Enhanced Upward Translations for Systems with Clusters

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I don't find the paper suitable for publication in its present form; the paper may be considered for publication after the following remarks are taken into account:

(1) All over the manuscript, the authors state that MLFMM is Kernel-Independent. Such statement is wrong in Computational Electromagnetics (which is what I know). An example of Kernel-independent matrix-vector product accelerator is the ACA algorithm, which is purely algebraic and can be adapted to any problem with any Kernel. This should be corrected. The MLFMM as presented in the seminal references is only valid for the KErnel associated witht the free-space Green's function.

(2) The authors describe as "far-field" the interactions where the MLFMM is applied. Normally, these distances may be of fractions of wavelength; so, they should not be considered "far-field" under no circumstances. The term "far-field" in electromagnetics denotes severals wavelengths of separation distance.

(3) The paper discusses the improved accuracy of a modified version of the MLFMM by identifying the most important sources. Are these sources identified at each step in the iterative search of the solution? This may be time consuming as compared with the conventional MLFMM, which sets the hierarchical tree partition once at the beginning, prior to the iterative search of the solution.

(b) Clearly, the proposed algorithm improves the accuracy of the solution, but probably at the cost of increasing the required time (i.e. time-complexity). This should be discussed in the paper with time graphs.

 

 

Comments on the Quality of English Language

No comments

Author Response

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Reviewer 2 Report

Comments and Suggestions for Authors

This is an important and active research topic. You have done a reasonable good work and it will be recommended for publishing subject to satisfactory revising/updating:

1. statement of the problem: while it gives a good general introduction, leading to the current problem, however, it lacks of a in depth critique of the current upward translations; 

2. It is noted that a number of references are your own, and surely you should expand and include the current and relevant papers from other researchers?

3. How this work is precisely different from and moving forward from your published work such as Ref 17, Ref. 18, or other researcher's work;

4. Section 3; make explicit what are new from ref. 17 and ref 18; 

5. The justification for forming cluster 1 and cluster 2, and how the optimal value  𝑟𝑐𝑙 = ?𝑅𝑒 is obtained? how it would be different from problem to problem, and its influence on accuracy and efficiency?

6. The description of the use of clusters lacks of the visual and physical quantity, it can be improved;

 7. use the specific terminology and names and short sentences to increase readability and clarity;

 

Author Response

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Reviewer 3 Report

Comments and Suggestions for Authors

The article is well done and significant.  The theme of the article has been developing rapidly in recent years. The advantage of the article is the presentation of the proposed method in a clear way. The presented method improves the accuracy of the boundary element systems by using a modified kernel to evaluate the difference between the clusters.

To improve the article it would be better to add a chapter "State of Art" and present a brief review of the works of the other authors in the fast multipole method field.

After improving the article can be published

Author Response

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Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

I have noted the substantial change and am satisfied. Hence, recommend it for publishing now.