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Daripa, Prabir; Ghosh, Aditi

The FFTRR-based fast direct algorithms for complex inhomogeneous biharmonic problems with applications to incompressible flows. (English) Zbl 1377.65035

Numer. Algorithms 75, No. 4, 937-971 (2017).
The authors develop the fast Fourier transform (FFT) and recursive-relations based accurate and fast algorithms for several biharmonic problems in a unit disc in the complex plane using the direct method, where the solutions of the biharmonic problems are written directly in terms of Green’s function of these problems. These algorithms are implemented using MATLAB programs. Their performance in terms of accuracy and complexity is numerically evaluated and presented using several test problems. These fast algorithms are applied to solving incompressible slow viscous flow problems at low to moderate Reynolds numbers.
Reviewer: T. C. Mohan (Chennai)

MSC:

65E05 General theory of numerical methods in complex analysis (potential theory, etc.)
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
76D07 Stokes and related (Oseen, etc.) flows

Keywords:

complex biharmonic equation; Green’s function; fast algorithms; Stokes equations; steady incompressible flows; recursive relations; numerical implementation in Matlab; direct method; fast Fourier transform

Software:

Matlab
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References:

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