Evaluating the performance of the particle finite element method in parallel architectures (original) (raw)
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Towards a Massively Parallel simulations with PFEM-2
2013
In this work an implementation of the Particle Finite Element Method Two (PFEM-2) based on the distributed-memory architecture is presented. PFEM-2 consists on a material derivative based formulation of the transport equations with an hybrid spatial discretization which uses an eulerian mesh and lagrangian particles. Strategies for the parallelization of eulerian methods based on mesh or lagrangian solutions based on particles which solve fluid-dynamics problems are widely studied separately, however not enough works treat the use of both approaches together. Typical solutions for domaindistribution on eulerian frames are not proper to balance the work-load on some lagrangian stages, then to achieve good performance must be analyzed the use of weighted decomposition to the partitioning. Performance analysis of the implementation running over a beowulf cluster are presented. The weighted partitioning can be used to improve the speed-up when the diffusion of the problem is low, on the other hand, with large diffusion a classical eulerian decomposition is the best choice. However the overall cpu-time required to solve the presented incompressible flow cases with the PFEM-2 method is lower than using classical eulerian solvers, which give auspicious future thinking in solving massively parallel simulations.
PPM – A highly efficient parallel particle–mesh library for the simulation of continuum systems
Journal of Computational Physics, 2006
This paper presents a highly efficient parallel particle-mesh (PPM) library, based on a unifying particle formulation for the simulation of continuous systems. In this formulation, the grid-free character of particle methods is relaxed by the introduction of a mesh for the reinitialization of the particles, the computation of the field equations, and the discretization of differential operators. The present utilization of the mesh does not detract from the adaptivity, the efficient handling of complex geometries, the minimal dissipation, and the good stability properties of particle methods. The coexistence of meshes and particles, allows for the development of a consistent and adaptive numerical method, but it presents a set of challenging parallelization issues that have hindered in the past the broader use of particle methods. The present library solves the key parallelization issues involving particle-mesh interpolations and the balancing of processor particle loading, using a novel adaptive tree for mixed domain decompositions along with a coloring scheme for the particle-mesh interpolation. The high parallel efficiency of the library is demonstrated in a series of benchmark tests on distributed memory and on a shared-memory vector architecture. The modularity of the method is shown by a range of simulations, from compressible vortex rings using a novel formulation of smooth particle hydrodynamics, to simulations of diffusion in real biological cell organelles. The present library enables large scale simulations of diverse physical problems using adaptive particle methods and provides a computational tool that is a viable alternative to mesh-based methods.
Validation of the particle finite element method (PFEM) for simulation of free surface flows
Engineering Computations, 2008
Purpose -The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows. Design/methodology/approach -A numerical simulation of a number of examples for which experimental data are available is performed. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Some examples are chosen from the civil engineering field: a study of the flow over a flip bucket is analyzed for both 2D and 3D models, and the flow under a planar sluice gate is studied in 2D. Other examples, such as a 2D and 3D "dam break" with an obstacle are taken from the smooth particle hydrodynamics literature. Findings -Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Different mesh sizes are considered for evaluating their influence on the final solution. Originality/value -Details of the input data for all the examples studied are given. The aim is to identify benchmark problems for future comparisons between different numerical approaches for free surface flows. This is the basis of the volume of fluid (VOF) technique. This scalar function is convected according to the flow velocity field once a suitable discretization of the space is provided. This allows using existing Eulerian codes and this justifies the success of the VOF method in the CFD community. This formulation permits to deal naturally with separation (or reattachment) of parts of the fluid domain; nevertheless some concerns remain particularly on the imposition of the Dirichlet boundary conditions on the free surface. Even if all the advantages of Eulerian methods on fixed meshes can be retained, the VOF approach tends to introduce some diffusion in the position of sharp interfaces (see for examples Zalesak's circle benchmark ).
2014
The latest version of the Particle-Finite Element Method (PFEM), which incorporates the novel explicit integration strategy named eXplicit Integration of Velocity and Acceleration following Streamlines (X-IVAS), has proven to be fast and accurate to solve homogeneous flows, mainly thanks to the possibility of using large time-steps. In this work the extension of this strategy to solve multiphase flows is presented, where the calculation of the interface evolution is of fundamental importance. In Eulerian formulations, one of the most used strategies to determine the interface position is the advection of an indicator function. This approach is followed, by example, in the Volume of Fluid (VoF) technique, which can add limiters as a method of guaranteeing boundedness and/or sharpness of phasefractions. On the other hand, Lagrangian frames use typically marker particles. In the case of PFEM, the same set of particles transported for flow calculation allows to carry a marker function t...
Computational Efficiency of Parallel Unstructured Finite Element Simulations
High Performance Computing on Vector Systems, 2006
In this paper we address various efficiency aspects of finite element (FE) simulations on vector computers. Especially for the numerical simulation of large scale Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems efficiency and robustness of the algorithms are two key requirements. In the first part of this paper a straightforward concept is described to increase the performance of the integration of finite elements in arbitrary, unstructured meshes by allowing for vectorization. In addition the effect of different programming languages and different array management techniques on the performance will be investigated. Besides the element calculation, the solution of the linear system of equations takes a considerable part of computation time. Using the jagged diagonal format (JAD) for the sparse matrix, the average vector length can be increased. Block oriented computation schemes lead to considerably less indirect addressing and at the same time packaging more instructions. Thus, the overall performance of the iterative solver can be improved. The last part discusses the input and output facility of parallel scientific software. Next to efficiency the crucial requirements for the IO subsystem in a parallel setting are scalability, flexibility and long term reliability. 2
THE PARTICLE FINITE ELEMENT METHOD — AN OVERVIEW
International Journal of Computational Methods, 2004
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.
Parallel finite element computations in fluid mechanics
Computer Methods in Applied Mechanics and Engineering, 2006
We provide an overview of the role of parallel finite element computations in fluid mechanics. We emphasize the class of flow problems involving moving boundaries and interfaces. Some of the computationally most challenging flow problems, such as fluid-object and fluid-structure interactions as well as free-surface and two-fluid flows, belong to this class. In the development of the methods targeting this class of problems, the computational challenges involved need to be addressed in such a way that 3D computation of complex applications can be carried out efficiently on parallel computers. This requirement has to be one of the key factors in designing various components of the overall solution approach, such as solution techniques for the discretized equations and mesh update methods for handling the changes in the spatial domain occupied by the fluid. This overview includes a description of how the computational challenges are addressed and how the computational schemes can be enhanced with special preconditioning techniques.