We present a parallel GPU solution of the Caputo fractional reaction-diffusion equation in one spatial dimension with explicit finite difference approximation. The parallel solution, which is implemented with CUDA programming model, consists of three procedures: preprocessing, parallel solver, and postprocessing. The parallel solver involves the parallel tridiagonal matrix vector multiplication, vector-vector addition, and constant vector […]

June 22, 2014 by hgpu

In this paper, the adaptability of the neutron diffusion numerical algorithm on GPUs was studied, and a GPUaccelerated multi-group 3D neutron diffusion code based on finite difference method was developed. The IAEA 3D PWR benchmark problem was calculated in the numerical test. The results demonstrate both high efficiency and adequate accuracy of the GPU implementation […]

May 14, 2014 by hgpu

We have developed a numerical model that simulates the growth of small avascular solid tumors. At its core lies a set of partial differential equations that describe diffusion processes as well as transport and reaction mechanisms of a selected number of nutrients. Although the model relies on a restricted subset of molecular pathways, it compares […]

March 19, 2014 by hgpu

The paper proposes a high-productivity framework for multi-GPU computation of mesh-based applications. In order to achieve high performance on these applications, we have to introduce complicated optimized techniques for GPU computing, which requires relatively-high cost of implementation. Our framework automatically translates user-written functions that update a grid point and generates both GPU and CPU code. […]

January 25, 2014 by hgpu

Parallel algorithms for modern high performance computing systems are required for fast modelling of high dimensional convection-diffusion processes in air. Such algorithms, designed for alternate-triangular finite difference splitting schemes applied to convection-diffusion equation, have been considered. An algorithm for single GPU systems and an algorithm for clusters with graphical processors has been described, algorithms’ performance […]

October 24, 2013 by hgpu

Solving a banded linear system efficiently is important to many scientific and engineering applications. Current solvers achieve good scalability only on the linear systems that can be partitioned into independent subsystems. In this paper, we present a GPU based, scalable Bi-Conjugate Gradient Stabilized solver that can be used to solve a wide range of banded […]

August 16, 2013 by hgpu

In this paper we study a parallel form of the SOR method for the numerical solution of the Convection Diffusion equation suitable for GPUs using CUDA. To exploit the parallelism offered by GPUs we consider the fine grain parallelism model. This is achieved by considering the local relaxation version of SOR. More specifically, we use […]

May 20, 2013 by hgpu

In this thesis, I present the theory and modeling of poro-elasto-plastic rheology coupled to a non-linear diffusion equation with a step increase in permeability at the onset of slip. This theoretical model is implemented in the graphic processing unit (GPU) architecture and programmed using the nVidia CUDA programming language. The numerical models are benchmarked by […]

April 25, 2013 by hgpu

We present a real-time subsurface scattering simulation to perform real-time rendering of translucent particle-based fluids. After particle-based fluid simulation, we immediately build voxelized fluids, calledVoronoi fluids, with particle locations and neighbour lists using GPUs. And then, we perform a multiple subsurface scattering simulation over the Voronoi fluids with the diffusion equation (DE). We employ Finite […]

April 12, 2013 by hgpu

High quality global illumination can enhance the visual perception of depth cue and local thickness of volumetric data but it is seldom used in scientific visualization because of its high computational cost. This paper presents a novel grid-based illumination technique which is specially designed and optimized for volume visualization purpose. It supports common light sources […]

January 4, 2013 by hgpu

Solving complex convection-diffusion equations is very important to many practical mathematical and physical problems. After the finite difference discretization, most of the time for equations solution is spent on sparse linear equation solvers. In this paper, our goal is to solve 2D Nonlinear Unsteady Convection-Diffusion Equations by accelerating an iterative algorithm named Jacobi-preconditioned QMRCGSTAB on […]

June 20, 2011 by hgpu

The computational power of modern graphics processing units (GPUs) has become an interesting alternative in high performance computing. The specialized hardware of GPUs delivers a high degree of parallelism and performance. Various applications in scientific computing have been implemented such that computationally intensive parts are executed on GPUs. In this article, we present a GPU […]

June 5, 2011 by hgpu