Abstract:Modern finite element analysis (FEA) involves usually large systems of linear equations.The efficiency in solving linear systems is the key in achieving overall efficiency of FEA.Since the 1990s, great progresses have been made in the solution of linearsystems. Conventional variable bandwidth or wave frontal schemes have been replaced byvarious sparse schemes. That has resulted in a break through in thesolution speed. With the achievements in hardware the analysis of 10\,000 to 100\,000 nodes finite elementcalculations on microcomputers becomes possible. This paper reviews developments of thedirect solution in the last 20 years, emphasizing on the fill-in's minimization and speeding offloating point operations.