Application of the iterative solution method with Schur complement reduction to mixed finite elements based in a tetrahedral discretization |
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| Institution: | 1. Consiglio Nazionale delle Ricerche, Istituto di Ricerca Sulle Acque, Via Salaria km 29.300, 00015 Monterotondo, RM, Italy;2. Dipartimento DICATAM, Università degli Studi di Brescia, Via Branze 43, 25123 Brescia, Italy;3. Consiglio Nazionale delle Ricerche, Istituto di Ricerca Sulle Acque, UOS Brugherio, Via del Mulino, 19, 20861 Brugherio, MB, Italy;1. Department of Earth and Planetary Sciences, University of Tennessee, Knoxville, TN, USA;2. Chemical and Engineering Materials Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA;3. Department of Biosystems Engineering and Soil Science, University of Tennessee, Knoxville, TN, USA;4. Department of Geosciences, Texas Tech University, Lubbock, TX, USA;5. Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA |
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| Abstract: | The iterative solution method for mixed finite element methods is applied to a 3-D domain partitioned with tetrahedral elements. For the particular discretization technique of first partitioning the domain with hexahedral cells, and then subsequently partitioning cells with five tetrahedral elements, a Schur complement decomposition is devised wherein the actual number of equations solved is reduced by 80%. Although this Schur complement reduction requires a fair amount of computational overhead, its application within the iterative solution method can reduce overall solution time by about 44%, depending on closure criterion and other factors. |
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| Keywords: | Mixed finite element method Elliptic equation Tetrahedral discretization Iterative solution method |
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