The document discusses using benchmark problems from the CHiMaD to educate researchers on the phase-field method. It describes challenges students face in learning phase-field, such as determining simulation parameters and understanding physical meanings. The benchmark problems address these challenges by providing good parameterizations, exposing students to different problem types, and serving as references. Specific examples are given of benchmark problems being used to train new students, refresh experienced students, and teach a course. While the problems are generally effective, the document suggests providing more discretization guidance and uploaded results for comparison to make the problems even more useful for education.

1. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
Educating Researchers Using the CHiMaD
Benchmark Problems
Dong-Uk Kim, Shuaifang Zhang, and Michael R Tonks
Materials Science and Engineering, University of Florida

2. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Introduction
 Challenges learning the phase-field (PF) method
 How the benchmark (BM) problems address these challenges
 Specific examples of using BM problems for education
 Issues and strengths for each problem
 What changes could make them more useful for education?
Outline
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3. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 “Resources and a crash course on the phase field technique.“
 “Tools to verify and showcase the quality of your simulations.”
The PFHub BM problems have various purposes
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4. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Training students new to phase-field
 Refresher for students with 1 – 3 yrs of experience
 Experienced PF user learning a new code
 Training course with various skill levels
At the University of Florida, we have been using the BM
problems specifically for education
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5. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Good parameterizations are needed for simulation to run
 Relation between interfacial energy penalty, double-well potential penalty, and
phase-field interface thickness
 Choice of ∆𝑥 and ∆𝑡
 Characteristic length and time scale of the coupled physics
 Estimation of the simulation time
 Determination of optimal phase-field interface thickness
There are various challenges that face people learning the
phase field method
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6. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Making connection to physical meaning
 It’s hard to capture the explicit physical meaning from the PF equations
 Phase-field is a virtual object that tracks the positions of interface indirectly.
 Sometimes, it just has mathematical meaning to reproduce sharp interface
equations at certain asymptotic limits
 It is easy to mistake model artifacts for physical behaviors.
 Experimental data should be interpreted in ‘phase-field’ way
There are various challenges that face people learning the
phase field method
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7. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Too focused on one type problem
 There are many things to consider at the same time for a single problem
 Model parameters, numerical parameters, validity of the solutions, and so on
 Lower the chance of exposure to various type of problems
 General numerical solving issues
 Choice of numerical methods
 Choice of code framework
 Getting used to the code framework
 Visualization of the results
 Verification of the results
There are various challenges that face people learning the
phase field method
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8. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Good parameterizations are needed for simulation to run
 All BM problems provide a good set of parameters
 Too focused on one type problem
 BM problems cover various types of physics:
 Phase-separation, Oswald ripening, solidifications, micro-elasticity, fluid dynamics, and
electrostatics
 General numerical solving issues
 Calculation domain size and simulation times to plot are given in BM problems – this
is a big hint to determining ∆𝑥 and ∆𝑡.
 Learning from other people
 Previously posted results are also good references for determining convergence criteria.
How BM problems address these challenges
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9. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Training new students
 All new students joining the Tonks research group use BM problem 1 and 2 to learn
how the phase field method works
 Eight students have gone through this training since Sept, 2015
 One student is doing this right now
 Refresher for experienced students
 After using the phase-field method for 1 – 3 years, students were asked to do all the
first four benchmark problems and post their results
 Seven students were tasked with doing this, about half are done so far
Specific examples of using BM problems for education
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10. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Experienced PF users learning new code
 BM#1: basic procedure to solve partial differential equations with MOOSE
 BM#2: dealing with multi-phase system
 BM#3: writing my own Kernels and utilizing Materials. New feature added
 BM#5: exposure to use of MOOSE navier_stokes physics module
 BM#6: better understandings of MOOSE’s Neumann boundary condition
 Cahn-Hilliard-Navier-Stokes coupled physics
Specific examples of using BM problems for education
(ctn.)
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11. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Michael Tonks and Andrea Jokisaari taught a one-day tutorial-style Phase-Field
MOOSE training at TMS 2018
 BM problems 1 and 4 were used for the tutorial
 We had 20+ attendees with a large range of computational experience
 One attendee had never compiled a code before
 Elizabeth Holm from Carnegie-Mellon also attended
 The BM problems provided standardized problems with known solutions that
simplified the development of the training.
 We also directed the attendees to the other BM problems for future work
Specific examples of using BM problems for education
(cont)
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12. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Survey from 8 people
 Year’s experience with the phase-field method;
Feedback from Tonks’ group members
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13. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
As new users to phase-field
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“The benchmark problems gave me good exposure both to the different systems
modeled in phase field and the various capabilities of the software I was using.”
“I learned to write code/input file, and I got to play with numerical
parameters (petsc options) and better understand what they do”
“How all the pieces fit together”
Q: What did you learn by doing BM problems?

14. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
As experienced users to phase-field
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“I primarily found it helpful to get familiar with some
MOOSE features that I rarely/never used before.”
“They give me a broad set of problems to refresh my skills. When you work
in only one area it is easy to forget about different classes of problems.”
“The second time is when I actually learned something from doing them, the
first time there was way too much to learn to get a deep understanding.”
“Have a better picture of the phase field model, and
know more about the model out of research.”
Q: What did you learn by doing BM problems?

15. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Numerical issues
“Convergence issues.”
“I didn't know how to make 'T' shape domain, so I
learned using a software to construct geometries
and meshes. I also had an issue on plotting a result in
3D.”
“The numerical method I was using required a
higher order element, which is not easy to
converge.”
 Human errors
“I believe my biggest issue was with finding a typo in
the initial condition”
“The initial condition equation I wrote is wrong, and
it took me some time to realize that.”
Issues with BMP#1; spinodal decomposition
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16. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Good example practice for beginning
“I got practice writing a simple, compact input file”
“It was a good review of the basics.”
“I think the problem 1 was a good introduction to phase field. Simple but very useful”
 Capturing the model concept
“Learned how free energies are worked into the model”
 Improvements in numerical skills
“I've learned how to write MOOSE input file and how to solve Cahn-Hilliard equation
with the 1st order shape functions.”
“Doing the differently shaped domains helped me to get used to doing more than just
squares or rectangles”
“I know more about MOOSE and the split method used in MOOSE(Numerical stuff)”
Strengths for BMP#1
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17. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Complexity of multi-phase system and human
errors
“Typing in all of the long equations without errors -
comparing the initial free energy to previous
benchmarks - this should be included in the writeup
for troubleshooting “
“For the input file, I had to write so many duplicate
lines to solve the multi-phase-field equations.
 Numerical issues
“Numerical convergence issue. Adjust initial time step
to be small enough.”
“In problem 2 I had an issue with mesh adaptivity
causing the solutions to go haywire early in the
simulation. I resolved it using a MOOSE option that
lets you delay when mesh adaptivity begins.”
Issues with BMP#2; Oswald ripening
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18. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 New exposure to a new problem
“It was my first exposure to a model designed specifically for Ostwald ripening.”
 Good example problem for coupled physics
“Good introduction to coupled equations”
“How to couple conserved and non-conserved parameters”
“I could write more compact input file after learning about MOOSE action for multi-
phase systems.”
 Experience with troubleshooting of convergence issue for coupled system
“Time step can determine the convergence"
Strengths for BMP#2
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19. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Complexity of physics
“I had never solved an anisotropic interface
problem before. It helped me see the unique
struggles with anisotropy”
“Dealing with anisotropic interface energies”
 Required new features beyond playing with
the input files
“Need to write a new kernel to solve this
problem. Write a new kernel and fix it”
“Creating new kernels with equations”
 Resolution and calculation time issues
“This problem required relatively higher
resolution than other problems, and the
calculation time was too long.”
Issues with BMP#3; dendritic growth
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20. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Better understanding on solidification problems
“Problem 3 helped me understand how dendritic growth works in the phase field
method and gave me exposure to the necessary kernels.”
“Better understanding the anisotropic solidification process. Also the functional
derivative”
 Improvements in numerical skills
“Taking advantages of DerivativeParsedMaterial of MOOSE, I developed a different
approach to deal with the anisotropy function more general and independent of the
dimension.”
Strengths for BMP#3
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21. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Issues; numerical skills
“I had issues with mesh displacements causing
highly contorted results. I fixed it by fixing the way
I was pinning the mesh down.”
“I am getting the wrong behavior”
 Strengths; better understandings in phase-
field-mechanics coupling
“It was my first major exposure to solid
mechanics.”
“Coupling with stress”
Issues and strengths for BMP#4
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22. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Issues; numerical skills
“I had to learn how to construct the mesh”
“I believe there’s something wrong with the outlet boundary”
 Strengths; exposure to a new physics
“I’ve learned how to use MOOSE navier_stokes module”
Issues and strengths for BMP#5
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23. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
Issues
 Common issues
 Numerical issue
 Human error
 Problem specific issues
 BM#2 & BM#3: complexity of physics
Summarized issues and strengths of each BM problems
Strengths
 Gives new exposures to various
problems
 Well-balanced examples for each
physics
 Overall, all problems are doable.
 Some aspects are challenging for
beginners.
 Inspires improvement of numerical
skills
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24. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
 Discretization information
 General guide line for determining ∆𝑥 and ∆𝑡
 More information about mesh construction (especially, BM #5 and #6 that
contain curved boundaries)
 More uploaded results for BM problems 2 and up, for comparison
 Fewer parts to each problem to make it easier for people to complete
What changes could make them more useful for
education?
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25. DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING