This paper presents an end-to-end massively parallelized procedure for the solution of boundary value problems on Graphics Processing Units (GPU). The proposal is an integrated strategy that not only entails the calculation of nodal contributions, and the stiffness matrix assembly using the Meshless Local Petrov Galerkin Method (MLPG) but also the iterative solution of the system of algebraic equations in combination with methods from the Conjugate Gradient (CG) family. This end-to-end solution is fully developed using the Compute Unified Device Architecture (CUDA) platform without the need for extra data movement between the device and host after the matrix assembly. This is possible thanks to the parallel nature of the MLPG; each node designates a thread on the device. The introduced solution is wholly executed in the GPU, with minimal auxiliary structures or global synchronization points. The proposed approach was applied to the solution of a simple electromagnetic problem, and a sevenfold speedup was observed.

Abstract. This paper presents an approach for extending the vector space model (VSM) to perform XML retrieval. The model is extended to support important aspects of XML structural and semantic information such as element nesting level, matching tag names in the query and the collection and the relation between tag names and content of an element. Potential use of the model for heterogeneous as well as for the unstructured collection is also shown. We compared our model with the standard vector space model and obtained a gain for unstructured and structured queries. For unstructured collections the vector space model effectiveness is preserved.

In this paper, a strategy to parallelize the meshless local Petrov-Galerkin (MLPG) method is developed. It is executed in a high parallel architecture, the well known graphics processing unit. The MLPG algorithm has many variations depending on which combination of trial and test functions is used. Two types of interpolation schemes are explored in this paper to approximate the trial functions and a Heaviside step function is used as test function. The first scheme approximates the trial function through a moving least squares interpolation, and the second interpolates using the radial point interpolation method with polynomial reproduction (RPIMp). To compare these two approaches, a simple electromagnetic problem is solved, and the number of nodes in the domain is increased while the time to assemble the system of equations is obtained. Results shows that with the parallel version of the algorithm it is possible to achieve an execution time 20 times smaller than the CPU execution time, for the MLPG using RPIMp versions of the method.Index Terms-Computer unified architecture (CUDA), meshless local Petrov-Galerkin (MLPG), parallel processing.

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Meshless methods are increasingly gaining space in the study of electromagnetic phenomena as an alternative to traditional mesh-based methods. One of their biggest advantages is the absence of a mesh to describe the simulation domain. Instead, the domain discretization is done by spreading nodes along the domain and its boundaries. Thus, meshless methods are based on the interactions of each node with all its neighbors, and determining the neighborhood of the nodes becomes a fundamental task. The k-nearest neighbors (kNN) is a well-known algorithm used for this purpose, but it becomes a bottleneck for these methods due to its high computational cost. One of the alternatives to reduce the kNN high computational cost is to use spatial partitioning data structures (e.g., planar grid) that allow pruning when performing the k-nearest neighbors search. Furthermore, many of these strategies employed for kNN search have been adapted for graphics processing units (GPUs) and can take advantage of its high potential for parallelism. Thus, this paper proposes a multi-GPU version of the grid method for solving the kNN problem. It was possible to achieve a speedup of up to 1.99x and up to 3.94x using two and four GPUs, respectively, when compared against the single-GPU version of the grid method.