Geodesic
A network programming approach in solving Darcy's equations by mixed finite-element methods
Electronic transactions on numerical analysis, Tome 22 (2006), pp. 41-70
We use the null space algorithm approach to solve the augmented systems produced by the mixed finite-element approximation of Darcy's laws. Taking into account the properties of the graph representing the triangulation, we adapt the null space technique proposed in [5], where an iterative-direct hybrid method is described. In particular, we use network programming techniques to identify the renumbering of the triangles and the edges, which enables us to compute the null space without floating-point operations. Moreover, we extensively take advantage of the graph properties to build efficient preconditioners for the iterative algorithm. Finally, we present the results of several numerical tests.
Classification : 65F05, 65F10, 64F25, 65F50, 65G05
Keywords: augmented systems, sparse matrices, mixed finite-element, graph theory 
@article{ETNA_2006__22__a6,
     author = {Arioli,  M. and Manzini,  G.},
     title = {A network programming approach in solving {Darcy's} equations by mixed finite-element methods},
     journal = {Electronic transactions on numerical analysis},
     pages = {41--70},
     year = {2006},
     volume = {22},
     zbl = {1112.65023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__22__a6/}
}
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Arioli,  M.; Manzini,  G. A network programming approach in solving Darcy's equations by mixed finite-element methods. Electronic transactions on numerical analysis, Tome 22 (2006), pp. 41-70. http://geodesic.mathdoc.fr/item/ETNA_2006__22__a6/