Advances in FEEL++ : A domain specific embedded language in C++ for partial differential equations

Abstract

This paper presents an overview of a unified seamlessly parallel framework for finite element and spectral element methods in 1D, 2D and 3D in C++ called FEEL++. The article provides a digression through the design of the library as well as the main abstractions handled by it, namely, meshes, function spaces, operators, linear and bilinear forms and an embedded variational language. In every case, the closeness between the language developed in FEEL++ and the equivalent mathematical objects is highlighted. More advanced mathematical methods e.g. the mortar, Schwartz (non)overlapping, three fields and two ficticious domain-like methods (the Fat Boundary Method and the Penalty Method) are described here.