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Implementation of the skyline algorithm in finite-element computations of Saint-Venant equations | ||
| Journal of Applied Research in Water and Wastewater | ||
| مقاله 3، دوره 1، شماره 2، شهریور 2014، صفحه 61-65 اصل مقاله (1.05 M) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Reza Karimi1؛ Ali Akbar Akhtari* 1؛ Omid Seyedashraf2 | ||
| 1Department of Civil Engineering, Razi University, Kermanshah, Iran. | ||
| 2Department of Civil Engineering, Kermanshah University of Technology, Kermanshah, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Skyline solver؛ Sparse matrices؛ Dam-break flow؛ Saint-Venant equations | ||
| مراجع | ||
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Fang C., Sheu T., Two element-by-element iterative solutions for shallow water equations, SIAM Journal on Scientific Computing 22 (2001) 2075-2092. Golub G.H., Van Loan C.F., Matrix Computations, Johns Hopkins University Press, Baltimore, 1996. Irons, B.A., A frontal solution program for finite element analysis, International Journal for Numerical Methods in Engineering 2 (1970) 5-32. Karimi R., Numerical Solution of the Dam Break Problem With Finite Element Method, Thesis, Razi University, 2012. Nour-Omid B., Taylor R.L., An algorithm for assembly of stiffness matrices into a compacted data structure, Engineering Computations 1 (1984) 312-317. Poole D. Linear Algebra: A Modern Introduction, Cengage Learning, Thomson Brooks Cole, 2006. Quecedo M., Pastor M., A reappraisal of Taylor–Galerkin algorithm for drying–wetting areas in shallow water computations, International Journal for Numerical Methods in Fluids 38 (2002) 515-531. Reddy J. N., An introduction to the finite element method, McGraw-Hill Higher Education, New York City, New York, 2006. Seyedashraf O., Development of Finite Element Method for 2D Numerical Simulation of Dam-Break Flow Using Saint-Venant Equations, MSc. Thesis, Razi University, 2012. Shen C., Zhang J., Parallel Two Level Block ILU Preconditioning Techniques for Solving Large Sparse Linear Systems, Parallel Computing, 28 (2002) 1451-1475. Tseng M.H., Chu C.R., The simulation of dam-break flows by an improved predictor–corrector TVD scheme, Advances in Water Resources, 23 (2000) 637-643. | ||
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