FELICITY: A Matlab/C++ Toolbox for Developing Finite Element Methods and Simulation Modeling

Abstract

\bfA \bfb \bfs \bft \bfr \bfa \bfc \bft. This paper describes a MATLAB/C++ finite element toolbox, called FELICITY, for simulating various types of systems of partial differential equations (e.g., coupled elliptic/parabolic problems) using the finite element method. It uses MATLAB in an object-oriented way for high-level manipulation of data structures in finite element codes, while utilizing a domain-specific language (DSL) and code generation to automate low-level tasks such as matrix assembly (via the MATLAB mex interface). We describe the fundamental functionality of the toolbox's MATLAB interface, such as using higher order Lagrange (simplicial) meshes, defining finite element spaces, allocating degreesof-freedom, assembling discrete bilinear and linear forms, and interpolation over meshes. Moreover, we describe in-depth how automatic code generation is implemented in FELICITY. Two example problems and their implementation are provided to demonstrate the ability of FELICITY to solve coupled problems with interacting subdomains of different co-dimension. Future improvements are also discussed. \bfK \bfe \bfy \bfw \bfo \bfr \bfd \bfs. finite elements, coupled systems, geometric flows, code generation, MATLAB, open source software \bfA \bfM \bfS \bfs \bfu \bfb \bfj \bfe \bfc \bft \bfc \bfl \bfa \bfs \bfs \bfi fi\bfc \bfa \bft \bfi \bfo \bfn \bfs .

Multigrid methods for saddle point problems: Optimality systems

“…In this section we report numerical results of the symmetric W -cycle and V -cycle algorithms in two and three dimensional convex domains for β = 10 −2 , 10 −4 and 10 −6 , where the preconditioner C −1 k is based on a V (4, 4) multigrid solve for (3.11). The norm E k of the error propagation operator is determined by a power iteration, and we employed the MATLAB/C++ toolbox FELICITY [23] in our computation.…”

A robust solver for a second order mixed finite element method for the Cahn–Hilliard equation

“…In this section, we report the results of several numerical experiments in two and three dimensions. All computations were carried out using the FELICITY MATLAB/C++ Toolbox [38].…”

Approximating solutions of linear elliptic PDE's on a smooth manifold using local kernel

“…For comparison, we provide numerical estimates using finite element method (FEM). Numerically, we used FELICITY, an FEM toolbox for Matlab [29].…”