Scientific computation is the field of study that uses computers to implement mathematical models of physical phenomena such as FEM in deformation measurement in virtual reality. Scientific and engineering problems that would be almost impossible to solve by hand whereas on a computer, it can be handled properly. A numerical algorithm calculating for different fields […]

April 9, 2014 by hgpu

## Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear […]

March 27, 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

In this paper, we investigated the effect of adding more small curves to the initial condition which determines the required number of iterations of a fast level set (LS) evolution. As a result, we discovered two new theorems and developed a proof on the worst case of the required number of iterations. Furthermore, we found […]

March 14, 2014 by hgpu

Massively parallel processors, such as graphical processing units (GPUs), have in recent years proven to be effective for a vast amount of scientific appli- cations. Today, most desktop computers are equipped with one or more pow- erful GPUs, offering heterogeneous high-performance computing to a broad range of scientific researchers and software developers. Though GPUs are […]

March 12, 2014 by apek

We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial differential equations and are widely used in the simulation of tsunami wave propagations. Our algorithms are tailored to take advantage of the single instruction […]

March 10, 2014 by hgpu

We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs. The method involves two stages, setup and solve. In the setup stage, hierarchical coarse grids are constructed through aggregation of the fine grid nodes. […]

March 10, 2014 by hgpu

Memory bound applications such as solvers for large sparse systems of equations remain a challenge for GPUs. Fast solvers should be based on numerically efficient algorithms and implemented such that global memory access is minimised. To solve systems with up to one trillion (10^12) unknowns the code has to make efficient use of several million […]

February 17, 2014 by hgpu

A standard technique to numerically solve elliptic partial differential equations on structured grids is to discretize them via finite differences and then to apply an efficient geometric multi-grid solver. Unfortunately, finding the optimal choice of multi-grid components and parameters is challenging and platform dependent, especially, in cases where domain knowledge is incomplete. Auto-tuning is a […]

February 17, 2014 by hgpu

Stencil computations are very regular and well adapted to GPU execution. However, the PCI-E bus that connects a discrete GPU to the system memory has a relatively low bandwidth when compared to the GPU compute power. The AMD APU architecture contains both CPU and GPU on the same chip and shared memory between them, which […]

January 26, 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

In recent years, a new approach to analyze fracturing has been developed. The so-called phase field models approximate cracks by a scalar, macroscopic field variable that distinguishes between broken and undamaged material. The phase field approach to fracture has significant advantages over more established methods. However it is necessary to solve a coupled set of […]

December 8, 2013 by hgpu