Multigrid third-order least-squares solution of Cauchy–Riemann equations on unstructured triangular grids


  • H. Nishikawa

    Corresponding author
    1. W. M. Keck Foundation Laboratory for Computational Fluid Dynamics, Department of Aerospace Engineering, University of Michigan, FXB Building, 1320 Beal Avenue, Ann Arbor, MI 48109-2140, U.S.A.
    • FXB 1320 Beal Avenue, Ann Arbor, MI 48109-2140, U.S.A.
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In this paper, a multigrid algorithm is developed for the third-order accurate solution of Cauchy–Riemann equations discretized in the cell-vertex finite-volume fashion: the solution values stored at vertices and the residuals defined on triangular elements. On triangular grids, this results in a highly overdetermined problem, and therefore we consider its solution that minimizes the residuals in the least-squares norm. The standard second-order least-squares scheme is extended to third-order by adding a high-order correction term in the residual. The resulting high-order method is shown to give sufficiently accurate solutions on relatively coarse grids. Combined with a multigrid technique, the method then becomes a highly accurate and efficient solver. We present some results to demonstrate its accuracy and efficiency, including both structured and unstructured triangular grids. Copyright © 2006 John Wiley & Sons, Ltd.