What is the exact equation building by EulerimplicitSolver ?

[ouafi98]

Sorry for the bad english, I'm a french speaker.

Hello, I'm new in SOFA and I was looking at the system solved by the SparseLDLSolver (A* dv = b )who is build by the EulerImplicitSolver and wondering what are the exact equation (or system of equations).

I take a look at the cpp file " EulerImplicitSolver.cpp ", I've understood the construction of the matrix A but the line 135

" mop.addMBKv(b, -f_rayleighMass.getValue(), 1, h+f_rayleighStiffness.getValue()); // b = f0 + ( rm M + B + (h+rs) K ) v "

I don't understand the construction of the vector b.

by discretizing myself, in the vector b of course we have the internal elastic force f0, the changing created by the velocity hKv,
What I don't understand are:

• Where is the gravity ?
• How and Where B is computed ? (I thought B was equal to alpha * K + beta * M)
• Why and How rayleighMass, rayleighStiffness, B impact the term b ? (for me B only impact the matrix A not the rhs)

Please help me understand that. If someone can write down the exact equation building by the " EulerImplicitSolver.cpp " with all the matrices and vectors involving in it even without show me where they are computed in the c++ code It would solve all my understanding problems.

Thanks before

[hugtalbot]

Dear @ouafi98

Thank you for this nice question.
This documentation page about the EulerImplicitSolver should help. You have also some insight in the code (in doxygen here, see Detailed Description)

Let us know whether you need more assistance.
Best wishes,

[ouafi98]

Thanks @hugtalbot for the quick reply.