Conjugate-gradient methods for nonlinear finite-element analysis on supercomputers

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:7019972

Ho, S P

A mixed method, which combines a nonlinear conjugate gradient and Newton's methods, has proved effective for solution of three-dimensional nonlinear finite-element models. The class of problems to which the methods have been applied consists of finite deformations of nearly incompressible hyperelastic solids. Incrementation of a penalty parameter allows the effective use of conjugate-gradient methods, in contrast to the failure of search methods when Lagrange multipliers are employed. The global nature of the nonlinear conjugate-gradient scheme has proven effective in approaching solution points far removed from initial estimates of the solution. On the other hand, the quadratic convergence rate of Newton's method is utilized, to good effect, once the solution has been closely approximated by the conjugate-gradient calculation. The use of vector computers (e.g., Cray X-MP, Cyber 205) was considered from the beginning in the design of the algorithms and the computer code. Comparisons between global matrix and element by element algorithms show that the element-by-element algorithm is better than the global-matrix algorithm when quadratic or higher-order elements are used. Comparison of the method presented here with other iterative schemes, made using ITPACK, demonstrate the effectiveness of this method.

• Research Organization: Texas Univ., Austin (USA)
• OSTI ID: 7019972
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210* -- Supercomputers-- (1987-1989)
ALGORITHMS
COMPUTER CODES
FINITE ELEMENT METHOD
ITERATIVE METHODS
MATHEMATICAL LOGIC
NEWTON METHOD
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PROGRAMMING
THREE-DIMENSIONAL CALCULATIONS
VECTOR PROCESSING