An improved GPS method with a new pseudo-peripheral nodes finder in finite element analysis

Finding pseudo-peripheral nodes with the largest eccentricity is important in matrix bandwidth and profile reduction algorithms in finite element analysis. A heuristic parameter, called the “width–depth ratio” and denoted by κκ, is presented for finding the pseudo-peripheral nodes with larger pseudo-diameter compared with the GPS (Gibbs–Poole–Stockmeyer) pseudo-peripheral nodes finder. A novel nodes renumbering algorithm is thus developed by using our nodes finder based on GPS method. Simulations show that proposed nodes finder is reliable and effective in locating the proper pseudo-peripheral nodes with larger pseudo-diameters. A shielded microstrip line is given as an example to testify the ability of the proposed algorithm in application. The results, including time, pseudo-diameter, bandwidths and profiles, all indicate that our method is more competitive than GPS algorithm to be used as the nodes renumbering algorithm.

► We propose a heuristic parameter, “width–depth ratio”, to find good pseudo-diameter.
► We develop a new pseudo-peripheral nodes finder.
► We develop an improved GPS (Gibbs–Poole–Stockmeyer) algorithm.
► Larger pseudo-diameter leads to smaller bandwidth and profile.
► Smaller bandwidth and profile leads to less matrix solving time.