A Case Study in Porting Strategy: The Axisymmetric Damage Model




			A CASE STUDY IN PORTING STRATEGY: THE AXISYMMETRIC DAMAGE MODEL David O'Neal, NCSA/UIUC N. J . Pagano, AFRL G. A. Schoeppner, AFRL G. P. Tandon, AdTech This file is available for download in *.pdf* format. Click here Key obstacles and the solutions we applied in moving the Axisymmetric Damage Model code from its largely non-portable, serial form to a multithreaded version are the focus of this report. Performance and scaling characteristics are covered and a summary of relevant tasks is presented in closing. Introduction: The axisymmetric damage model (ADM) is one of four micromechanical stress field models developed and maintained by N. J. Pagano's group at the AFRL Materials Directorate, Wright-Patterson AFB. These models serve to establish rigorous field theories to compute accurate stresses and energy release rates for fracture mechanics problems in composite bodies. In turn, these solutions, coupled with experimental research, can establish appropriate failure criteria to be used in the design of composite structures for air and space vehicles. Discretizations are based on sets of concentric cylinders that extend into the matrix material and surround an individual core. Each shell has constant thickness and constant inner and outer radii. Damage may be introduced in the form of annular cracks within the constituents and/or debonds between them. The number of shells and their respective thicknesses are dictated by the details of the composite domain, the damage itself, the desired accuracy, and choice of boundary conditions. Cylinders are further subdivided into sections of arbitrary constant lengths, each of which may include different types of damage. Sections may be analyzed independently and then integrated into the global solution downstream of the analysis kernel. Even though this dimension is usually rather small, we chose to implement a multithread design based on it first. The approach held the promise of a significant improvement in performance in exchange for what was viewed as a modest porting effort. The tedious chore of implementing finely grained parallelism was reserved for a future experiment with a dependency analysis tool. Objectives: The two primary goals of the project were to study numerical characteristics of the existing AFRL research code, specifically those requiring 128-bit precision floating point data and operations, and then implement a multiprocessor version. Methods/procedures/apparatus: All of the ADM models are based on Reissner's variational theorem (Reissner, 1950). The ADM code (Pagano, 1991) is associated with axisymmetric cracking and boundary conditions. Others support fundamentally different cases, i.e. axisymmetric problems incorporating the effects of friction (Tandon and Pagano, 1996), transverse and shear loading and associated cracking patterns in composite cylinders (Pagano and Tandon, 1994), and transverse cracking and delamination problems (Schoeppner and Pagano, 1998), but all share the same basic data structures and programming logic which implies that modifications made to ADM are applicable to the other codes as well. Data structures were scoped and promoted as required. Parallel programming directives were added by-hand. Results and Discussion: Speedups for the ADM multithread port are problem dependent. Load balance problems are evident for some cases. Sectional calculations can occasionally be decomposed further, thus the load associated with such threads will wane. Timings through parallel sections of code correspond to that of the section requiring the most time. For our test problems, overhead associated with multithread executables ranged from 15% to 30%. Timing charts associated with the original and current ADM implementations were produced for validation problems consisting of ten material layers and four independent sections (10x4) and six material layers and eight independent sections (8x6). Acceptable performance and speedup was observed for small partition sizes (up to 8 processors). Conclusions and Recommendations: Conclusions and Recommendations: Eigenvalues produced by a 64-bit version of the matrix diagonalizer correspond to the quad-precision results to seven digits, thus there is reason to believe that 64-bit data can be used throughout the program. If it is possible to transition the entire code to a standard 64- bit floating point system, the associated performance improvement could exceed a factor of 100 (Bai and Tang, 1996). This is the focus of our on-going MDM project (1999-2000). References: Bai, Zhaojun, and Tang, P. T. P., Quadruple Precision FORTRAN Routine for Eigen Analysis of Real Nonsymmetric Matrices, Technical Report and User's Guide, Department of Mathematics, University of Kentucky, Lexington, KY (1996). Brown, H. W., Analysis of Axisymmetric Micromechanical Concentric Cylinder Model, USAF Wright Laboratory, Materials Directorate, Internal Report (1991). Harraby, S. A., The Solution of Ordinary Differential Equations arising from Stress Transfer Mechanics, NPL Report DITC 223/93, National Physical Laboratory, Middlesex, UK (1993). Pagano, N. J., Axisymmetric Micromechanical Stress Fields in Composites, Proceedings of the 1991 IUTAM Symposium on Local Mechanics Concepts for Composite Material Systems, Springer Verlag, Berlin, pages 1-26 (1991). Pagano, N. J., and Tandon, G. P., 2D Damage Modes in Unidirectional Composites under Transverse Tension and/or Shear, v. 1, Mech. of Comp. Mater. and Struc., pages 119-155 (1994). Press, W., Flannery, B., Teukolsky, S., and Vetterling, W., Numerical Recipes in Fortran, Second Edition, chapters 8 and 11, Cambridge University Press (1996). Reissner, E., On a Variational Theorem in Elasticity, J. Math. Phys., v. 29, pages 90-95 (1950). Schoeppner, G. A., and N. J. Pagano, Stress Fields and Energy Release Rates in Cross-Ply Laminates, Int. J. Solids, Structures, v. 35, pages 1025-1055 (1998). Tandon, G. P., and Pagano, N. J., Matrix Crack Impinging on a Frictional Interface in Unidirectional Brittle Matrix Composites, Int. J. Solids, Structures, v. 33, pages 4309-4326 (1996). Tandon, G. P., and Schoeppner, G. A., Axisymmetric Damage Model (ADM) User Manual, USAF Wright Laboratory, Materials Directorate (1992). Related documents and images: http://www.ncsa.uiuc.edu/EP/CSM/publications/1998/ugc98_oneal.pdf http://www.ncsa.uiuc.edu/EP/CSM/presentations/UGC98_ADM_PPT.pdf Acknowledgements: ASC MSRC, AFRL/MLBM (Materials Directorate), AdTech Research Systems, SPAWAR, NCSA