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Foundations of mimetic finite difference method
2014The mimetic discretization technology relies on a discrete vector and tensor calculus (DVTC) that deals with discrete fields and discrete operators. The DVTC makes it possible to reproduce (or mimic) fundamental identities of continuum calculus, such as kernels of operators (see Sect. 2.6) and the Helmholtz decomposition theorems (see Sect.
Lourenço Beirão da Veiga +2 more
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The Mimetic Finite Difference Method for Elliptic Problems
2014This book offers a systematic and thorough examination of theoretical and computational aspects of the modem mimetic finite difference (MFD) method. The MFD method preserves or mimics underlying properties of physical and mathematical models, thereby improving the fidelity and predictive capability of computer simulations.
L. Beirao da Veiga +2 more
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Benchmark 3D: A Mimetic Finite Difference Method
2011In the two-dimensional discretisation benchmark session at the FVCA5 conference, we participated with a Mimetic Finite Difference (MFD) method [7]. In this paper, we present results for the three-dimensional case using the same method. Since the previous conference, the equivalence of MFD, Hybrid Finite Volume and Mixed Finite Volume methods has been ...
Peter Bastian +2 more
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Modeling 3-D anisotropic elastodynamics using mimetic finite differences and fully staggered grids
Computational Geosciences, 2023Harpreet Sethi +3 more
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GPU-based 3D anisotropic elastic modeling using mimetic finite differences
Second International Meeting for Applied Geoscience & Energy, 2022Harpreet Singh +3 more
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Benchmark 3D: Mimetic Finite Difference Method for Generalized Polyhedral Meshes
2011Let ? be a subset of R3 with a Lipschitz continuous boundary. We consider the mixed (velocity-pressure) formulation of the diffusion problem.
K Lipnikov, G Manzini
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Uniform Poincaré inequalities for the discrete de Rham complex of differential forms
arXiv.orgIn this paper we prove discrete Poincar\'e inequalities that are uniform in the mesh size for the discrete de Rham complex of differential forms developed in [Bonaldi, Di Pietro, Droniou, and Hu, An exterior calculus framework for polytopal methods, J ...
Daniele A. Di Pietro +3 more
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A mimetic finite difference discretization for the incompressible Navier–Stokes equations
International Journal for Numerical Methods in Fluids, 2008AbstractThe results of a mimetic finite difference discretization of the three‐dimensional, incompressible Navier–Stokes equations are compared with more traditional finite difference schemes. The proposed method handles both momentum advection and diffusion in a vorticity‐preserving manner and allows for simple treatment of rigid wall boundary ...
ABBA', ANTONELLA, BONAVENTURA, LUCA
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Flux reconstruction and solution post-processing in mimetic finite difference methods
Computer Methods in Applied Mechanics and Engineering, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cangiani, A., Manzini, G. M.
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A Dual Grid Geometric Electromagnetic Particle in Cell Method
SIAM Journal on Scientific ComputingGeometric particle-in-cell discretizations have been derived based on a discretization of the fields that is conforming with the de Rham structure of the Maxwell's equation and a standard particle-in-cell ansatz for the fields by deriving the equations ...
K. Kormann, Eric Sonnendrücker
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