditional control-flow architectures. We have observed region proposal tasks are potentially suitable for…
Driven by Moore's Law, the dimensions of transistors have been pushed down to the nanometer scale. Advanced quantum transport (QT) solvers are required to accurately simulate such nano-devices. The non-equilibrium Green's function (NEGF)…
We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…
Multiplication is a core operation in modern neural network (NN) computations, contributing significantly to energy consumption. The linear-complexity multiplication (L-Mul) algorithm is specifically proposed as an approximate…
Modern parallel computing devices, such as the graphics processing unit (GPU), have gained significant traction in scientific and statistical computing. They are particularly well-suited to data-parallel algorithms such as the particle…
Fortran's prominence in scientific computing requires strategies to ensure both that legacy codes are efficient on high-performance computing systems, and that the language remains attractive for the development of new high-performance…
Federated learning (FL) is a new paradigm to train AI models over distributed edge devices (i.e., workers) using their local data, while confronting various challenges including communication resource constraints, edge heterogeneity and…
We propose two schemes for interpolation of the one-particle Green's function (GF) calculated within coupled-cluster singles and doubles (CCSD) method for a periodic system. They use Wannier orbitals for circumventing huge cost for a large…
Phase-field models are widely employed to simulate microstructure evolution during processes such as solidification or heat treatment. The resulting partial differential equations, often strongly coupled together, may be solved by a broad…
Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
Resampling by interpolation is the traditional method to process interferograms from non-uniformly sampled Fourier transform spectrometers. The non-uniform fast Fourier transform (NUFFT) is an alternative approach that has been mostly…