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.     

Adaptive full domain covering meshes for parallel finite element computations

Summary  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.      

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.     

An object-oriented framework for finite element pavement analysis

In this study, we developed an object-oriented (OO) framework with interactive graphics to assist pavement studies using finite element analysis (FEA). FEA has been proven to be effective in studying various pavement failure problems; however, it is time consuming and error prone to manually generate the load sequences where non-regular tire footprints, non-uniform tire-pavement contact stresses, and transverse wheel wander distributions are used. After FEA, extracting the deformations for failure analysis is necessary but tedious. The OO framework developed in this study handles the preprocessing and postprocessing tasks for the FEA of pavements. It has a graphical user interface and is platform independent. It was successfully used in developing a new criterion for characterizing pavement failures that involved approximately four hundred different FEA simulations.     

An object-oriented blackboard based approach for automated finite element modeling and analysis of multichip modules

This paper addresses the application of the blackboard system architecture and object-oriented data abstraction techniques to the domain of finite element modeling and analysis. Specifically, a hierarchical object-oriented database was used to represent the physical system at different levels of abstraction including the user-defined physical system level, a computer-generated, simplified physical model level, and the finite element model level. Object link relationships within a given abstraction level and across different abstraction levels resulted in seamless bidirectional information exchange. The blackboard system architecture employed provided a framework for distributed cooperative problem solving, for the application of simplifying domain-specific modeling assumptions, and for integrating the various software modules that are involved in the entire finite element modeling and analysis process. These methodologies were implemented in a prototype computational tool calledIMCMA theIntelligentMultichipModuleAnalyzer. An example illustrates howIMCMA automates finite element thermal analysis of small integrated circuit features in multichip modules through a two-step finite element submodeling process.     

An adaptive parallel algorithm for finite language decomposition

The computationally hard problem of finite language decomposition is investigated. A finite language L is decomposable if there are two languages L₁ and L₂ such that L = L₁L₂. Otherwise, L is prime. The main contribution of the paper is an adaptive parallel algorithm for finding all decompositions L₁L₂ of L. The algorithm is based on an exhaustive search and incorporates several original methods for pruning the search space. Moreover, the algorithm is adaptive since it changes its behavior based on the runtime acquired data related to its performance. Comprehensive computational experiments on more than 4000 benchmark languages generated over alphabets of various sizes have been carried out. The experiments showed that by using the power of parallel computing the decompositions of languages containing more than 200000 words can be found. Decompositions of languages of that size have not been reported in the literature so far.

     

Development of an object-oriented finite element program with adaptive mesh refinement for multi-physics applications

In this paper, an object-oriented framework for numerical analysis of multi-physics applications is presented. The framework is divided into several basic sets of classes that enable the code segments to be built according to the type of problem to be solved. Fortran 2003 was used in the development of this finite element program due to its advantages for scientific and engineering programming and its new object-oriented features. The program was developed with h-type adaptive mesh refinement, and it was tested for several classical cases involving heat transfer, fluid mechanics and structural mechanics. The test cases show that the adaptive mesh is refined only in the localization region where the feature gradient is relatively high. The overall mesh refinement and the h-adaptive mesh refinement were justified with respect to the computational accuracy and the CPU time cost. Both methods can improve the computational accuracy with the refinement of mesh. The overall mesh refinement causes the CPU time cost to greatly increase as the mesh is refined. However, the CPU time cost does not increase very much with the increase of the level of h-adaptive mesh refinement. The CPU time cost can be saved by up to 90%, especially for the simulated system with a large number of elements and nodes.     

A mesh-refinement scheme for finite element computations

The paper considers the use of unorthodox grids where rapid transition from refined zones to coarser zones is effected, thus introducing exposed nodal freedoms at the zone interfaces. A technique for automated mesh enrichment of finite element discretizations is devised. Suitable convergence criteria are designed to delineate those subregions of a domain where refinement is necessary. Enriched and unaltered regions are separated by a fringe of semirefined elements. A valid finite element theory is provided for the fringe elements. A pilot numerical study illustrates the practical implementation of the automated refinement strategy. The principal features of the program are described.     

An adaptive finite element technique for structural dynamic analysis

An adaptive finite element discretization technique, which utilizes specially derived Ritz vectors, is presented for solving structural dynamics problems. The special Ritz vectors are applied as the bases of transformation in geometric coordinates for mode superposition dynamic analysis. To capture the low frequency response and the high frequency response using multigrid principles, a hierarchical formulation for the formation of the coefficient matrices is proposed and it is utilized in the framework of the adaptive h-refinement. Assuming that the solution can be resolved into a set of orthogonal vectors and the refined mesh which passes the refinement criteria for all the vectors can satisfy the refinement criteria for the solution, the Ritz vectors are used as sources to discretize the continuous spatial domain. An a posteriori energy norm of residual error serves as the error measure. Finally, the performance and the efficiency of the proposed technique is demonstrated by solving several examples.     

EasyFEM—An object-oriented graphics interface finite element/finite volume software

An object-oriented finite element/finite volume software, EasyFEM, has been developed. The software, with a fully interactive graphics interface, analyses heat transfer, solid mechanics, and fluids problems by the finite element and the finite volume methods. The Coad and Yourdon methodology is used to describe the general structure of classes and objects implemented by the software. Details of the object-oriented classes for both the graphics pre- and post-processors, as well as for the analysis solutions, are described. Several case studies with graphical representations of numerical solutions are presented to illustrate some functionalities of the software.     

