Abstract
In Ben-Artzi et al. (SIAM J Numer Anal 47:3087–3108 (2009), [1]) a Cartesian embedded finite difference scheme for biharmonic problems has been introduced. The design of the scheme relies on a 19-dimensional polynomial space. In this paper, we show how to simplify the implementation by introducing a directional decomposition of this space. The boundary is handled via a level-set approach. Numerical results for non convex domains demonstrate the fourth order accuracy of the scheme.
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References
Ben-Artzi, M., Chorev, I., Croisille, J.-P., Fishelov, D.: A compact difference scheme for the biharmonic equation in planar irregular domains. SIAM J. Numer. Anal. 47, 3087–3108 (2009)
Ben-Artzi, M., Croisille, J.-P., Fishelov, D.: A fast direct solver for the biharmonic problem in a rectangular grid. SIAM J. Sci. Comput. 31, 303–333 (2008)
Ben-Artzi M., Croisille J.-P., Fishelov, D.: Navier-Stokes Equations in Planar Domains. Imperial College Press (2013)
Chen, G., Li, Z., Lin, P.: A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow. Adv. Comput. Math. 2008, 113–133 (2008)
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Ben-Artzi, M., Croisille, JP., Fishelov, D. (2018). An Embedded Compact Scheme for Biharmonic Problems in Irregular Domains. In: Georgiev, K., Todorov, M., Georgiev, I. (eds) Advanced Computing in Industrial Mathematics. Studies in Computational Intelligence, vol 728. Springer, Cham. https://doi.org/10.1007/978-3-319-65530-7_2
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DOI: https://doi.org/10.1007/978-3-319-65530-7_2
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