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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



A fast Cauchy-Riemann solver

Authors: Michael Ghil and Ramesh Balgovind
Journal: Math. Comp. 33 (1979), 585-635
MSC: Primary 65F05; Secondary 65N15
MathSciNet review: 521278
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Abstract: We present a solution algorithm for a second-order accurate discrete form of the inhomogeneous Cauchy-Riemann equations. The algorithm is comparable in speed and storage requirements with fast Poisson solvers. Error estimates for the discrete approximation of sufficiently smooth solutions of the problem are established; numerical results indicate that second-order accuracy obtains even for solutions which do not have the required smoothness. Different combinations of boundary conditions are considered and suitable modifications of the solution algorithm are described and implemented.

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Keywords: Fast direct solvers, Cauchy-Riemann equations, elliptic first-order systems, transonic flow
Article copyright: © Copyright 1979 American Mathematical Society

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