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High-order compact solvers for the three-dimensional Poisson equation. (English) Zbl 1081.65099
Summary: New compact approximation schemes for the Laplace operator of fourth- and sixth-order are proposed. The schemes are based on a Padé approximation of the Taylor expansion for the discretized Laplace operator. The new schemes are compared with other finite difference approximations in several benchmark problems. It is found that the new schemes exhibit a very good performance and are highly accurate. Especially on large grids they outperform noncompact schemes.

65N06Finite difference methods (BVP of PDE)
65F10Iterative methods for linear systems
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
Full Text: DOI
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[2] For the smaller matrices this was checked with routines DSYTRD and DSTERF from LAPACK.
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