Parallel Finite Element Computations Research Articles

Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations

Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations

Parallel iterative stabilized finite element methods based on the quadratic equal-order elements for incompressible flows

Combining the quadratic equal-order stabilized method with the approach of local and parallel finite element computations and classical iterative methods for the discretization of the steady-state Navier–Stokes equations, three parallel iterative stabilized finite element methods based on fully overlapping domain decomposition are proposed and compared in this paper. In these methods, each processor independently computes an approximate solution in its own subdomain using a global composite mesh that is fine around its own subdomain and coarse elsewhere, making the methods be easy to implement based on existing codes and have low communication complexity. Under some (strong) uniqueness conditions, stability and convergence theory of the parallel iterative stabilized methods are derived. Numerical tests are also performed to demonstrate the stability, convergence orders and high efficiency of the proposed methods.

Numerical analysis of pulsatile flows in a slot-die manifold

We analyze the effects of inlet periodic pulsatile flows on the flow inside a slot-die manifold for different locations of the inlet feed port. This type of flow rate disturbance can be caused by a coating liquid pumping mechanism that may lead to coating thickness nonuniformity. In this study, we analyze the transient behavior of the three-dimensional flows inside the slot-die manifold using parallel finite element computations. For a small magnitude of inlet flow rate disturbance with a given frequency, the local flow rate per unit width and the velocity profile at the feed slot exit become periodic. Therefore, the amplification factor can be used to quantify the effect of the inlet pulsatile flows. We found that the flow inside the feed slot, which is the confined channel with a high aspect ratio, dominates the dynamics of the outlet flow. However, the overall trend of the amplification factor along the cross-web direction resembles the steady-state pressure profile inside the cavity, and hence the steady-state profile of the outlet flow rate per unit width, which is strongly affected by the choice of the inlet port location.

Distributed evolutionary multi-objective mesh-partitioning algorithm for parallel finite element computations

Majority of the mesh-partitioning algorithms attempt to optimise the interprocessor communications, while balancing the computational load among the processors. However, it is desirable to simultaneously optimise the submesh aspect ratios in order to significantly improve the convergence characteristics of the domain decomposition based Preconditioned-conjugate-gradient algorithms, being used extensively in the state-of-the-art parallel finite element codes. Keeping this in view, a new distributed multi-objective mesh-partitioning algorithm using evolutionary computing techniques is proposed in this paper. Effectiveness of the proposed distributed mesh-partitioning algorithm is demonstrated by solving several unstructured meshes of practical-engineering problems and also benchmark problems.

Parallel finite element computation of incompressible flows

A stabilized finite element formulation for three-dimensional unsteady incompressible flows is implemented on a distributed memory parallel computer. A matrix-free version of the GMRES algorithm is utilized to solve the equation systems in an implicit manner. The scalability of the computations on a 64-processor Linux cluster is evaluated for moderate to large size problems. A method for estimating the speedup for large-scale problems, where computations on a single processor is not possible, is proposed. Superlinear speedup is observed, perhaps for the first time, for a large-scale problem that is associated with more than 44 million nodes and 176 million equations. The performance of the various subactivities of the program is monitored to investigate the cause. It is found that the formation of the RHS vector and the preconditioner achieves a very high level of superlinear speedup as the number of processors increase. As a result, even though the network time for interprocessor communication increases with increase in processors, an overall superlinear speedup is realized for large-scale problems. The superlinear speedup is attributed to cache related effects. A comparison between the performance of matrix and matrix-free versions of the GMRES algorithm is carried out. It is found that for large-scale applications the matrix-free version outperforms its counterpart for reasonable dimensions of the Kyrylov subspace. The effect of mesh partitioning on the scalability is also studied. A significant reduction in communication time is observed with partitioning that leads to an overall improvement of speedup. The parallel implementation is utilized to study the wake instabilities in flow past a stationary circular cylinder at Re = 150, 200 and 300. The Re = 150 flow is found to be two-dimensional while mode-A and mode-B instabilities are observed at Re = 200 and 300, respectively. The Re = 300 flow is associated with a low frequency modulation in addition to the vortex shedding frequency.

Adaptive full domain covering meshes for parallel finite element computations

In this work, we present a new parallelization concept for adaptive finite element methods. Compared to classical domain decomposition approaches, the concept of adaptive full domain covering meshes reduces the parallel communication overhead. Furthermore, it provides an easy way to transform sequential codes into parallel software by changing only a few lines of source code.

