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

Power and energy consumption are becoming an increasing concern in high performance computing. Compared to multi-core CPUs, GPUs have a much better performance per watt. In this paper we discuss efforts to redesign the most computation intensive parts of BLAST, an application that solves the equations for compressible hydrodynamics with high order finite elements, using […]

May 20, 2014 by hgpu

By consulting the state-of-the-art methods on massive linear equations solving and parallel computing, the main issue of calculation have been extracted from finite element method. The author test some solving routines on the CPU based as well as design and implement on GPU by using CUDA. The coalesced access result on GPU shows a ten […]

May 7, 2014 by hgpu

Computer-based surgical simulation and non-rigid medical image registration in image-guided interventions are examples of applications that would benefit from real-time deformation simulation of soft tissues. The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models which then can be discretized by the Finite Element Method (FEM) for a numerical solution. […]

May 5, 2014 by hgpu

In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solver. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O(p^2 log(N/p)) for one dimensional problems, O(Np^2) for two dimensional problems, and O(N^(4/3)p^2) for three dimensional problems, where N is the number of degrees of freedom, […]

April 21, 2014 by hgpu

The paper presents a highly efficient way of simulating the dynamic behavior of deformable objects by means of the finite element method (FEM) with computations performed on Graphics Processing Units (GPU). The presented implementation reduces bottlenecks related to memory accesses by grouping the necessary data per node pairs, in contrast to the classical way done […]

April 14, 2014 by hgpu

We present a performance analysis of a parallel implementation of both conjugate gradient and preconditioned conjugate gradient solvers using graphic processing units with CUDA parallel programming model. The solvers were optimized for a fast solution of sparse systems of equations arising from Finite Element Analysis (FEA) of electromagnetic phenomena. The preconditioners were Incomplete Cholesky factorization […]

March 12, 2014 by hgpu

How do we build maintainable, robust, and performance-portable scientific applications? This thesis argues that the answer to this software engineering question in the context of the finite element method is through the use of layers of Domain-Specific Languages (DSLs) to separate the various concerns in the engineering of such codes. Performance-portable software achieves high performance […]

December 11, 2013 by hgpu

We present a multi-frontal direct solver for two dimensional isogeometric finite element method simulations with NVIDIA CUDA and perform numerical experiments for linear, quadratic and cubic B-splines. We compare the computational cost O(Np^2) for 2D parallel shared memory implementation with the corresponding estimate O(N^1.5p^3) for a standard 2D sequential implementation. We conclude the presentation with […]

November 23, 2013 by hgpu