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Analysis of preconditioners for hyperbolic partial differential equations. (English) Zbl 0861.65072

It sometimes happens that in the solution of a hyperbolic system one is not interested in the fastest waves. Thus, a meteorologist may wish to solve the equations of gas dynamics without keeping track of sound waves or gravity waves. In such instances implicit methods are required, and the question addressed here is that of finding efficient solvers. Several methods are analyzed in detail, and it is shown that semicirculant preconditioners can be much more efficient than incomplete LU decomposition.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65F35 Numerical computation of matrix norms, conditioning, scaling
76N15 Gas dynamics (general theory)
65F10 Iterative numerical methods for linear systems
35L65 Hyperbolic conservation laws
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