Diego N. Brandão

Performance Evaluation of Optimized Implementations of Finite Difference Method for Wave Propagation Problems on GPU Architecture

The scattering of acoustic waves in non-homogeneous media has been of practical interest for the petroleum industry, mainly in the determination of new oil deposits. A family of computational models that represent this phenomenon is based on finite difference methods. The simulation of these phenomena demands a high computational cost. In this work we employ GPU for the development of solvers for a 2D wave propagation problem with finite difference methods. Although there are many related works that use the same implementation presented in this paper, we propose a detailed and novel performance and memory bottleneck analysis for this hardware architecture.

A probabilistic cellular automata model for highway traffic simulation

Abstract This work presents a probabilistic model for the microscopic simulation of traffic roads based on Nagel-Schreckenberg’s model. Each driver’s behavior is described through the combination of a continuous probability function with an anticipatory feature that leads to a counter flow velocity tunning. The simulations developed and described herein give rise to a phase diagram which resembles and enriches the fundamental diagram, in its theoretical as well as for real data.

Hermite finite elements for diffusion phenomena

Two new Hermite finite elements are shown to be an advantageous alternative to well-known mixed methods in the simulation of diffusion processes in heterogeneous anisotropic media. Both are N-simplex based for N = 2 and N = 3 and provide flux continuity across inter-element boundaries. One of the methods denoted by P 2 H was introduced by the first author and collaborator for the case of homogeneous and isotropic media. Its extension to the case of heterogeneous and/or anisotropic cases is exploited here, keeping an implementation cost close to the popular Raviart-Thomas mixed finite element of the lowest order, known as RT 0 . The other method studied in detail in this work is a new Hermite version of the latter element denoted by RT 0 M . Formal results are given stating that, at least in the case of a constant diffusion, RT 0 M is significantly more accurate than RT 0 , although both elements have essentially the same implementation cost. A thorough comparative numerical study of the Hermite methods and RT 0 is carried out in the framework of highly heterogeneous media among other cases. It turns out that both are globally superior all the way, and roughly equivalent to each other in most cases.

Tuning Up TVD HOPMOC Method on Intel MIC Xeon Phi Architectures with Intel Parallel Studio Tools

This paper focuses on the parallelization of TVD Method scheme for numerical time integration of evolutionary differential equations. The Hopmoc method for numerical integration of differential equations was developed aiming at benefiting from both the concept of integration along characteristic lines as well as from the spatially decomposed Hopscotch method. The set of grid points is initially decomposed into two subsets during the implementation of the integration step. Then, two updates are performed, one explicit and one implicit, on each variable in the course of the iterative process. Each update requires an integration semi step. This is carried out along characteristic lines in a Semi-Lagrangian scheme based on the Modified Method of Characteristics. This work analises two strategies to implement the parallel version of TVD Hopmoc based on the analysis performed by Intel Tools such Parallel and Threading Advisor. A naive solution is substituted by a chunk loop strategy in order to avoid fine-grain tasks inside main loops.

Sound Wave Propagation Applied in Games

Many games and other interactive virtual environments are known for their focus in rendering natural phenomena, such as accurate visuals and physics, in the most believable manner. Several advances in the aforementioned fields took place during the last decade but, unfortunately, this effort has not been reflected in libraries for spatial audio. These libraries traditionally do not accurately simulate sound wave propagation through the virtual environment, never taking into consideration the speed of sound, reflection and absorbency by scene geometry, phenomena whose simulation could be used to render many interesting effects in real time. In this paper, we propose the use of a sound wave propagation simulation based on the finite difference method, running on the GPU, that can be used to compute how a sound pulse spreads through a virtual environment. In the prototypes implemented, the simulation data is interactively used to determine the perceived direction of a sound source in a closed building, and rendering a mimic of a shock-wave in an open scene

Finite-Element Non-conforming h-Adaptive Strategy Based on Autonomous Leaves Graph

Adaptive mesh refinement techniques are used in order to decrease the computational cost associated with the numerical solution of Partial Differential Equations. In this work, the refined mesh is represented by a graph data structure. More precisely. this scheme follows the Autonomous Leaves Graph concepts. The objective is to construct an adaptive mesh refinement with lower cost than tree-based schemes. Moreover, the Autonomous Leaves Graph was initially proposed with the Finite Volume Method and a Modified Hilbert Curve was used for the total-ordering of the control volumes. This work proposes to integrate the Autonomous Leaves Graph and the Finite Element Method as well as to adapt the Modified Hilbert Curve for this scheme. Furthermore, a non-conforming h -adaptive strategy is implemented. This approach is applied in the solution of the Poisson equation problem and the experimental results are discussed.

Implementação Hıbrida MPI/OpenMP do Método HOPMOC na Resolução da Equação de Convecção-Difusão

A utilizacao da computacao paralela na resolucao de certos problemas descritos por equacoes diferenciais parciais permite um ganho significativo no tempo de computacao. Este trabalho apresenta uma implementacao paralela do metodo HOPMOC em um ambiente de maquinas multicore. O metodo HOPMOC utiliza conceitos do metodo das caracteristicas modificado associado com metodo Hopscotch. Tal construcao lhe fornece caracteristicas ideais para abordagens em computacao paralela em ambientes de memoria distribuida. O presente trabalho utiliza uma abordagem hibrida para o HOPMOC: o MPI e utilizado para comunicacao no ambiente distribuido, enquanto o OpenMP permite o paralelismo no ambiente de memoria compartilhada de cada no do cluster. Resultados preliminares demonstram ganhos significativos de eficiencia da implementacao hibrida apresentada quando comparado com uma versao sequencial do HOPMOC.

An Architecture Using a Finite Difference Method to Calculate Realistic Sound Equalization in Games

Most games and other interactive virtual environments focus on rendering natural phenomena in the most believable manner by using accurate visuals and physics. However, not much effort has been put into accounting for the physics of sound. The simulation of the real behavior of sound through an environment, when considering the speed of sound, reflection, and absorption, is computationally expensive and is usually left aside. In this work, an algorithm that calculates sound wave propagation using a finite difference method is used and extended to present a novel approach to sound rendering. This approach reaches the objective more quickly, and the sound generated has no perceptible loss of accuracy. The approach is designed to be implemented in GPU architectures and eventually enable real-time results.

An adaptive graph for volumetric mesh visualization

Abstract This work presents an adaptive strategy in order to visualize volumetric data generated from numerical simulations of partial differential equations. The mesh is represented by a graph data structure. Moreover, the Autonomous Leaves Graph is extended to the three-dimensional case. This scheme intends to achieve better transversal cost than a treelike (e.g., bintree, quadtree and octree) space arrangement approach. Furthermore, this strategy intends to reduce the computational cost of constructing the discretization and the visualization of data. The total-ordering of the mesh volumes used in the discretization and the visualization processes is by the 3D Modified Hilbert space-filling Curve. To evaluate the performance, the strategy is applied on a Heat Conduction simulation problem using finite difference discretizations and the experimental results are discussed. Comparisons are made between numerical results obtained when using the Hilbert Curve and its modified version. In addition, experiments are shown when visualization is made from inside and outside the volume. The results expose the efficiency of using this strategy.