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Eigenvalue translation method for stabilizing an unsymmetric Lanczos reduction process. (English) Zbl 0938.76091

Summary: The unsymmetric Lanczos reduction method has been recently developed to reduce the size of a large-scale linear system which is the discretized form of a time-dependent partial differential equation problem with a large physical domain. This has been applied to solve the time-dependent advection-dispersion equation discretized by finite element or finite difference methods. However, the reduced system sometimes suffers time instability because of relocation of the approximate eigenvalues into the left half plane. This paper develops a method for stabilizing the reduced system while preserving the accuracy of the solution. The unstable eigenvalues are translated from the left half complex plane to the right half, leaving eigenvalues in right half plane unchanged. The results of numerical simulations of the synthetic and practical field contaminant transport problems show the efficiency and accuracy of this method.

MSC:

76M99 Basic methods in fluid mechanics
76R99 Diffusion and convection
76S05 Flows in porous media; filtration; seepage
65F10 Iterative numerical methods for linear systems
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