Related papers: A Batched GPU Methodology for Numerical Solutions …
This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An…
Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small…
Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodyamics (lattice QCD), where the…
While many approaches have been proposed to analyze the problem of matrix multiplication parallel computing, few of them address the problem on heterogeneous processor platforms. It still remains an open question on heterogeneous processor…
In this paper, an easy-to-implement and computationally effective numerical method based on the new orthogonal hybrid functions is developed to solve system of fractional order differential equations numerically. The new orthogonal hybrid…
The widely-adopted practice is to train deep learning models with specialized hardware accelerators, e.g., GPUs or TPUs, due to their superior performance on linear algebra operations. However, this strategy does not employ effectively the…
The flexible flow shop scheduling problem is an NP-hard problem and it requires significant resolution time to find optimal or even adequate solutions when dealing with large size instances. Thus, this paper proposes a dual island genetic…
We present a shared-memory algorithm to compute high-quality solutions to the balanced $k$-way hypergraph partitioning problem. This problem asks for a partition of the vertex set into $k$ disjoint blocks of bounded size that minimizes the…
This paper presents a generalised and efficient wall boundary treatment in the smoothed particle hydrodynamics (SPH) method for 3-D complex and arbitrary geometries with single- and multi-phase flows to be executed on graphics processing…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
A new method of numerical solution for partial differential equations is proposed. The method is based on a fast matrix multiplication algorithm. Two-dimensional Poison equation is used for comparison of the proposed method with…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
The Radial Basis Function-generated finite differences became a popular variant of local meshless strong form methods due to its robustness regarding the position of nodes and its controllable order of accuracy. In this paper, we present a…
Recent enhancements to the Primal-Dual Hybrid Gradient (PDHG) algorithm have enabled GPUs to efficiently solve large linear programming problems, often faster than the long-dominant simplex and interior-point methods. The solutions found by…
Methods for solving hyperbolic systems typically depend on unknown ordering (e.g., Gauss-Seidel, or sweep/wavefront/marching methods) to achieve good convergence. For many discretisations, mesh types or decompositions these methods do not…
In this paper we solve on GPUs massive problems with large amount of data, which are not appropriate for solution with the SIMD technology. For the given problem we consider a three-level parallelization. The multithreading of CPU is used…
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…
Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…
The significant resource demands in LLM serving prompts production clusters to fully utilize heterogeneous hardware by partitioning LLM models across a mix of high-end and low-end GPUs. However, existing parallelization approaches often…