Implementation of the skyline algorithm in finite-element computations of Saint-Venant equations

Abstract

Solving a large sparse set of linear equations is of the problems widely seen in every numerical investigation in the entire range of engineering disciplines. Employing a finite element approach in solving partial derivative equations, the resulting stiffness matrices would contain many zero-valued elements. Moreover, storing all these sparse matrices in a computer memory would slower the computation process. The objective of this study is to attain insight into Skyline solver in order to store the non-zero valued entries of large linear systems and enhance the calculations. Initially, the Skyline solver is introduced for symmetric or non-symmetric matrices. Accordingly, an implementation of the proposed solver is conducted using various grid form sets and therefore, several stiffness matrices with different sizes to evaluate the solver's capability in solving equation systems with a variety of dimensions. Comparing the obtained numerical results it was concluded that Skyline algorithm could solve the equation systems tens of times faster than a regular solver; especially in conducting iterative mathematical computations like Saint-Venant Equations.