Olaf O. Storaasli

Parallel-vector solution of large-scale structural analysis problems on supercomputers

This direct method is based on the Choleski factorization procedure and uses a skyline storage scheme. Unique features of the method include its parallel computation at the outermost DO-loop and vector computation at the innermost DO-loop

Structural dynamic analysis on a parallel computer: The finite element machine

Abstract The development of general-purpose finite element computer software systems has provided the capability to analyze a wide range of linear and non-linear structural problems. However, these software systems are severely limited for non-linear response calculations because of the available speed on current sequential computers. Recent and projected advances in parallel multiple instruction multiple data (MIMD) computers provide an opportunity for significant gains in computing speed and for broadening the range of structural problems which may be solved. The key to these gains is the effective selection and implementation of algorithms which exploit parallel computing. This paper documents experiences solving transient response calculations on an experimental MIMD computer, termed the Finite Element Machine. The paper describes the algorithm used, its implementation for parallel computations, and results for representative one- and two-dimensional dynamic response test problems. The results show computation speedups of up to 7.83 for eight processors, and indicate that significant speedups of solution time are possible for non-linear dynamic response calculations through the use of many processors and appropriate parallel integration algorithms. The results are extremely encouraging and suggest that significant speedups in structural computations can be achieved through advances in parallel computers.

Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

Abstract Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve , is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14–16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for non-linear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on non-linear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

Three parallel computation methods for structural vibration analysis

The Lanczos (1950), multisectioning, and subspace iteration sequential methods for vibration analysis presently used as bases for three parallel algorithms are noted, in the aftermath of three example problems, to maintain reasonable accuracy in the computation of vibration frequencies. Significant computation time reductions are obtained as the number of processors increases. An analysis is made of the performance of each method, in order to characterize relative strengths and weaknesses as well as to identify those parameters that most strongly affect computation efficiency.

On the role of minicomputers in structural design

Results are presented of exploratory studies on the use of a minicomputer in conjunction with large-scale computers to perform structural design tasks, including data and program management, use of interactive graphics, and computations for structural analysis and design. An assessment is made of minicomputer use for the structural model definition and checking and for interpreting results. Included are results of computational experiments demonstrating the advantages of using both a minicomputer and a large computer to solve a large aircraft structural design problem.

Concurrent processing for nonlinear analysis of hollow rectangular structural sections

A concurrent processing algorithm is developed for a materially nonlinear analysis of hollow square and rectangular structural sections and implemented on a special purpose multiprocessor computer at NASA Langley Research Center referred to as the Finite Element Machine (FEM). The cross-sectional thrust-moment-curvature relations are generated concurrently using a tangent stiffness approach, and yield surfaces are obtained that represent the interaction between axial load and biaxial moments. For the study, a maximum speed-up factor of 7.69 is achieved on eight processors.

Linear static structural and vibration analysis on high-performance computers

Abstract Parallel computers offer the opportunity to significantly reduce the computation time necessary to analyze large-scale aerospace structures. This paper presents algorithms developed for and implemented on massively-parallel computers hereafter referred to as Scalable High-Performance Computers (SHPC), for the most computationally intensive tasks involved in structural analysis, namely, generation and assembly of system matrices, solution of systems of equations and calculation of the eigenvalues and eigenvectors. Results on SHPC are presented for large-scale structural problems (i.e. models of High-Speed Civil Transport). The goal of this research is to develop a new, efficient technique which extends structural analysis to SHPC and makes large-scale structural analyses tractable.

Concurrent processing in nonlinear column stability

A concurrent processing algorithm is developed for materially nonlinear stability analysis of imperfect columns with biaxial partial rotational end restraints. The algorithm for solving the governing nonlinear ordinary differential equations is implemented on a multiprocessor computer called the “finite element machine”, developed at the NASA Langley Research Center. Numerical results are obtained on up to nine concurrent processors. A substantial computational gain is achieved in using the parallel processing approach.

Parallel-vector out-of-core equation solver for computational mechanics

Abstract A parallel/vector out-of-core equation solver is developed for shared-memory computers, such as the Cray Y-MP machine. The input/output (I/O) time is reduced by using the a synchronous BUFFER IN and BUFFER OUT, which can be executed simultaneously with the CPU instructions. The parallel and vector capability provided by the supercomputers is also exploited to enhance the performance. Numerical applications in large-scale structural analysis are given to demonstrate the efficiency of the present out-of-core solver.

Space station static and dynamic analyses using parallel methods

Abstract Algorithms for high-performance parallel computers are applied to perform static analyses of large-scale Space Station finite-element models (FEMs). Several parallel-vector algorithms under development at NASA Langley are assessed. Sparse matrix solvers were found to be more efficient than banded symmetric or iterative solvers for the static analysis of large-scale applications. In addition, new sparse and “out-of-core” solvers were found superior to substructure (superelement) techniques which require significant additional cost and time to perform static condensation during global FEM matrix generation as well as the subsequent recovery and expansion. A method to extend the fast parallel static solution techniques to reduce the computation time for dynamic analysis is also described. The resulting static and dynamic algorithms offer design economy for preliminary multidisciplinary design optimization and FEM validation against test modes. The algorithms are being optimized for parallel computers to solve one-million degrees-of-freedom (DOF) FEMs. The high-performance computers at NASA afforded effective software development, testing, efficient and accurate solution with timely system response and graphical interpretation of results rarely found in industry. Based on the authors experience, similar cooperation between industry and government should be encouraged for similar large-scale projects in the future.