Group implicit concurrent algorithms in nonlinear structural dynamics

During the 70's and 80's, considerable effort was devoted to developing efficient and reliable time stepping procedures for transient structural analysis. Mathematically, the equations governing this type of problems are generally stiff, i.e., they exhibit a wide spectrum in the linear range. The algorithms best suited to this type of applications are those which accurately integrate the low frequency content of the response without necessitating the resolution of the high frequency modes. This means that the algorithms must be unconditionally stable, which in turn rules out explicit integration. The most exciting possibility in the algorithms development area in recent years has been the advent of parallel computers with multiprocessing capabilities. So, this work is mainly concerned with the development of parallel algorithms in the area of structural dynamics. A primary objective is to devise unconditionally stable and accurate time stepping procedures which lend themselves to an efficient implementation in concurrent machines. Some features of the new computer architecture are summarized. A brief survey of current efforts in the area is presented. A new class of concurrent procedures, or Group Implicit algorithms is introduced and analyzed. The numerical simulation shows that GI algorithms hold considerable promise for application in coarse grain as well as medium grain parallel computers

Effective network grid synthesis and optimization for high performance very large scale integration system design

制度:新 ; 文部省報告番号:甲2642号 ; 学位の種類:博士(工学) ; 授与年月日:2008/3/15 ; 早大学位記番号:新480

Scheduling system of affine recurrence equations by means of piecewise affine timing functions

Many systematic methods exist for mapping algorithms to processor arrays. The algorithm is usually specified as a set of recurrence equations, and the processor arrays are synthesized by finding timing and allocation functions which transform index points in the recurrences into points in a space-time domain. The problem of scheduling (i.e. finding the timing function) of recurrence equations has been studied by a number of researchers. Of particular interest here are Systems of Affine Recurrence Equations (SAREs). The existing methods are limited to affine (or linear) schedules over the entire domain of computation. For some algorithms, there are points in the computation domain where the dependencies point in opposite directions, and an affine schedule does not exist, although a valid Piecewise Affine Schedule (PAS) can exist. The objective of this thesis is to examine these schedules and obtain a systematic method for deriving such schedules for SAREs. PAS can be found by first partitioning the computation domain and then obtaining a new SARE by renaming the variables. By partitioning the computation domain, we can obtain additional parallelism from the dependency graph, and find faster schedules over subspaces of the domain. In this paper, we describe a procedure for partitioning the domain and to generate a new SARE by renaming the variables. Some heuristics are introduced for partitioning the domain based on the properties of dependence vectors. After the partitioning and renaming, an existing method (due to Mauras et al.) is applied to find the schedules. Examples of Toeplitz System and Algebraic Path Problem are used to illustrate the results

On the synthesis of integral and dynamic recurrences

PhD ThesisSynthesis techniques for regular arrays provide a disciplined and well-founded approach to the design of classes of parallel algorithms. The design process is guided by a methodology which is based upon a formal notation and transformations. The mathematical model underlying synthesis techniques is that of affine Euclidean geometry with embedded lattice spaces. Because of this model, computationally powerful methods are provided as an effective way of engineering regular arrays. However, at present the applicability of such methods is limited to so-called affine problems. The work presented in this thesis aims at widening the applicability of standard synthesis methods to more general classes of problems. The major contributions of this thesis are the characterisation of classes of integral and dynamic problems, and the provision of techniques for their systematic treatment within the framework of established synthesis methods. The basic idea is the transformation of the initial algorithm specification into a specification with data dependencies of increased regularity, so that corresponding regular arrays can be obtained by a direct application of the standard mapping techniques. We will complement the formal development of the techniques with the illustration of a number of case studies from the literature.EPSR