On the State-Of-The-Art of Finite Element Procedures and a Meshless Technique

2009 ◽  
pp. 23-49
Author(s):  
J.-F. Hiller ◽  
S. De ◽  
K.J. Bathe
Keyword(s):  
Finite Element ◽  
State Of The Art ◽  
The State

Towards an Ultimate Finite Element Oriented Solver on Unstructured Meshes

1995 ◽  
Author(s):  
Vladimir Belsky ◽  
Jacob Fish
Keyword(s):  
Finite Element ◽  
Iterative Methods ◽  
Computational Efficiency ◽  
State Of The Art ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
The State ◽  
Thin Shells ◽  
Direct Solution ◽  
Numerical Tests

Abstract The paper investigates computational efficiency of various finite element solvers, including the state-of-the-art iterative methods based on multigrid-like and Modified Incomplete Cholesky preconditioners, as well as sparse direct solver recently developed at NASA Langley. These methods are compared to the newly developed Finite Element Oriented Solver (FEOS), which combines the advantages of the iterative and direct solution techniques. Numerical tests are conducted for both well-conditioned three dimensional problems as well as poor-conditioned problems, such as thin shells. The proposed FEOS solver has been found to possess a remarkable robustness and computational efficiency, by far superior to its comprising ingredients.

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