The Top 10 Computational Methods of the 20th Century (IACM)

In response to the Dongarra and Sullivan list, Dan Givoli published a list of the 20th Century numerical algorithms and methods that have most influenced the field of computational mechanics:

1. the Finite Element Method (including the Boundary Element Method);
2. Iterative Linear Algebraic Solvers, include Krylov Spaces, Conjugate Gradient Methods, and GMRES;
3. Algebraic Eigenvalue Solvers, including the Lanczos and QR methods;
4. Matrix Decomposition Methods, including spectral and polar decomposition;
5. Finite Difference Methods for Wave Problems, including the methods of Newmark, Lax-Wendroff, Hilbert-Hughes-Taylor, the shock wave techniques of Godunov, upwinding and flux-splitting;
6. Nonlinear Algebraic Solvers, including Quasi Newton methods such as BFGS, and arclength or continuation methods;
7. the Fast Fourier Transform;
8. Nonlinear Programming, in particular, Quadratic Programming
9. Soft Computing Methods, such as neural networks, genetic algorithms, and fuzzy logic.
10. Multiscale methods, including the multigrid method and wavelets.

Reference 1:

Dongarra and Sullivan,
Top Ten Algorithms of the Century,
Computing in Science and Engineering,
January/February 2000.

Reference 2:

Dan Givoli,
The Top 10 Computational Methods of the 20th Century,
IACM Expressions,
Number 11, September 2001, pages 5-9.

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