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How do we scale the 'non-linear residual'????
Posted: Wed Apr 03, 2019 6:33 pm
by ronnysingh
From one of the other discussion posts, I saw that Simvascular uses the generalized-alpha method and the 'non-linear residual' as defined in equation (24) and (10) of [1]. Firstly, is this is the way Simvascular defines residual?
Qualitatively, I understand that the accuracy of the simulation improves as the residual decreases. Quantitatively, I want to write something along the lines of, "We required the scaled residual criteria defined in (citation 1) to be less than 0.0001 for convergence. This corresponds conceptually to a percentage error of less than 0.1 percent in the solution to the Navier-Stokes equations (citation 2)....."
Do you guys have any recommendations on what flow quantity or flow scale I can use to non-dimensionalize or scale the 'non-linear residual' I get from my simulations?
References
1.Jansen, K.E., Whiting, C.H. and Hulbert, G.M., 2000. A generalized-alpha method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Computer methods in applied mechanics and engineering, 190(3-4), pp.305-319.
Thanks a lot,
Re: How do we scale the 'non-linear residual'????
Posted: Fri Apr 05, 2019 5:23 pm
by wgyang
I think the residual value printed in histor.dat is not exactly the same. It is a root mean square residual i.e. residual norm/sqrt(number of nodes). If interested, you can find the calculation in subroutine rstatic. If you want to non-dimensionalize the residual, you can divide it by the value at the previous iteration or just look at the 4th column in histor.dat which is the logarithm of the residual change, specifically, it is 10 * log10 ( current residual value / residual value at the beginning of analysis ).
Re: How do we scale the 'non-linear residual'????
Posted: Sun Apr 07, 2019 12:40 pm
by joshuapatel
ronnysingh wrote: ↑Wed Apr 03, 2019 6:33 pm
From one of the other discussion posts, I saw that Simvascular uses the generalized-alpha method and the 'non-linear residual' as defined in equation (24) and (10) of [1]. Firstly, is this is the way Simvascular defines residual?
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Qualitatively, I understand that the accuracy of the simulation improves as the residual decreases. Quantitatively, I want to write something along the lines of, "We required the scaled residual criteria defined in (citation 1) to be less than 0.0001 for convergence. This corresponds conceptually to a percentage error of less than 0.1 percent in the solution to the Navier-Stokes equations (citation 2)....."
Do you guys have any recommendations on what flow quantity or flow scale I can use to non-dimensionalize or scale the 'non-linear residual' I get from my simulations?
References
1.Jansen, K.E., Whiting, C.H. and Hulbert, G.M., 2000. A generalized-alpha method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Computer methods in applied mechanics and engineering, 190(3-4), pp.305-319.
Thanks a lot,
same issue happend with me
Re: How do we scale the 'non-linear residual'????
Posted: Wed Nov 06, 2019 12:03 am
by reneedegutis
ronnysingh wrote: ↑Wed Apr 03, 2019 6:33 pm
From one of the other discussion posts, I saw that Simvascular uses the generalized-alpha method and the 'non-linear residual' as defined in equation (24) and (10) of [1]. Firstly, is this is the way Simvascular defines residual?
http://simvascular.github.io/ https://domyhomeworkonline.net/ https://stats.stackexchange.com/
Qualitatively, I understand that the accuracy of the simulation improves as the residual decreases. Quantitatively, I want to write something along the lines of, "We required the scaled residual criteria defined in (citation 1) to be less than 0.0001 for convergence. This corresponds conceptually to a percentage error of less than 0.1 percent in the solution to the Navier-Stokes equations (citation 2)....."
Do you guys have any recommendations on what flow quantity or flow scale I can use to non-dimensionalize or scale the 'non-linear residual' I get from my simulations?
References
1.Jansen, K.E., Whiting, C.H. and Hulbert, G.M., 2000. A generalized-alpha method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Computer methods in applied mechanics and engineering, 190(3-4), pp.305-319.
Thanks a lot,
Hello @ronnysingh,
Did you manage to find the solution? I just wanted to clarify whether you tried to use RMSE as well and in which cases.
Renee Degutis