Parallel finite element computations of three-dimensional flow problems using padfem 2

In this paper, numerical results of different flow problems for the three-dimensional incompressible Navier–Stokes equations are presented. The problems describe a flow around an obstacle as well as a flow through a system of pipes. Furthermore, chemical species are added in case of the pipe flow. This additionally comprises a transport problem for the introduced species. The numerical approximation is accomplished with a finite element characteristic projection method based on the schemes of Chorin and Vankan. The numerical method for solving the three-dimensional Navier–Stokes equations and the species equations using the parallel adaptive finite element framework padfem 2 are illustrated. Mean values like lift and drag coefficient, pressure decay and species distribution are presented and compared with existing reference values. Finally, some efficiency results of the used solvers are given.

Parallel computing of multi-scale continental deformation in the Western United States: Preliminary results

Lithospheric deformation in the western United States is one of the best examples of diffuse continental tectonics that deviate from the plate tectonics paradigm. Conceptually, diffuse continental deformation is known to result from (1) weak and heterogeneous rheology of continents and (2) driving forces that arise from plate boundaries as well as within the continental lithosphere. However, the dynamic interplay of continental rheology and driving forces, hence the geodynamics of continental tectonics, remains poorly understood. The heterogeneous rheology and multiple driving forces cause continents to deform over different spatiotemporal scales with different physical processes, yet most geodynamic models for continental tectonic avoid dealing with such multiphysics partly because of (1) the limited observational constraints of lithospheric structure and deformation, and (2) high demands on computing algorithms and resources. These constraints, however, have relaxed significantly in recent years to permit exploration of some of the multi-scale physics governing continental tectonics. Here we present preliminary results of modeling multi-scale tectonics in the western United States using parallel finite element computation. In a 3D subcontinental-scale model, we used fine numerical meshes to incorporate all major tectonic boundaries and rheological heterogeneities in the model to explore their interplay with tectonic driving forces in controlling active tectonics in the western US. In another model for the entire San Andreas Fault system, we explored strain localization and simulated fault behavior at multi-timescales ranging from rupture in seconds to secular fault creep in tens of thousands of years. These models can help to integrate data grids with distributed high-performance computing resources in the emerging geosciences cyberinfrastructure.

A unified framework of multi-objective cost functions for partitioning unstructured finite element meshes

Good performance of parallel finite element computations on unstructured meshes requires high-quality mesh partitioning. Such a decomposition task is normally done by a graph-based partitioning approach. However, the main shortcoming of graph partitioning algorithms is that minimizing the so-called edge cut is not entirely the same as minimizing the communication overhead. This paper thus proposes a unified framework of multi-objective cost functions, which take into account several factors that are not captured by the graph-based partitioning approach. Freely adjustable weighting parameters in the framework also promote a flexible treatment of different optimization objectives. A greedy-style post-improvement procedure is designed to use these cost functions to improve the quality of subdomain meshes arising from the graph-based partitioning approach. Both serial and parallel implementation of the post-improvement procedure have been done. Numerical experiments show that communication overhead can indeed be reduced by this improvement procedure, thereby increasing the performance of parallel finite element computations.

Parallel finite element computations in fluid mechanics

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.

Generating optimised partitions for parallel finite element computations employing float-encoded genetic algorithms

Generating optimised partitions for parallel finite element computations employing float-encoded genetic algorithms

Iterative mesh partitioning strategy for improving the efficiency of parallel substructure finite element computations

This work presents an iterative mesh partitioning approach to improve the efficiency of parallel substructure finite element computations. The proposed approach employs an iterative strategy with a set of empirical rules derived from the results of numerical experiments on a number of different finite element meshes. The proposed approach also utilizes state-of-the-art partitioning techniques in its iterative partitioning kernel, a cost function to estimate the computational cost of each submesh, and a mechanism that adjusts element weights to redistribute elements among submeshes during iterative partitioning to partition a mesh into submeshes (or substructures) with balanced computational workloads. In addition, actual parallel finite element structural analyses on several test examples are presented to demonstrate the effectiveness of the approach proposed herein. The results show that the proposed approach can effectively improve the efficiency of parallel substructure finite element computations.

Parallel finite element computation of free-surface flows

In this paper we present parallel 2D and 3D finite element computation of unsteady, incompressible free-surface flows. The computations are based on the Deformable-Spatial-Domain/Stabilized Space-Time (DSD/SST) finite element formulation, which takes automatically into account the motion of the free surface. The free-surface height is governed by a kinematic free-surface condition, which is also solved with a stabilized formulation. The meshes consist of triangles in 2D and triangular-based prism elements in 3D. The mesh update is achieved with general or special-purpose mesh moving schemes. As examples, 2D flow past spillway of a dam and 3D flow past a surface-piercing circular cylinder are presented.

