Application of the substructure-frontal method for repeated solution of large sparse matrix equations to field problems

A highly efficient method for the repeated solution of large sparse matrix equations arising in field problems, called the substructure-frontal method (SFM), is introduced. The whole calculation region is divided into two subregions, Ω_I and Ω _II. Ω_II consists of areas where the material parameters have to be modified in the next iteration and where the calculation results should be recorded. Ω_I is the remaining area. In a repeated solution of any field problem one only has to deal with Ω_I once. Thus, the computer time for the calculation is greatly reduced. The principle of SFM, its computer program implementation, and its practical applications are described. A comparison of computing time for SFM and other methods is given, illustrating its high efficiency