Parallel Finite Element System Research Articles

The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods

We present a parallel data structure for the discretization of partial differential equations which is based on distributed point objects and which enables the flexible, transparent, and efficient realization of conforming, nonconforming, and mixed finite elements. This concept is realized for elliptic, parabolic and hyperbolic model problems, and sample applications are provided by a tutorial complementing a lecture on scientific computing.The corresponding open-source software is based on this parallel data structure, and it supports multilevel methods on nested meshes and 2D and 3D as well as in space–time. Here, we present generic results on porous media applications including multilevel preconditioning and multilevel Monte Carlo methods for uncertainty quantification.

Parallel Finite Element Analysis with Internet.

As computers can be connected to each other through the internet, we are able to use a remote computer even if it is located overseas in the same way as using a computer which is located nearby. This paper describes a parallel finite element system using the domain decomposition method, which is implemented on a computer network made from remote computers at the Internet. The above system was successfully applied to the 3 D structural analyses with a high parallel efficiency.

Parallel finite elements on a massively parallel computer with domain decomposition

In order to analyze large scale and complex problems in limited processing time, a parallel finite element system is developed on a massively parallel computer called the nCUBE2 consisting of 128 processing units. Adopted for a parallel numerical algorithm for the finite element analysis is the domain decomposition method (DDM) combined with an iterative solver, i.e. the conjugate gradient (CG) method, where a whole analysis domain is fictitiously divided into a number of subdomains without overlapping. The finite element analyses of the subdomains are performed under the constraint of both displacement continuity and force equivalence among subdomains. Such a constraint can be satisfied through iterative calculation, i.e. the CG method. The present DDM-based parallel finite element algorithm is combined with a hierarchical model for data and processor management to have the workload balanced dynamically among the processors. The present system is successfully applied to a 3D structural problem with a high parallel of more than 90%.

Parallel non-linear finite element dynamic response

This paper investigates some of the design characteristics of explicit and implicit methods for parallel computers and suggests a hybrid approach which incorporates both methods. Several key issues are discussed as well as experiences in implementing all three methods. A range space/preconditioned conjugate gradient method is also discussed which has good potential for parallel implementation. It is concluded that the next generation parallel general purpose transient finite element systems should have the capability of handling all classes of structural analysis on a wide variety of shared/local memory parallel computers. An approach is outlined for the design of a future general purpose parallel finite element system.

Parallel processing techniques for FE analysis: Stiffnesses, loads and stresses evaluation

As new computer architectures emerge using parallel processing methods for more processing power, the need to explore and exploit parallelism in Finite Element Analysis, a numerical method that uses large amounts of calculations, arises naturally. In this work we present parallel processing techniques for the generation of element stiffnesses, element loads, the assembly process and the evaluation of the element stresses. These techniques can be used for the application of the Finite Element Method for structural analysis work on parallel computers. PARFES, a Parallel Finite Element System, which implements these techniques on particular parallel computers, is discussed. Our target parallel computer is a Multiple Instruction Multiple Data type that follows the Communicating Sequential Processes model of computation. The parallel programming language OCCAM is used for the current implementation of PARFES and our main objectives, apart from using parallel processing, are portability and Actaptability of the system among MIMD parallel computers that follow the CSP model of computation.

Parallel processing techniques for FE analysis: System solution

In a companion paper (D. Zois, Parallel processing techniques for FE analysis: stiffnesses, loads and stresses evaluation, Comput. Struct. 28, 247–260, 1988) parallel processing techniques for element stiffness generations, load generations, the assembly process and the evaluation of the stresses after the system solution are presented for Finite Element (FE) analysis. In the present paper a new parallel system solution method called Asynchronous Systolic Multiple Gauss Jordan (ASMGJ), which can be used for the system solution on a message-passing MIMD parallel computer, is presented. The ASMGJ method consists of a computation algorithm, a communication algorithm and a storage handling algorithm. These algorithms are presented in the present paper, together with examples of how they can be used on a parallel computer of the above type. The ASMGJ method has been implemented as the system solution procedure in PARFES, a Parallel Finite Element System, which can be used on message-passing MIMD parallel computers for the linear static analysis of structures by the FE method. The current implementation of PARFES has been written in OCCAM, a new programming language that supports effectively parallel processing and executes on a VAX 8600 computer.

On the design of a pipelined/systolic finite element system

A parallel finite element system is suggested based on the idea of pipelining the computations corresponding to the different finite elements. The systolic architecture is used extensively in the design to satisfy a regular and smooth flow of data in the pipe. Also a node numbering algorithm is developed in order to allow for the application of a frontal technique in the solution of the linear system of equations resulting from the analysis.

A Quantitative Evaluation of the Feasibility of, and Suitable Hardware Architectures for, an Adaptive, Parallel Finite-Element System

Abstract : This paper describes an experimental implementation of a design for an adaptive, parallel finite-element system. The implementation was used to simulate the performance of this design on several microprocessor-based multiprocessor architectures. We conclude that it will be possible to build hardware/software finite-element systems which exploit data segmentation to achieve flexibility, modularity, and the ability to process very large problems. (Author)

Design of an Adaptive, Parallel Finite-Element System

Abstract : A design for a novel prototype finite element system is presented which meets the following four goals: the system constitutes an application-independent finite element solver for a certain class of linear elliptic problems based on a weak mathematical formulation; it incorporates extensive adaptive approaches to minimize the critical decisions demanded of the user; it incorporates adaptive error estimation techniques to provide an optimal solution within a prescribed cost range; and it takes advantage of natural parallelism and modularity to increase the size of the practically solvable problems. The overall system structure is described in terms of parallel processes and is implementable on a wide variety of hardware configurations. The experiments planned to evaluate the various new approaches are also presented. (Author)