Felicity: a Matlab/c++ Toolbox for Developing

This paper describes a Matlab/C++ finite element toolbox, called FELICITY, for 4 simulating various types of systems of partial differential equations (e.g. coupled elliptic/parabolic 5 problems) using the finite element method. It uses Matlab, in an object-oriented way, for high level 6 manipulation of data structures in finite element codes, while utilizing a domain-specific language 7 (DSL) and code generation to automate low-level tasks such as matrix assembly (via the Matlab 8 mex interface). We describe the fundamental functionality of the toolbox’s Matlab interface, such as 9 using higher order Lagrange (simplicial) meshes, defining finite element spaces, allocating degrees10 of-freedom, assembling discrete bilinear and linear forms, and interpolation over meshes; moreover, 11 some “under the hood” aspects of FELICITY are discussed. Two example problems and their 12 implementation are given to demonstrate the ability of FELICITY to solve coupled problems with 13 interacting sub-domains of different co-dimension. Future work is also discussed. 14