A regularization method for solving the Poisson equation for mixed unbounded-periodic domains

Research output: Research - peer-reviewJournal article – Annual report year: 2018

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Abstract Regularized Green's functions for mixed unbounded-periodic domains are derived. The regularization of the Green's function removes its singularity by introducing a regularization radius which is related to the discretization length and hence imposes a minimum resolved scale. In this way the regularized unbounded-periodic Green's functions can be implemented in an FFT-based Poisson solver to obtain a convergence rate corresponding to the regularization order of the Green's function. The high order is achieved without any additional computational cost from the conventional FFT-based Poisson solver and enables the calculation of the derivative of the solution to the same high order by direct spectral differentiation. We illustrate an application of the FFT-based Poisson solver by using it with a vortex particle mesh method for the approximation of incompressible flow for a problem with a single periodic and two unbounded directions.
Original languageEnglish
JournalJournal of Computational Physics
Pages (from-to)439–447
StatePublished - 2018
CitationsWeb of Science® Times Cited: 1

    Research areas

  • The Poisson equation, Unbounded and periodic domains, Mixed boundary conditions, Regularization methods, Green's function solution, Vortex methods
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ID: 140922263