Related papers: A Generalized Solution Method for Parallelized Com…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…
Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are currently stagnate. This situation has created the well-known bottleneck for…
In this paper, we present an advanced high-order compact gas-kinetic scheme (CGKS) for 3D unstructured mixed-element meshes, augmented with a geometric multigrid technique to accelerate steady-state convergence. The scheme evolves…
We present a method for electronic structure calculations that retains all of the advantages of real space and addresses the inherent inefficiency of a regular grid, which has equal precision everywhere. The computations are carried out on…
Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…
This paper proposes a novel parallel stochastic gradient descent (SGD) method that is obtained by applying parallel sets of SGD iterations (each set operating on one node using the data residing in it) for finding the direction in each…
In this paper we introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison,…
Elastic geodesic grids deploy from flat to spatial configurations via complex nonlinear motion that is difficult to represent robustly for simulation. We present a geometric guidance framework that discretizes deployment as synchronized,…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
This article presents a compact implementation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. Each iteration of the algorithm consists of applying a pair of complementary Gauss-Jordan…
Eulerian nonlinear uncertainty propagation methods often suffer from finite domain limitations and computational inefficiencies. A recent approach to this class of algorithm, Grid-based Bayesian Estimation Exploiting Sparsity, addresses the…
The Spherical Geometry Algorithm (SGA) demonstrates superior capability in achieving efficient and precise spaceborne SAR image formation processing, even under challenging imaging conditions including non-linear radar trajectories and…
We present a simple and effective method for evaluating double-and single-layer potentials for Laplace's equation in three dimensions close to the boundary. The close evaluation of these layer potentials is challenging because they are…
To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…
Self-gravity computation by multipole expansion is a common approach in problems such as core-collapse and Type Ia supernovae, where single large condensations of mass must be treated. The standard formulation of multipole self-gravity…
We describe a version of an algorithm for evolving self-gravitating collections of particles that should be nearly ideal for parallel architectures. Our method is derived from the ``self-consistent field'' (SCF) approach suggested…
We briefly review our works for graviton and spherical graviton potentials in a plane-wave matrix model. To compute them, it is necessary to devise a configuration of the graviton solutions, since the plane-wave matrix model includes mass…
A new grid system on a sphere is proposed that allows for straight-forward implementation of both spherical-harmonics-based spectral methods and gridpoint-based multigrid methods. The latitudinal gridpoints in the new grid are equidistant…
Small corrections in the argument of the latitude can be used to improve the accuracy of the SGP4 orbit propagator. These corrections have been obtained by applying the hybrid methodology for orbit propagation to SGP4, therefore yielding a…
We present a generic compact computational framework relying on structured random matrices that can be applied to speed up several machine learning algorithms with almost no loss of accuracy. The applications include new fast LSH-based…