Penalty finite element analysis of incompressible flows using element by element solution algorithms
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Finite element analysis of complex three-dimensional flows requires solution of a large system of algebraic equations. These equations are most often solved using direct methods, i.e., Gauss elimination method. However, for complex problems, direct methods demand prohibitively large CPU times and storage, thus making it difficult to solve these equations economically even on supercomputers. Iterative methods, on the other hand, do not require large storage and CPU times because the global system of equations are not formulated and factorized. These advantages over direct methods have revived the interest in iterative solvers. The element by element solvers using conjugate gradient methods have been used successfully for the solution of problems in fluid and solid mechanics and were shown to be advantageous over direct methods. In this paper we present an element by element algorithm for solution of incompressible flow problems using a penalty finite element model. The iterative methods (conjugate gradient and generalized minimum residual method) are compared with the frontal equation solver for efficiency, and the iterative solvers are found to be economical when a large number of equations are to be solved. © 1992.
author list (cited authors)
Reddy, M. P., Reddy, J. N., & Akay, H. U.