We show how to reduce the computational time of the practical implementation of the Raviart-Thomas mixed method for second-order elliptic problems. The implementation takes advantage of a recent result which states that certain local subspaces of the vector unknown can be eliminated from the equations by transforming them into stabilization functions; see the paper published online in JJIAM on August 10, 2023. We describe in detail the new implementation (in MATLAB and a laptop with Intel(R) Core (TM) i7-8700 processor which has six cores and hyperthreading) and present numerical results showing 10 to 20% reduction in the computational time for the Raviart-Thomas method of index $ k $, with $ k $ ranging from 1 to 20, applied to a model problem.
Citation: Sreevatsa Anantharamu, Bernardo Cockburn. Efficient implementation of the hybridized Raviart-Thomas mixed method by converting flux subspaces into stabilizations[J]. Mathematics in Engineering, 2024, 6(2): 221-237. doi: 10.3934/mine.2024010
We show how to reduce the computational time of the practical implementation of the Raviart-Thomas mixed method for second-order elliptic problems. The implementation takes advantage of a recent result which states that certain local subspaces of the vector unknown can be eliminated from the equations by transforming them into stabilization functions; see the paper published online in JJIAM on August 10, 2023. We describe in detail the new implementation (in MATLAB and a laptop with Intel(R) Core (TM) i7-8700 processor which has six cores and hyperthreading) and present numerical results showing 10 to 20% reduction in the computational time for the Raviart-Thomas method of index $ k $, with $ k $ ranging from 1 to 20, applied to a model problem.
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Sreevatsa Anantharamu, Bernardo Cockburn. Efficient implementation of the hybridized Raviart-Thomas mixed method by converting flux subspaces into stabilizations[J]. Mathematics in Engineering, 2024, 6(2): 221-237. doi: 10.3934/mine.2024010
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