1) The document reports on test results from FFTW on four problems with different boundary conditions and geometries. It provides free energy values, wall times, and time per iteration for each problem. 2) A phase parameter equation is introduced to represent shape for Problem 1 under zero-flux boundary conditions. Mobility is defined using the phase parameter. 3) Free energy values and wall times are given for Problems 1 and 2 under various boundary conditions and concentrations.

1. Test Results (FFTW)
Linyun Liang
October 16, 2015

2. Problem 1. Periodical boundary condition

3. 1.5% difference
Free energy
Wall time (min.)
0.003s/iteration
Problem 1. Periodical boundary condition

4. Problem 1. Zero-flux boundary condition
Introduce a phase parameter to represent the shape
ℎ = 𝜂3
6𝜂2
− 15𝜂 + 10
M = 𝑀 𝑥ℎ + 𝑀 𝑦 1 − ℎMobility:

5. Problem 1. Zero-flux boundary condition

6. Problem 1. Zero-flux boundary condition
Free energy
Wall time (hours)

7. Problem 1. T-shape

8. Problem 1. T-shape
Free energy
Wall time (hours)

9. Problem 2. Periodical boundary condition
ConcentrationFree energy vs

10. Problem 2. Periodical boundary condition
Concentration Phase parameter

11. Problem 2. Periodical boundary condition
Concentration Phase parameter

12. Problem 2. Periodical boundary condition
~0.03s/iterationFree energy
Time steps

13. Thanks for your attention!