Study and Discussion on Computational Efficiency of Ice–Structure Interaction by Peridynamic

Round 1

Reviewer 1 Report

This study is focused on the technical aspect of the application of peridynamics for modeling ice-structure interaction problems. In contrast to the studies cited in the review part of Introduction section, this paper is valuable from the point of view of engineering applicability of the numerical method. Thus, the conclusions of this article can be used not only in the problem of "ice-structure" interaction, but also in other areas.

The authors investigate three different methods to improve computational performance: updated Link-list algorithm, particle-pair method, MPI parallel computing technology. The authors also evaluated the efficiency of the combined application of these techniques. Finally, the authors have demonstrated the efficiency of peridynamics with performance improving approaches on the example of simulation of ice breaking by an icebreaker.

 

 2. Peridynamic theory for ice-structure interaction

2.1 Ordinary State-Based Peridynamic for ice model

 «Since bond-based PD has been commonly introduced in simulating ice-structure interaction. At this Section, we only take a short review of ordinary state-based PD, which is also the numerical framework of the present work. In PD theory. » - should these sentences be written together?

 «Ice particles interact with each other in a certain range, δ, is called horizon» - it is worth to identify this range in Fig. 1.

 2.2 Contact model for ice-structure interaction

 The authors describe two main algorithms for modeling the contact force. At the same time, the authors note that they use the second approach (Eqs. 5-8). Since the purpose of the article is to study the computational performance, the authors should give a little more information and compare the performance of the contact algorithms in terms of computational efficiency. Will there be a difference in computational speed depending on the contact algorithm used? How does the relative contact of broken ice parts affect the computational speed as level ice is crushed?

 2.3 Challenging in engineering application in view of computational cost

 «With a same input model and setup, the time steps needed by PD are much smaller than those required by FEM» - A comparison of computational time for the same model between FEM and PD methods would be very valuable information for engineering applications of peridynamics. It would be great if the authors could provide some comments on this issue.

 3. Computation efficiency of optimization methods

3.1 Updated link-list search method to improve family member search of ice domain

 The approach in this paper involves discretizing the set of particles into separate arrays. This greatly simplifies the family particles search algorithm for each particle to searching for particles only in neighboring grid cells. In this subsection the authors investigated the decrease of global search time in the "horizon" using the Updated link-list search method at different sizes of the whole model.

However, the authors should clarify whether a single grid can also be resized. Figure 2 illustrates the grids containing 9 particles. In the case of the ice-construction interaction problems, significant deformation of the material is not expected, since ice is a brittle material with a small value of critical strains. Is it possible in this case to reduce the number of particles in one grid to 4, thereby reducing the number of family particles for each particle even more? If yes, what is the optimal size of one grid cell?

 I also wonder if PD is a strongly RAM-locked method (is there an upper limit of particles that is optimal to compute on a given amount of RAM?)

 3.2 Particle-pair method to accelerate time integration in solving ice constitutive model

 A typo in the picture description: «Figure 6. The array of particle-pair refers to the case in Figure 55» - probably meaning «… to the case in Figure 5»

 3.3 MPI parallel technology

 In this section, the authors investigated the acceleration of calculations due to the parallelization technology of calculations on several cores. As a result, it was noted that a gradual increase in the number of cores will not always lead to faster computation due to the increase in the number of links between the domains into which the model is partitioned. However, this judgment is not entirely correct, since there are other factors involved. For example, I recommend that the authors include the dependence of MPI on the read/write speed of the storage device (SSD) in their analysis. Since output logging is a repeatable process in calculations, the generation of output files for each core is dependent on the performance of the hard disk drive. MPI technology has been widely used for a long period of time and can linearly improve model performance on a sufficiently large number of cores (more than 100). However, in the article, the authors obtained a decrease in performance when using 10 cores compared to 8, which suggests the influence of additional factors.

