Profile SPD System

The Profile SPD (Symmetric Positive Definite) system solver uses a skyline storage scheme that stores only the elements from the first non-zero entry in each column up to the diagonal. This can be more efficient than band storage for matrices with irregular profiles.

Description

The Profile SPD system: - Uses skyline (profile) matrix storage - Optimized for symmetric positive definite matrices - Stores only non-zero elements up to diagonal - Adapts to irregular matrix profiles - Uses specialized Cholesky factorization

Parameters

Parameter

Type

Description

None

This system solver doesn’t take any parameters

Usage Example

# Create a Femora instance


# Create a Profile SPD system solver
fm.analysis.system.create_system("ProfileSPD")

Notes

  • More efficient than Band SPD for matrices with irregular profiles

  • Memory usage adapts to actual matrix structure

  • Requires matrix to be symmetric positive definite

  • Performance depends on the quality of node numbering

  • Works well with RCM numbering scheme

  • Good choice for problems with irregular mesh patterns

  • Not suitable for non-symmetric or indefinite matrices