| Author | Jacob Fish, Vladimir Belsky and M. Pandheeradi |
|---|---|
| Title | Iterative and Direct Solvers for Interface Problems with Lagrange Multipliers |
| Year | 1994 |
| Journal | Computing Systems in Engineering |
| Volume | 6 |
| Pages | 261-273 |
| Abstract | Special purpose iterative and direct solvers are proposed for solving nonpositive definite symmetric linear systems arising from the three-field hybrid variational principle, which enforces compatibility between independently modeled substructures in the weak sense. The basic idea of the proposed family of solvers is to transform a nonpositive definite linear system to an equivalent positive definite system, which then can be solved by either iterative or direct method without pivoting. The two-level iterative approach proposed in the paper consists of resolving the lower frequency response of the source problem by means of equivalent positive definite collocation problem and by capturing higher frequency response using projected conjugate gradient method. Numerical experiments in 2D and shells indicate that the total CPU time of the two-level iterative process is less than 20% higher than that of a corresponding collocation problem, but the benefit from increased accuracy and modeling flexibility clearly overshadows this increased cost. |