We present a computational framework for high-performance tensor contractions on GPUs. High-performance is difficult to obtain using existing libraries, especially for many independent contractions where each contraction is very small, e.g., sub-vector/warp in size. However, using our framework to batch contractions plus application-specifics, we demonstrate close to peak performance results. In particular, to accelerate large […]

January 29, 2016 by hgpu

The Explicit Finite Element Method is a powerful tool in nonlinear dynamic finite element analysis. Recent major developments in computational devices, in particular, General Purpose Graphical Processing Units (GPGPU’s) now make it possible to increase the performance of the explicit FEM. This dissertation investigates existing explicit finite element method algorithms which are then redesigned for […]

January 22, 2016 by hgpu

A graphics processing unit (GPU) parallelization approach was implemented to improve the efficiency of nonlinear dynamic analysis. The GPU parallelization approach speeded up the computation of implicit time integration and reduced total calculation time. In addition, a parallel equations solver is introduced to solve the equation system. Numerical examples of reinforced concrete (RC) frames were […]

December 8, 2015 by hgpu

Finite Element Analysis helps designers at the early stages of product design through simulation and behavioral prediction. This thesis is on transient finite element analysis, specifically, structural dynamics, where the behavior of a product due to time-dependent loads is desired. A critical computational challenge in structural dynamics is that it typically requires significant amounts of […]

November 12, 2015 by hgpu

Finite Element Methods (FEM) are ubiquitous in science and engineering where they are used in fields as diverse as structural analysis, ocean modeling and bioengineering. FEM allow us to find approximate solutions to a system of partial differential equations over an unstructured mesh. The first phase of solving a FEM problem, local assembly, involves computing […]

November 3, 2015 by hgpu

In this dissertation, the hardware and API architectures of GPUs are investigated, and the corresponding acceleration techniques are applied on the traditional frequency domain finite element method (FEM), the element-level time-domain methods, and the nonlinear discontinuous Galerkin method. First, the assembly and the solution phases of the FEM are parallelized and mapped onto the granular […]

October 31, 2015 by hgpu

Finite Element Methods are techniques for estimating solutions to boundary value problems for partial differential equations from an approximating subspace. These methods are based on weak or variational forms of the BVP that require less of the problem functions than what the original PDE would suggest in terms of order of differentiability and continuity. In […]

June 7, 2015 by hgpu

This thesis, entitled "High Performance Computing for solving large sparse systems. Optical Diffraction Tomography as a case of study" investigates the computational issues related to the resolution of linear systems of equations which come from the discretization of physical models described by means of Partial Differential Equations (PDEs). These physical models are conceived for the […]

March 30, 2015 by hgpu

In an ideal world, scientific applications are computationally efficient, maintainable and composable and allow scientists to work very productively. We argue that these goals are achievable for a specific application field by choosing suitable domain-specific abstractions that encapsulate domain knowledge with a high degree of expressiveness. This thesis demonstrates the design and composition of domain-specific […]

February 1, 2015 by hgpu

The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite element matrix construction, which is also time-consuming for unstructured meshes, has been less investigated. The generation of the global […]

January 21, 2015 by fjramireg

In recent years clock speeds and memory bandwidths of Graphics Processing Units (GPUs) increased dramatically compared to CPUs. Also GPU vendors developed and freely released new programming tools to make scientific computing on GPUs easier. With these recent developments the use of GPUs for general purpose computing becomes a popular research field. Researchers previously demonstrated […]

January 16, 2015 by hgpu

In the finite element method simulation we often deal with large sparse matrices. Sparse matrix-vector multiplication (SpMV) is of high importance for iterative solvers. During the solver stage, most of the time is in fact spent in the SpMV routine. The SpMV routine is highly memory-bound; the processor spends much time waiting for the needed […]

August 15, 2014 by hgpu