Non-iterative solution of finite-element equations in incompressible solids
Abbreviated Journal Title
Finite-element equations for incompressible and near-incompressible media give rise to a matrix with a diagonal block of zeroes or very small numbers. The matrices are not amenable to conventional techniques involving pivoting on diagonal entries. Uzawa methods have been applied to the associated linear systems. They are iterative and converge when the matrix is nonsingular. In the current study an alternate form of the matrix is used which is amenable to a solution without iteration. It likewise is applicable whenever the matrix is nonsingular. The solution process consists of a block LU factorization, followed by Cholesky decomposition of a positive definite diagonal block together with several forward and backward substitution operations. Two illustrative examples are developed.
"Non-iterative solution of finite-element equations in incompressible solids" (2004). Faculty Bibliography 2000s. 4611.