Mauricio Kischinhevsky

Modelling and numerical simulations of contaminant transport in naturally fractured porous media

Models for incompressible underground flows through naturally fractured formations subjected to high-level nuclear waste contamination are introduced and studied. They consider a chain of contaminants that decay into other species, allowing the monitoring of descendant radioactive species as well. A simulator that describes scenarios of long distance effects in case of leakage from a repository placed in such rock formations was developed. The simulator includes features like high accuracy and slowly increasing time steps in order to handle phenomena of timescale of centuries with detailed description of the transient phase, where few days is the adequate time scale.

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.

Convergence analysis of the Hopmoc method

The Hopmoc method combines concepts of the modified method of characteristics (MMOC) and the Hopscotch method. First, Hopmoc resembles Hopscotch because it decomposes the set of grid points into two subsets. Namely, both subsets have their unknowns separately updated within one semi-step. Furthermore, each subset undergoes one explicit and one implicit update of its unknowns in order to lead to a symmetrical procedure. Such decomposition inspired the use of a convergence analysis similar to the one used in alternating direction implicit methods. Secondly, the steps are evaluated along characteristic lines in a semi-Lagrangian approach similar to the MMOC. In this work, both consistency and stability analysis are discussed for Hopmoc applied to a convection–diffusion equation. The analysis produces sufficient conditions for the consistency analysis and proves that the Hopmoc method presents unconditional stability. In addition, numerical results confirm the conducted convergence analysis.

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.

A New Heuristic for Bandwidth and Profile Reductions of Matrices Using a Self-organizing Map

In this work, a heuristic for bandwidth and profile reductions of symmetric and asymmetric matrices using a one-dimensional self-organizing map is proposed. Experiments and comparisons of results obtained were performed in relation to results of the Variable neighborhood search for bandwidth reduction. Simulations with these two heuristics were performed with 113 instances of the Harwell-Boeing sparse matrix collection and with 2 sets of instances with linear systems composed of sparse symmetric positive-definite matrices. The linear systems were solved using the Jacobi-preconditioned Conjugate Gradient Method. According to the results presented here, the best heuristic in the simulations performed was the Variable neighborhood search for bandwidth reduction. On the other hand, when the vertices of the corresponding graph were originally ordered in a sequence given by a space-filling curve, no gain was obtained when applying a heuristic for reordering the graph vertices.

Hybrid MPI/OpenMP/OpenACC Implementations for the Solution of Convection-Diffusion Equations with the HOPMOC Method

The need for fast solution of large scientific and industrial problems has long motivated the quest for improvements both in software as well as in hardware, since the inception of computing tools. In this context, vectorization, parallelization of tasks have been important strategies for the improvement of hardware efficiency during the last decades. Operator splitting techniques for the numerical solution of partial differential equations are also an attempt towards the same goal, on the software side. This work presents two parallel implementations of the Hopmoc method to solve parabolic equations with convective dominance on a cluster with multiple multicore nodes or GPUs. The Hopmoc method is based both on the modified method of characteristics and the Hopscotch method. It is implemented through an explicit-implicit operator splitting technique. Hopmoc has been studied on distributed memory machines under MPI. In this work Hopmoc is implemented on clusters of multiple cores or GPUs in one single programming model. Previous results had shown that Hopmoc is a scalable parallel procedure with respect to distributed memory machines. New numerical results of the technique presented herein show performance improvements of up to 300 times when compared with the sequential version.

An evaluation of four reordering algorithms to reduce the computational cost of the Jacobi-preconditioned conjugate gradient method using high-precision arithmetic

In this work, four heuristics for bandwidth and profile reductions are evaluated. Specifically, the results of a recent proposed heuristic for bandwidth and profile reductions of symmetric and asymmetric matrices using a one-dimensional self-organising map is evaluated against the results obtained from the variable neighbourhood search for bandwidth reduction heuristic, the original reverse Cuthill-McKee method, and the reverse Cuthill-McKee method with starting pseudo-peripheral vertex given by the George-Liu algorithm. These four heuristics were applied to three datasets of linear systems composed of sparse symmetric positive-definite matrices arising from discretisations of the heat conduction and Laplace equations by finite volumes. The linear systems are solved by the Jacobi-preconditioned conjugate gradient method when using high-precision numerical computations. The best heuristic in the simulations performed with one of the datasets used was the Cuthill-McKee method with starting pseudo-peripheral vertex given by the George-Liu algorithm. On the other hand, no gain was obtained in relation to the computational cost of the linear system solver when a heuristic for bandwidth and profile reduction is applied to instances contained in two of the datasets used.

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.

Autonomous Leaves Graph Applied to the Boundary Layer Problem

In physics and fluid mechanics, the boundary layer is the fluid layer in the immediate vicinity of a bounding surface. It is important in many aerodynamic problems. This work presents a numerical simulation of the bidimensional laminar boundary-layer problem considering a steady incompressible flow with no-slip condition on the surface by Autonomous Leaves Graph based on finite volume discretizations. In addition, a Modified Hilbert Curve numbers the control volumes. Initially, the numerical solution of the flat-plate problem is compared to its analytical solution, namely Blasius Solution. Secondly, simulations of the flow along a NACA airfoil shape are presented. Computer experiments show that an adaptive mesh refinement using the Autonomous Leaves Graph with the Modified Hilbert Curve numbering is appropriate for a aerodynamic problem. Finally, results illustrate that the method provides a good trade-off between speed and accuracy.

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.