Parallel-vector computations for geometrically nonlinear finite element analysis

Existing procedures for nonlinear finite element analysis are reviewed. Common computational steps among existing methods are identified. Parallel-vector solution strategies for the generation and assembly of element matrices, solution of the resulting system of linear equations, calculations of the unbalanced loads, displacements and stresses are all incorporated into the Newton-Raphson (NR), modified Newton-Raphson (mNR), and BFGS methods. Furthermore, a mixed parallel-vector Choleski-Preconditioned Conjugate Gradient (C-PCG) equation solver is also developed and incorporated into the piecewise linear procedure for nonlinear finite element analysis. Numerical results have indicated that the Newton-Raphson method is the most effective nonlinear procedure and the mixed C-PCG equation solver offers substantial computational advantages in a parallel-vector computer environment.     

Adaptive multigrid for finite element computations in plasticity

The solution of the system of equilibrium equations is the most time-consuming part in large-scale finite element computations of plasticity problems. The development of efficient solution methods are therefore of utmost importance to the field of computational plasticity. Traditionally, direct solvers have most frequently been used. However, recent developments of iterative solvers and preconditioners may impose a change. In particular, preconditioning by the multigrid technique is especially favorable in FE applications.The multigrid preconditioner uses a number of nested grid levels to improve the convergence of the iterative solver. Prolongation of fine-grid residual forces is done to coarser grids and computed corrections are interpolated to the fine grid such that the fine-grid solution successively is improved. By this technique, large 3D problems, invincible for solvers based on direct methods, can be solved in acceptable time at low memory requirements. By means of a posteriori error estimates the computational grid could successively be refined (adapted) until the solution fulfils a predefined accuracy level. In contrast to procedures where the preceding grids are erased, the previously generated grids are used in the multigrid algorithm to speed up the solution process.The paper presents results using the adaptive multigrid procedure to plasticity problems. In particular, different error indicators are tested.     

On reliability in finite element computations

Direct computation of engineering data from finite element solutions with reasonable guarantee of reliability is discussed with reference to practical engineering problem solving. The discussion focuses on a model problem for which experimental and numerical data are available.     

An adaptive mixed finite element method for wind field adjustment

In this paper we present an adaptive strategy to obtain an incompressible wind field that adjusts to an experimental one, and verify boundary conditions of physical interest. We use an augmented lagrangian formulation for solving this problem. Our method is based on an Uzawa iteration to update the lagrange multiplier and on an elliptic adaptive inner iteration for velocity. Several examples show that the proposed method is efficient and reliable.     

An adaptive finite element method for evolutionary convection dominated problems

We present an adaptive finite element method for evolutionary convection–diffusion problems. The algorithm is based on an a posteriori indicator of the size of the oscillations displayed by the finite element approximation. The procedure is able to refine or coarsen dynamically the mesh adjusting it automatically to evolving layers. The method produces nearly non-oscillatory approximations in the convection dominated regime. We check the performance of the adaptive method with some numerical experiments.     

An h-hierarchical adaptive scaled boundary finite element method for elastodynamics

A posteriori h-hierarchical adaptive scaled boundary finite element method (ASBFEM) for transient elastodynamic problems is developed. In a time step, the fields of displacement, stress, velocity and acceleration are all semi-analytical and the kinetic energy, strain energy and energy error are all semi-analytically integrated in subdomains. This makes mesh mapping very simple but accurate. Adaptive mesh refinement is also very simple because only subdomain boundaries are discretised. Two 2D examples with stress wave propagation were modelled. It is found that the degrees of freedom needed by the ASBFEM are only 5%–15% as needed by adaptive FEM for the examples.     

An adaptive finite element scheme for transient problems in CFD

An adaptive finite element scheme for transient problems is presented. The classic h-enrichment / coarsening is employed in conjunction with a triangular finite element discretization in two dimensions. A mesh change is performed every n timesteps, depending on the Courant number employed and the number of ‘protective layers’ added ahead of the refined region. In order to simplify the refinement/ coarsening logic and to be as fast as possible, only one level of refinement/coarsening is allowed per mesh change. A high degree of vectorizability has been achieved on the CRAY XMP 12 at NRL. Several examples involving shock-shock interactions and the impact of shocks on structures demonstrate the performance of the method, indicating that considerable savings in CPU time and storage can be realized even for strongly unsteady flows.     

Numerical techniques for plasticity computations in finite element analysis

Common numerical techniques for plasticity computations in finite element analysis are examined. The plasticity theory considered is the simple rate-independent von Mises criterion for small strains. Work hardening is represented by a general isotropic model or by a linear, isotropic-kinematic mixed model. Algorithms to integrate the rate equations, strategies for stress updating over a time (load) step in implicit codes, and tangent operators consistent with the integration algorithm are discussed. The elastic predictor-radial return algorithm and a consistent tangent operator satisfy the requirements for a stable, accurate and efficient numerical procedure. An extension of this model for plane stress with mixed hardening is described. Two numerical examples are given to demonstrate the accuracy and efficiency for plane stress analyses.     

Tuning the Schur complement computations for finite element partitions

The domain decomposition method (DDM) is an efficient algorithmic tool for the parallelization of finite element computer codes. A variant of the DDM with direct solution algorithm is based on computation of Schur complement matrices for finite element partitions. This paper describes a simple technique that considerably improves execution rate of computationally intensive routines of the Schur complement computations. The technique uses ‘block of columns’ matrix operations and loop unrolling to reduce load instructions from cache memory and to increase instruction-level parallelism. For superscalar RISC processors, experimental results show that it is possible to improve performance of the DDM solution procedure by several times.