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

The last decade saw the long tradition of frequency scaling of processing units grind to a halt, and efforts were re-focused on maintaining computational growth by other means; such as increased parallelism, deep memory hierarchies and complex execution logic. After a long period of "boring productivity", a host of new architectures, accelerators, programming languages and […]

July 24, 2014 by hgpu

The numerical solution of partial differential equations using the finite element method is one of the key applications of high performance computing. Local assembly is its characteristic operation. This entails the execution of a problem-specific kernel to numerically evaluate an integral for each element in the discretized problem domain. Since the domain size can be […]

July 10, 2014 by hgpu

We have developed a graphics processor unit (GPU-) based high-speed fully 3D system for diffuse optical tomography (DOT). The reduction in execution time of 3D DOT algorithm, a severely ill-posed problem, is made possible through the use of (1) an algorithmic improvement that uses Broyden approach for updating the Jacobian matrix and thereby updating the […]

June 6, 2014 by hgpu