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In a number of problems in computational physics, a finite sum of kernel functions centered at $N$ particle locations located in a box in three dimensions must be extended by imposing periodic boundary conditions on box boundaries. Even…
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the…
Computationally efficient numerical methods for high-order approximations of convolution integrals involving weakly singular kernels find many practical applications including those in the development of fast quadrature methods for…
Gaussian processes (GPs) are crucial in machine learning for quantifying uncertainty in predictions. However, their associated covariance matrices, defined by kernel functions, are typically dense and large-scale, posing significant…
We develop a hybrid Monte Carlo method to efficiently compute the physical observables from the samplings of the Laughlin and the Moore-Read wave functions of fractional quantum Hall (FQH) systems. With the advancements in methodology,…
This work proposes a mixed learning-based and optimization-based approach to the weighted-sum-rates beamforming problem in a multiple-input multiple-output (MIMO) wireless network. The conventional methods, i.e., the fractional programming…
Automatic detection and tracking of cells in microscopy images are major applications of computer vision technologies in both biomedical research and clinical practice. Though machine learning methods are increasingly common in these…
We demonstrate the high accuracy of the density splitting method to compute the gravitational potential and field in the plane of razor-thin, axially symmetric discs, as preliminarily outlined in Pierens & Hure (2004). Because residual…
We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast…
Convolutional Gridding is a technique (algorithm) extensively used in Radio Interferometric Image Synthesis for fast inversion of functions sampled with irregular intervals on the Fourier plane. In this thesis, we propose some modifications…
Due to the variety and importance of applications of treecodes and FMM, the combination of algorithmic acceleration with hardware acceleration can have tremendous impact. Alas, programming these algorithms efficiently is no piece of cake.…
A new transform over finite fields, the finite field Hartley transform (FFHT), was recently introduced and a number of promising applications on the design of efficient multiple access systems and multilevel spread spectrum sequences were…
To address increasing compute demand from recent multi-model workloads with heavy models like large language models, we propose to deploy heterogeneous chiplet-based multi-chip module (MCM)-based accelerators. We develop an advanced…
The $1/r$-expansion in the distance to the source is applied to the linearized $f(R)$ gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular…
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…
Fast Fourier Transform (FFT)-based solvers for the Poisson equation are highly efficient, exhibiting $O(N\log N)$ computational complexity and excellent parallelism. However, their application is typically restricted to simple, regular…
A metric-field approach to gravitation is presented. It is based on an idea of dependency of space-time properties on measuring instruments. Some bimetric equations that realize this idea are considered. They were tested by the binary…
Energy evaluation using fast Fourier transforms enables sampling billions of putative complex structures and hence revolutionized rigid protein-protein docking. However, in current methods efficient acceleration is achieved only in either…
Faraday Rotation Measure (RM) Synthesis, as a method for analyzing multi-channel observations of polarized radio emission to investigate galactic magnetic fields structures, requires the definition of complex polarized intensity in the…
The fast Fourier transform (FFT) based matrix-free ansatz interpolatory approximations of periodic functions are fundamental for efficient realization in several applications.In this work we design, analyze, and implement similar…