Enhancing Quasi-Newton Acceleration for Fluid-Structure Interaction

Round 1

Reviewer 1 Report

The authors present strategies to accelerate the computations of quasi-Newton techniques for partitioned simulation of coupled problems. They introduce a new filtering of the QR-decomposition that often occurs in these techniques and use adaptive scaling if parts of the array with variables have different magnitudes.

Remarks:

• Line below Eq (3): “do not converge” => “may not converge”, as this depends on the problem
• Line 121: If H(x) is a function of x and at the same time the argument of the function \tilde{R}, but that makes in confusing the actual argument of the function is and how the Jacobian is calculated (derivative with respect to …?)
• Equation 12: Shouldn’t the last minus be a plus? Compare with line 144.
• Please check line 183-184, because new columns in V are added to the left and in Q to the right, but deleting a column is performed to the right for both, which is probably not correct.
• Footnote 1: Python is zero-based, not one-based.
• Figure 2: With the lowest row of R equal to zero, isn’t the right column of Q meaningless?
• Line 237: reset to zero => reset to one?

Comments:

• Line 316: criteria => criterion
• Line 402: re-scaling => pre-scaling
• Line below 414: each test cases => each test case

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

In the manuscript, the Authors present two enhancements of quasi-Newton methods to accelerate the analysis of partitioned fluid-structure interaction problems. In particular, a pre-scaling and a new filter are proposed to improve runtime while not affecting convergence. Two test cases are reported.

The topic of the manuscript is interesting, the development is well done and easy to follow. However, to be considered for the publication improvements should be done and some clarifications should be added. Below the Authors can find specific comments.

A general comment on the manuscript. The Authors must remember that this should be a scientific paper, not a user manual for the software. References should be done with respect to the standard literature, not to what is currently implemented in the preCICE software. Moreover, the notation should be the standard used in the literature and not the “notation used in preCICE” (as stated in the manuscript).

Line 3: what does it mean “quasi-standard”?

Under equation 3. Do you mean that the standard Jacobi coupling does not converge in a general case without an acceleration? Please better comment on that, in particular referring to the standard literature on coupling schemes.

Section 2. The description of the methods is quite confusing and lacks important details. Please explain better the approaches.

Lines 325-326. The issue of the added mass effect is clear. The Authors state that they are using similar densities for fluid and solid. But looking at the Tables of the examples  (Figures 3, 4 and 6) the densities are very different (e.g. fluid density =1000, solid density=2500). Please correct the sentence, if wrong.

General comments. The Tables are quite difficult to understand, I suggest avoiding a section with the Tables and a second section with the Discussion. I suggest using the Tables directly in the discussion session.

The results obtained are very interesting however they are limited to two cases: the elastic tube and the dam break.

Are there any significant differences in the behaviour of the proposed techniques considering linear or quadratic elements? If not, as I believe, considering both cases (linear and quadratic) are unnecessary. If yes, what is the theoretical explanation?

The differences between the 2D and 3D dam-break tests are more evident. Do you think that these differences in the behaviour are due to the larger dimension of the coupling regions? Do you see any other reasons?

Considering the previous comments, I suggest removing one of the two versions of the elastic tube and adding another different test case to show that the proposed approach works in different situations.

It will be interesting to see the effect of the proposed approaches in cases in which added mass effect is important.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The Authors replied in detail to all the comments raised by the Reviewer and modified the manuscript accordingly. According to the Reviewer opinion, the paper can be considered for the publication.