The Mimetic Methods Toolkit: An object-oriented API for Mimetic Finite Differences

We introduce the Mimetic Methods Toolkit (MTK), an object-oriented Application Programming Interface, implementing Mimetic Finite Differences to assist in the development of scientific applications where the numerical solution of Partial Differential Equations is required. The MTK’s design is based on a variant of the Castillo–Grone Method for the construction of discrete differential operators that mimic important properties of their continuous counterparts. The MTK is built as a collection of abstract and concrete classes, thus allowing for an extensible framework, which fosters code reutilization, while intuitively educating the user about the theoretical aspects of Mimetic Finite Differences. We present an overview to Mimetic Finite Differences, and we discuss the computational modeling of the related concepts; in this way, we explain how the MTK implements these methods. In this article, we present examples to illustrate the MTK’s usage philosophy and the validity of the implementation of the MTK by comparing our results with previously studied reference solutions.