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There are a set of sophisticated methods of great importance as PDE solvers which are more powerful than simple iterative solvers
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Alternating Direction Iterative ADI Solvers
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This has already been discussed under the SP and BT NAS Benchmarks
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It can be viewed as a general preconditioning method when matrix to be inverted can be written as a diagonal matrix plus the sum of easily solved matrices with small coefficients
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Incomplete Cholesky Factorization
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And two more which deserve major discussion but which we will overview very superficially
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Domain Decomposition
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Multigrid Methods
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