3. Solvers and linear algebra

Regarding the methods for numbering unknowns, for storing assembled matrices and for solving the linear systems on which the various algorithms are based, several methods are now available: direct or iterative solver, sequential or parallel.

In « native » in code_aster:

• Direct solvers: multi-frontend method (OpenMP parallelized) and method \({\mathit{LDL}}^{T}\).

• Iterative solver: preconditioned conjugate gradient.

These methods are associated with algorithms for renumbering the degrees of freedom in order to optimize the memory size necessary to store the matrices.

Externally, the following solvers can be used:

• MUMPS: MPI out-of-core direct parallelized solvers;

• Pe TSC: library of iterative solvers, parallelized MPI;

For modal calculation: Lanczos and Sorensen methods, inverse power methods, for real and complex problems, symmetric or not.