TIOBE Survey of software developers shows Java to be the top language in use by 20% of programmers, followed by C with 17%, and C++ with 10%). Other companies cite Java's portability, robustness, and well defined APIs as reasons for change. NASA chose to use Java for processing Mars mission data because of increased productivity by their programmers. Since its inception in the mid 1990's Java has steadily gained acceptance by programmers, supplanting both C and C++ as the language of choice. Finally, we validate our 2Doperators via solving higher-dimensional elliptic problems. This also includes detailing the construction of a mimetic curloperator via a linear combination of the divergence of auxiliary Gaussianfluxes, thus avoiding the need for interpolation from classic discretiza-tion approaches based on Stokes’ theorem. This includes detailing the mathematics of this ex-tension. The contribution of thiswork is the extension to higher dimensions of the operators constructedby this algorithm. This algorithm con-structs supercritical-order mimetic operators. In previous works, we in-troduced the Castillo–Blomgren–Sanchez algorithm. This motivates defining the tenth or-der and the eighth order thresholds as critical orders of accuracy for thegradient and divergence operators, respectively. This method can not construct tenth-order gradientnor eighth-order divergence operators (nor higher), because the com-puted weights discretizing the corresponding weighted inner productsare not all positive for these cases. 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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