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# Are they referring to Regular and the Modified Newton-Raphson method?

## Are they referring to Regular and the Modified Newton-Raphson method?

(OP)
I am working in a programme called COMSOL, and trying to do a nonlinear analysis. I came across this text on their website and was wondering if they are talking about Regular and the Modified Newton-Raphson method? If so, is Automatic (Newton) equivalent to Modified Newton-Raphson method?

From "https://www.comsol.com/support/knowledgebase/1127"

Is the Constant and Automatic (Newton) mentioned here equivalent to Newton-Raphson method?

### RE: Are they referring to Regular and the Modified Newton-Raphson method?

(OP)
Also had an additional question and did not wanna start another thread, but is Newton-Raphson method related to any of the Arc Length methods mentioned here?

Source: Non-linear Modeling and Analysis of Solids and Structures, Steen Krenk

### RE: Are they referring to Regular and the Modified Newton-Raphson method?

Yes, Comsol used Newton-Raphson method and the difference between constant and automatic version is whether you manually specify constant damping factor or let the solver automatically select it for each iteration. Check the article "Solving Nonlinear Static Finite Element Problems" on Comsol’s blog and the documentation for more details.

Arc-length (Riks) method is a different approach for nonlinear problems and it was designed to solve cases where N-R method fails to converge.

### RE: Are they referring to Regular and the Modified Newton-Raphson method?

(OP)
Thank you FEA way, is it possible to see anywhere in my model the settings for arc length method (Riks)? - or if my model uses arc length method at all.

### RE: Are they referring to Regular and the Modified Newton-Raphson method?

Comsol doesn’t have built-in arc length solver. For this method you would need other software such as Abaqus. In Comsol you can only try to imitate this approach as we discussed in previous threads.

### RE: Are they referring to Regular and the Modified Newton-Raphson method?

(OP)
And this is getting very detailed, but you dont happen to know how the three methods mentioned here relate to arc length method (Riks)?

### RE: Are they referring to Regular and the Modified Newton-Raphson method?

There are several variants of this method (or improvements to the original concept) developed by other authors. They are nicely summed up in Crisfield’s book ("Non-Linear Finite Element Analysis of Solids and Structures").

### RE: Are they referring to Regular and the Modified Newton-Raphson method?

(OP)
Thank you. Do you know if COMSOL uses Regular Newton-Raphson or Modified Newton-Raphson? I did look at the article about it ("Solving Nonlinear Static Finite Element Problems"), but it did not mention if it uses the modified version, only regular it seems.

### RE: Are they referring to Regular and the Modified Newton-Raphson method?

Sorry, I've got to ask ... why do you care what integration method is used by the program ?

If the result is sensitive to the integration method, then how do you know that whatever approach they use is right ?

Maybe you want know out of interest ... then probably better to ask COMSOL helpdesk.

### RE: Are they referring to Regular and the Modified Newton-Raphson method?

(OP)
It might seem unecessary, but I find it helpful to ask such questions, and then work my way from there. Ive read a lot of papers and articles online, but nothing learns me aswell as direct questions of things I wonder and cannot find answer to online.

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