Multilevel solution of cell vertex CauchyRiemann equations
 Author
 Alfio Borzì, K William Morton, Endre Süli and Michèle Vanmaele (UGent)
 Organization
 Abstract
 In this paper a multilevel algorithm for the solution of the cell vertex finite volume CauchyRiemann equations is developed. These equations provide a linear algebraic system obtained by the finite volume cell vertex discretization of the inhomogeneous CauchyRiemann equations. Both square and triangular cells are employed. The system of linear equations resulting from the cell vertex discretization is overdetermined and its solution is considered in the least squares sense. By this approach a consistent algebraic problem is obtained which differs from the original one by O(h(2)) perturbation of the righthand side. A suitable cellbased convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence a standard multilevel scheme is presented and discussed which combines the given smoother and a cellbased transfer operator of the residuals and a nodebased prolongation operator of the unknown variables. Some remarkable reduction properties of these operators are shown. A full multilevel algorithm is constructed which solves the discrete problem to the level of truncation error by employing one multilevel cycle at each current level of discretization.
 Keywords
 cell vertex finite volume method, CauchyRiemann equations, multilevel methods, least squares, FINITEELEMENT, SCHEME, FLOWS
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU273958
 MLA
 Borzì, Alfio, K William Morton, Endre Süli, et al. “Multilevel Solution of Cell Vertex CauchyRiemann Equations.” SIAM JOURNAL ON SCIENTIFIC COMPUTING 18.2 (1997): 441–459. Print.
 APA
 Borzì, A., Morton, K. W., Süli, E., & Vanmaele, M. (1997). Multilevel solution of cell vertex CauchyRiemann equations. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 18(2), 441–459.
 Chicago authordate
 Borzì, Alfio, K William Morton, Endre Süli, and Michèle Vanmaele. 1997. “Multilevel Solution of Cell Vertex CauchyRiemann Equations.” Siam Journal on Scientific Computing 18 (2): 441–459.
 Chicago authordate (all authors)
 Borzì, Alfio, K William Morton, Endre Süli, and Michèle Vanmaele. 1997. “Multilevel Solution of Cell Vertex CauchyRiemann Equations.” Siam Journal on Scientific Computing 18 (2): 441–459.
 Vancouver
 1.Borzì A, Morton KW, Süli E, Vanmaele M. Multilevel solution of cell vertex CauchyRiemann equations. SIAM JOURNAL ON SCIENTIFIC COMPUTING. 1997;18(2):441–59.
 IEEE
 [1]A. Borzì, K. W. Morton, E. Süli, and M. Vanmaele, “Multilevel solution of cell vertex CauchyRiemann equations,” SIAM JOURNAL ON SCIENTIFIC COMPUTING, vol. 18, no. 2, pp. 441–459, 1997.
@article{273958, abstract = {{In this paper a multilevel algorithm for the solution of the cell vertex finite volume CauchyRiemann equations is developed. These equations provide a linear algebraic system obtained by the finite volume cell vertex discretization of the inhomogeneous CauchyRiemann equations. Both square and triangular cells are employed. The system of linear equations resulting from the cell vertex discretization is overdetermined and its solution is considered in the least squares sense. By this approach a consistent algebraic problem is obtained which differs from the original one by O(h(2)) perturbation of the righthand side. A suitable cellbased convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence a standard multilevel scheme is presented and discussed which combines the given smoother and a cellbased transfer operator of the residuals and a nodebased prolongation operator of the unknown variables. Some remarkable reduction properties of these operators are shown. A full multilevel algorithm is constructed which solves the discrete problem to the level of truncation error by employing one multilevel cycle at each current level of discretization.}}, author = {{Borzì, Alfio and Morton, K William and Süli, Endre and Vanmaele, Michèle}}, issn = {{10648275}}, journal = {{SIAM JOURNAL ON SCIENTIFIC COMPUTING}}, keywords = {{cell vertex finite volume method,CauchyRiemann equations,multilevel methods,least squares,FINITEELEMENT,SCHEME,FLOWS}}, language = {{eng}}, number = {{2}}, pages = {{441459}}, title = {{Multilevel solution of cell vertex CauchyRiemann equations}}, url = {{http://dx.doi.org/10.1137/S1064827595281952}}, volume = {{18}}, year = {{1997}}, }
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