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**Contents**

The following capabilities are available in the MODULEF library:

- Automatic generation and modification of two- and three-dimensional meshes.
- Specification of material characteristics or external forces by sub-domain or boundary section.
- Choice of type of finite element method, for example, conforming, non-conforming, hybrid, or mixed. For non-conforming methods the flow and stresses can be computed along with the temperature or displacement, or separately.
- The finite element library contains about 30 elements for thermal analysis:
- two- and three-dimensional, and axisymmetric elements,

and about 55 elements for elasticity for isotropic and anisotropic materials:

- two-dimensional plane stress or plane strain elements,
- three-dimensional elements,
- axisymmetric elements,
- plate and shell elements, and
- elements for hyper-elastic compressible and incompressible materials in non-linear elasticity.

and 3 elements for magnetics.

- Linear systems can be solved using direct or iterative methods:
- Direct methods:
Cholesky, Crout or Gauss factorization is used depending on the nature of the system matrix. The matrix storing technique is a skyline storage in main or secondary memory.

- Iterative methods:
Symmetric or non-symmetric linear systems are solved iteratively using a choice of conjugate gradient methods with or without preconditioning, or relaxation. Compact storage is used to store the matrices (only non-zero entries are stored).

- Direct methods:
- Solution methods for eigenproblems include inverse iteration, subspace iteration, Lanczos and QR methods.
- The solution of time-dependent thermal problems and dynamic problems by:
- classical multi-step,
- Gear multi-step predictor-corrector,
- 3rd - order semi implicit Runga-Kutta.

- Non-linear elasticity:
- the solution of unilateral contact problems without friction by iterative algorithms,
- the calculation of stresses in two- or three-dimensional elasto-plasticity and the visualization of plastic zones,
- the calculation of large deformations of compressible or incompressible hyper-elastic solids (two- or three-dimensional, or axisymmetric).

- Solution of variational inequalities subject to bounded constraints by relaxation and complementarity.
- Solution of the Dirichlet problem for a biharmonic operator by a mixed finite element method of order 1 or 2.
- Calculation of velocities and pressure of a viscous incompressible fluid (Navier-Stokes equations).
- The computation of homogenized coefficients of composite structures.
- Decomposition of domains.
- Calculation of stresses and interpretation of results, for example:
- calculation of error norms,
- calculation of the sum of the element residues,
- gluing together of two adjacent meshes and their corresponding solutions, etc.

- Several modules are available for the display of results, interactively or in batch, for example to plot
two- or three-dimensional meshes, deformations, stresses, isovalues, velocities and streamlines in fluid
mechanics, etc.