Robust Iterative Solvers Research Articles

From a Direct Solver To a Parallel Iterative Solver in 3-d fOrming Simulation

The industrial simulation code FORGE3, devoted to three- dimensional forming applications, has been equipped with a robust iterative solver. Using an implicit approach, this code carries out the large deformations of viscoplastic incompressible materials with unilateral contact condi tions. It is based on a mixed-velocity/pressure finite ele ment method using tetrahedral unstructured meshes. Central to the Newton iterations dealing with the non linearities, a conjugate residual method with a diagonal or block diagonal preconditioning has been implemented. The convergence rate of the iterative solver is given. The advantage and performance of this iterative method are compared to the direct solution. The complete parallel version of the code is performed by using a single-program multiple-data programming model. The scalability of the parallel iterative solver is shown on real complex applica tions. Several results of parallel computing are given for both a cluster of workstations and for an IBM SP2 up to 34 processors.

Performance of iterative methods in ANSYS on cray parallel/vector supercomputers

Abstract This paper describes recent work using iterative methods for the solution of linear systems in the ANSYS program. The ANSYS program, a general purpose finite element code widely used in structural analysis applications, has now added an iterative solver option. The development of robust iterative solvers and their use in commercial programs is discussed. Discussion of the applicability of iterative solvers as a general purpose solver will include the topics of robustness; as well as memory requirements and CPU performance. A new iterative solver for general purpose finite element codes which functions as a “black-box” solver using element-specific information and the underlying problem physics to construct an effective and inexpensive preconditioner is described. Some results are given from realistic examples comparing the performance of the iterative solver implemented in ANSYS with the traditional parallel/vector frontal solver used in ANSYS and a robust shifted incomplete Choleski iterative solver.

A block-correction aided strongly implicit solver for the five-point formulation of elliptic differential equations

Abstract An efficient and robust iterative solver was proposed to solve the five-diagonal matrix equations that arise from implicit discretization of two-dimensional thermal and fluid flow problems. By regarding the well-known ADI solver and the direct solver as the lowest and the highest levels of matrix decomposition, a systematic investigation was carried out to identify which level of matrix decomposition is then most suitable for the five-point formulation currently in use. Also, the existing block-correction procedure is implemented by deliberately evaluating the residual. In this way, both the high- and low-frequency errors are efficiently reduced so that the new iterative solver provides savings of about an order of magnitude in the computational cost. As the grid size increases, the new solver presented here turns out to be more powerful and more robust than other iterative solvers previously available.