![]() We base thiswork on the method by Castillo and Grone, which constructs mimeticgradient and divergence operators using a discrete extension of Gauss’ di-vergence theorem. We focus on the construction of two- and three-dimensionalmimetic gradient, divergence, curl, and Laplacian operators. Our applications focus on the simulation of long-term geologic sequestration of carbon dioxide. The resulting method can be used to compute the concentrations of multiple solutes in distributed-memory computers. We also introduce a matrix storage scheme and provide preliminary tests of its performance. Its parallel programming aspects, and the related utility APIs. We discuss the API's design, structure, and usage philosophy, as well as This work is then used as the theoretical foundation for the Mimetic Methods Toolkit (MTK) a C++ API implementing mimetic discretization and quadrature schemes on logically-rectangular grids. We study the mathematical foundations and the underlying algorithms to construct higher-order one-dimensional mimetic operators, and we extend this knowledge to enable systematic derivations of their higher-dimensional counterparts. We explore the use of mimetic finite differences as an alternative numerical method to solve the partial differential equations that model the mass transport and concentration profiles of geologically sequestered carbon dioxide. ![]()
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