Re: [Getfem-users] How the equivalent mass matrix and rhs is assembled in Newmark scheme?

[Tetsuo Koyama]

Dear GetFEM++ Project

Hello.
> My textbook says that the M is the equivalent mass like following
Sorry this is the equation of the equivalent stiffness matrix.Please ignore it.

All I want to know is how the equivalent mass matrix, equivalent rhs
is made and the place of source.

If you gave me information, I will add it to document.

Best Regard Tetsuo.

2019年3月25日(月) 19:35 Tetsuo Koyama <address@hidden>:
>
> Dear GetFEM++ Project
>
> Hello. Thank you for your support. I made my research program using
> getfem++. And now I debugging one by one.
>
> Today's question is about the mass matrix assembling in Newmark
> scheme. Under this document says that getfem using M.Dot2_u = F(u)
> equation.
>
> http://getfem.org/userdoc/model_time_integration.html#the-implicit-newmark-scheme-for-second-order-problems
>
> My textbook says that the M is the equivalent mass like following
>
> K + (1/(beta*dt*dt))*M + gamma/beta/dt*C
>
> and equivalent rhs will be like following.
>
> external_force +
> M(1/(beta*dt*dt)*Previous_u+
> 1/(beta*dt)*Previous_Dot_u+
> (1/(2*beta)-1)*Previous_Dot2_u)+
> C(gamma/(beta*dt)*Previous_u+
> (gamma/beta-1)*Previous_Dot_u+
> (gamma/(2.0*beta)-1)*dt*Previous_Dot2_u)
>
> In my debugging it seems that the specification is different
> (calculation result is correct though).
> Could you give me the information of the specification of equivalent
> mass and equivalent rhs?
> I tried to read the source code, but it is over my ability now. I'm sorry.
> I would be appreciated if you could tell me the relevant part of the
> source code.