Dear All,
I wish to know what is the normal procedure or technique in FEM world for solving dynamic problems which is K-lamda*M=F , as you might guess those are stiffness, mass and external force matrices , repectively, non of the matrices are time dependant. So how those Linear equation is solved in scientific world and which method uses the Elmer?
Your comments will be appreciated,
Regards,
Dynamic solver solution techniques?
Re: Dynamic solver solution techniques?
Hi,
The basic FEM approach is:
1. Discretise the domain of interest with a number of simple geometric elements (tetraeder, bricks, prisms)
2. Approximate the field quantities (pressure, temperature, velocity ...) with a set of basis functions with compact support
3. Find some form of weak formulation by applying a set of test function => Basically your set of differential equations is only fulfilled on average and not pointwise
4. Assemble your discrete operators
5.1. If your system is linear, use a standard algorithm to solve it (see Elmer Solver manual for details).
5.2. If your system is nonlinear a fix point interation is performed => linearise the system, compute a new solution, linearise at the new solution, ...
I am not sure if this answers your question.
carsten
The basic FEM approach is:
1. Discretise the domain of interest with a number of simple geometric elements (tetraeder, bricks, prisms)
2. Approximate the field quantities (pressure, temperature, velocity ...) with a set of basis functions with compact support
3. Find some form of weak formulation by applying a set of test function => Basically your set of differential equations is only fulfilled on average and not pointwise
4. Assemble your discrete operators
5.1. If your system is linear, use a standard algorithm to solve it (see Elmer Solver manual for details).
5.2. If your system is nonlinear a fix point interation is performed => linearise the system, compute a new solution, linearise at the new solution, ...
I am not sure if this answers your question.
carsten
Re: Dynamic solver solution techniques?
Thanks casrtenp,
The thing you depicted is basically summarization of the FEM procedure we follow on for generic problem solving. Actually each item you specified is worth a tomes of books in itself. But I mainly concentrate on method we do for the solution of eigenproblems. To be more specific if I've K*X + C*X'+ M*X'' = F equation in hand how to transform it into eigen value problem and how to find the solution of it ?
Regards,
The thing you depicted is basically summarization of the FEM procedure we follow on for generic problem solving. Actually each item you specified is worth a tomes of books in itself. But I mainly concentrate on method we do for the solution of eigenproblems. To be more specific if I've K*X + C*X'+ M*X'' = F equation in hand how to transform it into eigen value problem and how to find the solution of it ?
Regards,