 Also, for my own understanding, I would like the authors to clarify the effect of MPI technology itself on performance. In my experience using different MPI libraries (IntelMPI, MS-MPI, etc.) can also significantly affect the result.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The present study explores the computational efficiency of different methods that could be applied to ice-structure interactions to improve the computational cost. Also, the present papers discussed the computational strategy to improve efficiency by using Peridynamic theory to calculate ice-structure interaction. The study shows to be interesting in numerical modeling for ice-wave interactions application to more engineering problems as this kind of problem involves many more design and environmental parameters. However, this reviewer has some comments and suggestions on this paper.

 1. Eq. (2) should be supported by a reference.

 2. The explanations of the variable should be after the equations (where they involve). For example, lines 139-144 should not be the proper place to explain those variables. It is suggested they should be explained after Eq. (1).

 3. Formula (6) should be supported by the references.

 4. In Eq. (8), the texts should be normal Font.

 5. As the present paper uses many more abbreviations, it is suggested that an Abbreviation Section should be included for readers' interest.

 6. In Figure 4, the authors need to discuss the percentage of differences in the comparison.

 7. The computational cost of the simulation must be discussed.

 8. Conclusion: The authors must highlight the limitations of the present study. 

Minor editing is required throughout the paper.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The present contribution is devoted to examining computational efficiency issues of the Peridynamic (PD) approach. It is independent on the application and ice structure interaction problem mentioned in the title is just anecdotic. Same paper could have been written for any other application of PD. Therefore, as a general comment I suggest making more explicit the application on the ice breaking problem and reducing the content devoted to the description of the computational efficiency (now there are too many figures).

On the other hand, English writing and style are well below the standards of an archival journal. I strongly suggest using the services of the journal to improve it.

The following specific comments must be addressed by the authors:

1.       Line 55: “, deicing” is “and deicing”.

2.       Line 71: please correct “Afterwards, In order”.

3.       Line 76: “is still a less developed field”, maybe “underdeveloped” is better.

4.       Line 108: “field” should be plural.

5.       Lines 125-129: Please revise grammar and punctuation in this paragraph.

6.       Please, show explicitly the horizon delta in Fig. 1.

7.       Check Eq. (4), possibly in denominator there is an absolute value of p.

8.       Line 188: “condition” and “mode” should be plural.

9.       Line 205: check grammar “established. This makes the discretization of ice domain and the hull must be very fine”.

10.   Eq. (9). Explain more this eq. how the iteration on the neighbors is performed?

11.   Line 214: “p is iterates over”, please correct.

12.   Line 217: “With a same input model”, please correct.

13.   Line 240: “is inspiring beginning of solving”, 3 consecutive -ing words.

14.   Paragraph 3.1. Please, state what is really new here, if not just referred to some previous work.

15.   Line 260: “gird”, please correct.

16.   Line 447: “Further study the influence of collaboration of multiple methods on computational efficiency and speedup” Check grammar.

17.   Caption Fig. 13b: “pariticle”.

18.   Line 529: “In order to solve the problem of low computing efficiency of the original PD algorithm in simulating the ice-structure interaction.”, where is the main sentence?

 

English writing and style are well below the standards of an archival journal. I strongly suggest using the services of the journal to improve it

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I have checked the authors' answers and manuscript changes that have been made. I consider that the authors have fully responded to the comments. For the time being, I am satisfied with the revised manuscript and recommend the article for publication.

Author Response

Thanks for the reviewer's comments.

Reviewer 2 Report

No more further comments.

Minor Editing of English language is required. 

Author Response

Thanks for the reviewer's comments.

We have proofread the manuscript and improved our language.

Reviewer 3 Report

Authors have improved their contribution following the raised comments. However, I still think that the issue of ice breaking is marginal in this contribution. In my opinion some of the figures can be skipped without lose of continuity as the main point is to show the computational acceleration obtained by the proposed approaches. This would make the paper more compact and, perhaps, more interesting to the readers.

A Repeated paragraph 4389-448 in 462-471 has been detected

English writing and style are below the standards of an archival journal. I strongly suggest using the services of the journal to improve it.

Author Response

Thank you for the reviewer's comments.

We have removed Figure 15 as we agree that its contribution was limited.

Furthermore, we have carefully proofread the manuscript and made improvements to the language.