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

The movement of poorly sorted material over steep areas constitutes a hazardous environmental problem. Computational tools help in the understanding and predictions of such landslides. The main drawback is the high computational effort required for obtaining accurate numerical solutions due to the high number of cells involved in the calculus. In order to overcome this […]

March 3, 2015 by alacasta

This paper presents a GPU-accelerated implementation of two-dimensional Smart Laplacian smoothing. This implementation is developed under the guideline of our paradigm for accelerating Laplacianbased mesh smoothing [13]. Two types of commonly used data layouts, Array-of-Structures (AoS) and Structure-of-Arrays (SoA) are used to represent triangular meshes in our implementation. Two iteration forms that have different choices […]

February 3, 2015 by hgpu

This work is related with the implementation of a finite volume method to solve the 2D Shallow Water Equations on Graphic Processing Units (GPU). The strategy is fully oriented to work efficiently with unstructured meshes which are widely used in many fields of Engineering. Due to the design of the GPU cards, structured meshes are […]

September 23, 2014 by alacasta

We propose a parallel ray-tracing technique to visualize signed distance fields generated from triangular meshes based on NVIDIA OptiX. Our method visualizes signed distance fields with various distance offset values at interactive rates (2-12 fps). Our method utilizes a parallel kd-tree implementation to query the nearest triangle and the sphere tracing method to visualize the […]

January 2, 2014 by hgpu

We present a simplification algorithm for triangular meshes, implemented on the GPU. The algorithm performs edge collapses driven by a quadric error metric. It uses data parallelism as provided by OpenCL and has no sequential segments in its main iterative structure in order to fully exploit the processing power of the GPU. Our implementation produces […]

July 5, 2013 by hgpu

We propose a parallel method for computing local Laplacian curvature flows for triangular meshes. Laplace operator is widely used in mesh processing for mesh fairing, noise removal or curvature estimation. If the Laplacian flow is used in global sense constraining a whole mesh with an iterative weighted linear system, it can be used even for […]

May 29, 2013 by hgpu

Flipping is a local and efficient operation to construct the convex hull in an incremental fashion. However, it is known that the traditional flip algorithm is not able to compute the convex hull when applied to a polyhedron in R3. Our novel Flip-Flop algorithm is a variant of the flip algorithm. It overcomes the deficiency […]

January 18, 2013 by hgpu

This paper presents a parallel, implementation-friendly analytic visibility method for triangular meshes. Together with an analytic filter convolution, it allows for a fully analytic solution to anti-aliased 3D mesh rendering on parallel hardware. Building on recent works in computational geometry, we present a new edge-triangle intersection algorithm and a novel method to complete the boundaries […]

January 16, 2013 by hgpu

The Delaunay edge-flip algorithm is a practical method for transforming any existing triangular mesh S into a mesh T(S) that satisfies the Delaunay condition. Although several implementations of this algorithm are known, to the best of our knowledge no parallel GPU-based implementation has been reported yet. In the present work, we propose a quadriphasic and […]

January 8, 2012 by hgpu

We present a Conforming Delaunay Triangulation (CDT) algorithm based on maximal Poisson disk sampling. Points are unbiased, meaning the probability of introducing a vertex in a disk-free subregion is proportional to its area, except in a neighborhood of the domain boundary. In contrast, Delaunay refinement CDT algorithms place points dependent on the geometry of empty […]

January 4, 2012 by hgpu

The numerical solution of two-layer shallow water systems is required to simulate accurately stratified fluids, which are ubiquitous in nature: they appear in atmospheric flows, ocean currents, oil spills, etc. Moreover, the implementation of the numerical schemes to solve these models in realistic scenarios imposes huge demands of computing power. In this paper, we tackle […]

November 15, 2011 by hgpu