FE Solver

• Author: Alex Griessman (alex.griessman@gmail.com)
• Repository https://github.com/mirrorscotty/fe-solver/

This is a basic framework for solving differential equations using finite element method. Currently it is capable of solving both 1D and 2D steady-state problems and transient problems.

Contents

• output - Functions for outputting simulation data
• scaling - Nondemensionalization stuff for heat and mass transfer problems
• solver - Actual finite element solver (both linear and nonlinear)
  • integration - Three and five point Gaussian quadrature
  • mesh - Basic 1D and 2D mesh routines
  • ode - Simple ODE solver using Euler's method

Building

This code was designed to be compiled as a library and statically linked. To build just the library, execute make fe-solver.a. Documentation can be built using Doxygen using make doc.

Usage

Include fe-solver.h in any C file that requires functions provided by this library, and instruct the compiler to link the executable against fe-solver.a. The PDE's to be solved should be written in weak form and then differentiated with respect to each dependent variable. Three functions should be written for each derivative, the time-dependent portion, the time-independent portion, and the load vector. Examples are provided here.

Dependencies

Compilation requires GCC and GNU Make. Building documentation requires Doxygen and LaTeX to generate PDF output. This code also requires the matrix library found here.