A class of data structures and object-oriented implementation for finite element methods on distributed memory systems

In this study we describe a class of data structures and object-oriented implementation for parallel finite element computations. Of particular interest are adaptive p (variable degree) finite elements on unstructured grids with parallel partitioning by subdomains. The approach is implemented using C+ + and Fortran for distributed multi-processor systems such as the Cray T3D/T3E MPP systems and networks of workstations. A supporting performance study for a parallel multiple front solution of a representative analysis problem is included to illustrate the approach.

Three-dimensional computations of solution hydrodynamics during the growth of potassium dihydrogen phosphate: II. Spin down

Three-dimensional, time-dependent flows that occur in the Lawrence Livermore National Laboratory system for rapid growth of potassium dihydrogen phosphate (KDP) crystals from solution are studied using massively parallel finite element computations. The simulation reveals that excellent global mixing occurs during the spin-down phase of a time-dependent stirring cycle. The large scale fluid motions in the radial and axial directions that promote mixing are caused primarily by effects of platform geometry, but are augmented to some degree by the intrinsic tendency of a decelerating rotational flow to reverse direction within Ekman layers that form at the boundaries. Along with Part I of this work [Y. Zhou and J.J. Derby, J. Crystal Growth 180 (1997) 497], which emphasized spin up and steady rotation, significant advances have been made in our understanding of hydrodynamic phenomena in this system.

Distributed finite element computations using object-oriented techniques

An object-oriented parallel finite element framework has been developed to facilitate rapid prototyping of a wide variety of parallel finite element computations. Parallel computing and object-oriented technologies are integrated to achieve efficiency in both computation and software development. The paper presents various reusable and extensible components that constitute the parallel finite element architecture.

Parallel finite element computation of missile aerodynamics

Parallel finite element computation of missile aerodynamics

Parallel finite element computation of missile aerodynamics

A flow simulation tool, developed by the authors at the Army HPC Research Center, for compressible flows governed by the Navier-Stokes equations is used to study missile aerodynamics at supersonic speeds, high angles of attack and for large Reynolds numbers. The goal of this study is the evaluation of this Navier-Stokes computational technique for the prediction of separated flow fields around high-length-to-diameter (L/D) bodies. In particular, this paper addresses two issues: (i) turbulence modelling with a finite element computational technique and (ii) efficient performance of the computational technique on two different multiprocessor mainframes, the Thinking Machines CM-5 and CRAY T3D. The paper first provides a discussion of the Navier-Stokes computational technique and the algorithm issues for achieving efficient performance on the CM-5 and T3D. Next, comparisons are shown between the computation and experiment for supersonic ramp flow to evaluate the suitability of the turbulence model.

A Parallel Matrix Class Library in C++ for Computational Mechanics Applications

The object–oriented design and implementation of a matrix class library in C++ for parallel computing is described. The main goal of this library is to support the management of matrix data in a distributed environment and the parallel solution of linear systems of algebraic equations typical of computational mechanics applications. By using the object–oriented paradigm, a clean and consistent interface to the library is provided, and the implementation details are hidden from the user. These features improve the clarity and expressiveness of the client code and consequently ease the task of parallel programming. The library was developed and tested originally using a network of Sun Sparc 10 workstations. Test examples subsequently were run on the Intel Paragon XP/S. In these examples, the portability of the library among different distributed environments was demonstrated, and some preliminary performance studies of the library were carried out. Finally, the utilization of the class library in parallel finite–element computations is discussed. It is shown that the present library greatly simplifies the implementation of matrix operations intrinsic to parallel finite–element applications.

Parallel finite element simulation of 3D incompressible flows: Fluid‐structure interactions

AbstractMassively parallel finite element computations of 3D, unsteady incompressible flows, including those involving fluid‐structure interactions, are presented. The computation with time‐varying spatial domains are based on the deforming spatial domain/stabilized space‐time (DSD/SST) finite element formulation. The capability to solve 3D problems involving fluid‐structure interactions is demonstrated by investigating the dynamics of a flexible cantilevered pipe conveying fluid. Computations of flow past a stationary rectangular wing at Reynolds number 1000, 2500 and 107 reveal interesting flow patterns. In these computations, at each time step approximately 3 × 106 non‐linear equations are solved to update the flow field. Also, preliminary results are presented for flow past a wing in flapping motion. In this case a specially designed mesh moving scheme is employed to eliminate the need for remeshing. All these computations are carried out on the Army High Performance Computing Research Center supercomputers CM‐200 and CM‐5, with major speed‐ups compared with traditional supercomputers. The coupled equation systems arising from the finite element discretizations of these large‐scale problems are solved iteratively with diagonal preconditioners. In some cases, to reduce the memory requirements even further, these iterations are carried out with a matrix‐free strategy. The finite element formulations and their parallel implementations assume unstructured meshes.