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

[Tetsuo Koyama]

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.