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Hybrid computational architectures based on the joint power of Central Processing Units and Graphic Processing Units (GPUs) are becoming popular and powerful hardware tools for a wide range of simulations in biology, chemistry, engineering,…
The simplex algorithm has been successfully used for many years in solving linear programming (LP) problems. Due to the intensive computations required (especially for the solution of large LP problems), parallel approaches have also…
OpenCL for FPGA enables developers to design FPGAs using a programming model similar for processors. Recent works have shown that code optimization at the OpenCL level is important to achieve high computational efficiency. However, existing…
The unknown parameters of simulation models often need to be calibrated using observed data. When simulation models are expensive, calibration is usually carried out with an emulator. The effectiveness of the calibration process can be…
Faced with physical and energy density limitations on clock speed, contemporary microprocessor designers have increasingly turned to on-chip parallelism for performance gains. Algorithms should accordingly be designed with ample amounts of…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…
As quantum computers continue to improve and support larger, more complex computations, smart control hardware and compilers are needed to efficiently leverage the capabilities of these systems. This paper introduces a novel approach to…
Solving large-scale sparse linear systems is a challenging computational task due to the introduction of non-zero elements, or "fill-in." The Graph Partitioning Problem (GPP) arises naturally when minimizing fill-in and accelerating…
Computation of a signal's estimated covariance matrix is an important building block in signal processing, e.g., for spectral estimation. Each matrix element is a sum of products of elements in the input matrix taken over a sliding window.…
Developing CPU scheduling algorithms and understanding their impact in practice can be difficult and time consuming due to the need to modify and test operating system kernel code and measure the resulting performance on a consistent…
This paper presents the design and analysis of parallel approximation algorithms for facility-location problems, including $\NC$ and $\RNC$ algorithms for (metric) facility location, $k$-center, $k$-median, and $k$-means. These problems…
Neural processing units (NPUs) are gaining prominence in power-sensitive devices like client devices, with AI PCs being defined by their inclusion of these specialized processors. Running AI workloads efficiently on these devices requires…
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms…
Proofs of convergence of adaptive finite element methods for the approximation of eigenvalues and eigenfunctions of linear elliptic problems have been given in a several recent papers. A key step in establishing such results for multiple…
MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and…
It is significant and challenging to solve eigenvalue problems of partial differential operators when many highly accurate eigenpair approximations are required. The adaptive finite element discretization based parallel orbital-updating…
Maximizing the performance potential of the modern day GPU architecture requires judicious utilization of available parallel resources. Although dramatic reductions can often be obtained through straightforward mappings, further performance…