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This repository contains programs for solving the Poisson equation using Mixed Finite Element Methods.

Compiling

Poisson1D

g++ -std=c++11 -march=native -O3 -o Poisson1D Poisson1D.cpp

Poisson2D

g++ -std=c++14 -march=native -O3 -o Poisson2D Poisson2D.cpp

Running

Each program requires a filename for input and output. For example,

Poisson1D

./Poisson1D in.json out.json

Poisson2D

./Poisson2D in2d.json out2d.json

Input

Input files are specifed and read using the JSON standard. Example files in.json and in2d.json show what keywords must be specified for valid input. In general, the options should be self-explanatory.

Poisson1D

Formulation

  • Standard
  • Mixed
  • Mimetic

Function

  • Two
  • ExpX3pX

Poisson2D

Formulation

  • Standard
  • Mixed
  • Dual-Mixed

Function

  • SinXSinY

Output

Both programs output the error in the solution to the terminal. If plotting is turned on then the program will call the python plotting utilities and plot the calculated and analytic solutions.