Explicit integration and subcycling in concurrent computers

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:5896604

Gilbertsen, N D

This dissertation discusses techniques for the implementation and improvement of vectorization and concurrency in nonlinear explicit structural finite element codes. In explicit integration methods, the computation of the element internal force vector consumes the bulk of the computer time. The program can be efficiently vectorized by subdividing the elements into blocks and executing all computations in vector mode. The structuring of elements into blocks also provides a convenient way to implement concurrency by creating tasks which can be assigned to available processors for evaluation. The techniques were implemented in a three dimensional nonlinear program with one-point quadrature shell elements. Concurrency and vectorization were first implemented in a single time step version of the program. An efficient implementation of subcycling, a mixed time integration method using different time steps for different parts of the mesh, was particularly difficult because of problems in scheduling processors and setting the optimal vector size. Techniques were developed to minimize processor idle time and to select the optimal vector length. A comparison of run times between the program executed in scalar, serial mode and the fully vectorized code executed concurrently using eight processors shows speed-ups of over 25. Using subcycling, the speed-up is three or more, depending on the problem and the number of processors used. Efficiency of concurrent execution decreases as the number of processors increase due to processor idleness, memory contention and the effect of nonparallelizable code. Conjugate gradient methods for solving nonlinear algebraic equations are also readily adapted to a parallel environment. A new technique for improving convergence properties of conjugate gradients in nonlinear problems is developed in conjunction with other techniques such as diagonal scaling.

• Research Organization: Northwestern Univ., Evanston, IL (USA)
• OSTI ID: 5896604
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGEBRA
ALGORITHMS
ARRAY PROCESSORS
COUNTING TECHNIQUES
MATHEMATICAL LOGIC
MATHEMATICS
OPTIMIZATION
PARALLEL PROCESSING
PROGRAMMING
SEQUENTIAL SCANNING
THREE-DIMENSIONAL CALCULATIONS
VECTOR PROCESSING