We present GPU implementations of two fast force calculation methods, based on series expansions of the Poisson equation. One is the Self-Consistent Field (SCF) method, which is a Fourier-like expansion of the density field in some basis set; the other is the Multipole Expansion (MEX) method, which is a Taylor-like expansion of the Green’s function. […]

June 18, 2014 by hgpu

Graphics Processing Units (GPUs), originally developed for computer games, now provide computational power for scientific applications. A study on the comparison of computational speed-up and efficiency of a GPU with a CPU for the Finite Pointset Method (FPM), which is a numerical tool in Computational Fluid Dynamics (CFD) is presented. As FPM is based on […]

January 19, 2014 by hgpu

The progress of high performance computing platforms is dramatic, and most of the simulations carried out on these platforms, result in improvements on one level, yet exposes shortcomings of the current CFD packages capabilities. Therefore, hardware-aware design and optimizations are crucial towards exploiting the modern computing resources. This thesis proposes optimizations aimed at acceleration numerical […]

December 21, 2013 by hgpu

We investigated the possible way for treatment of electrostatic interactions by solving numerically Poisson’s equation using Conjugate Gradient method and Stabilized BiConjugate Gradient method. The aim of the research was to test the execution time of prototype programs running on BLueGene/P and CPU/GPU system. The results show that the tested methods are applicable for electrostatics […]

December 11, 2013 by hgpu

In this paper a new scalable hydrodynamic code GPUPEGAS (GPU-accelerated PErformance Gas Astrophysic Simulation) for simulation of interacting galaxies is proposed. The code is based on combination of Godunov method as well as on the original implementation of FlIC method, specially adapted for GPU-implementation. Fast Fourier Transform is used for Poisson equation solution in GPUPEGAS. […]

November 6, 2013 by hgpu

Graphics Processing Units (GPUs) have emerged as highly capable computational accelerators for scientific and engineering applications. Many reports claim orders of magnitude of speedup compared to traditional Central Processing Units (CPUs), and the interest for GPU computation is high in the computational world. In this thesis, the capability of using GPUs to accelerate the full […]

October 19, 2013 by hgpu

Guermond and Minev proposed a directional splitting algorithm to solve the incompressible Stokes equations. Their algorithm applies the alternating direction implicit method to the viscosity term. The pressure update uses a direction splitting method in order to enforce the incompressibility constraint, as opposed to commonly used projection methods that require the solution of a Poisson […]

August 9, 2013 by hgpu

The FEM has proven to be one of the most efficient methods for solving differential equations. Designed to run on different computer architectures, technological improvements have led over the years to the fast solution of larger and larger problems. Among these technological improvements, we emphasize the development of GPU (Graphic Processor Unit). Scientific programming in […]

May 15, 2013 by hgpu

The paper presented theVortexin Cell (VIC) method for solving the fluid motion equations in3D and its implementation for parallelcomputationin multicore architecture of the Graphics Processing Unit (GPU). One of the most important components of the VIC method algorithm is the solution of the Poisson equation. Multigrid and full multigrid methods were chosen for its solution […]

October 4, 2012 by hgpu

In this project, boundary value problems of the electric field governed by the Laplace equation were formulated using different numerical methods such as FEM and BEM. The resulting systems of linear equations were then solved using different solving algorithms. The accuracy and complexity of FEM and BEM were compared. The space and time complexity of […]

July 13, 2012 by hgpu

In pursuit of obtaining high fidelity solutions to the fluid flow equations in a short span of time, Graphics Processing Units ( GPUs ) which were originally intended for gaming applications, are currently being used to accelerate Computational Fluid Dynamics codes. With a high peak throughput of about 1 TFLOPS on a PC, GPUs seem […]

July 4, 2012 by hgpu

This paper presents GPU-based solutions to the Poisson equation with homogeneous Dirichlet boundary conditions in two spatial dimensions. This problem has well-understood behavior, but similar computation to many more complex real-world problems. We analyze the GPU performance using three types of memory access in the CUDA memory model (direct access to global memory, texture access, […]

April 13, 2012 by hgpu