How to Improve Convergence for the MoM / FEM

The hybrid method of moments (MoM) / finite element method (FEM) is an iterative solution method, and under certain conditions, the iterative solution may fail to converge. Several model or solution settings are presented that could improve the model's convergence behaviour.

Sometimes when using the FEM, the Solver stops with the error message: 
ERROR 4673: Iterative solution of the system of linear equations failed, maybe try another pre-conditioner (solution settings).
The Solver stores the solution with the lowest residuum during the solution. Results are generated if this residuum is considered adequate, but the results may be less accurate if the stopping criterion for the residuum is not exactly met. In this case, the Solver output contains the warning: 
WARNING 830: Maximum number of iterations reached without convergence, using in the following the solution with the smallest residuum.
Note: Warning 830 indicates possible inaccurate results due to inadequate convergence.
One or a combination of the following changes can be made to the model:
  • Adjust the mesh.
  • Change the preconditioner.
  • Use double precision.
  • Change the FEM to use first order basis functions.
  • Change to the direct sparse solver for the FEM.

Adjusting the Mesh

Slight adjustments to the mesh size (smaller or larger elements) could lead to improved convergence. If a model is discretised too finely or too coarsely, convergence could be negatively affected.

Tip: Reduce the radii of thick wire segments, or replace them with metallic strips (2D meshes) or cylinders (3D meshes) to improve convergence.

Changing the Preconditioner

The multilevel LU / diagonal decomposition is the default preconditioner for the MoM / FEM. Changing to another preconditioner may help to achieve convergence for the FEM. Select one of the following preconditioners:

  • Use the multilevel ILU / diagonal decomposition preconditioner. Set the Fill-in level per row to 200 and the Stabilisation factor to 1.
  • Use the LU-decomposition of the FEM matrix.
    Note: This preconditioner is only available in EDITFEKO using the CG card.

Using Double Precision

The Solver uses single precision by default- a single byte is used to store a complex number.

Use double precision when higher accuracy is required and to help resolve convergence issues. Double precision uses two bytes to store a complex number in the matrix. This increases the number of significant digits and reduces numerical noise.
Note:
  • Double precision requires twice the memory compared to single precision.
  • Double precision does not improve convergence for the stabilised MLFMM.

Changing the FEM to Use First Order Basis Functions

The FEM uses higher order (order two) basis functions by default. For large volumes, the higher order results in a much smaller number of tetrahedra in the mesh.

Changing to the Direct Sparse Solver for the FEM

The direct sparse solver is not an iterative solution; therefore any convergence problems are avoided.