Mimetic Methods Toolkit: An object-oriented API implementing Mimetic Discretization Methods

In this work, we introduce the Mimetic Methods Toolkit (MTK), an object-oriented Application Programming Interface for the implementation of Mimetic Discretization Methods in developing computer applications of a scientific nature, where the numerical solution of Partial Differential Equations may be required. The MTK was designed based on 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 important theoretical aspects of the Mimetic Discretization Methods. In this work, we present an introduction to Mimetic Discretization Methods, and we discuss the computational modeling of the related concepts; in this way, we explain how does the MTK implement these methods. By means of examples, we illustrate the MTK’s usage philosophy and, finally, by means of comparing the attained result against previously studied reference solutions, we conclude the correctitude of the implementation efforts in the MTK. ∗Computational Science Research Center, 5500 Campanile Dr, San Diego State University, College of Sciences, San Diego, California, USA, 92182-1245. †Computational Science Research Center, 5500 Campanile Dr, San Diego State University, College of Sciences, San Diego, California, USA, 92182-1245. ‡Computational Science Research Center, 5500 Campanile Dr, San Diego State University, College of Sciences, San Diego, California, USA, 92182-1245.