Baher A . Haleem

University of Calgary, Civil Engineering, Graduate Student

Ain Shams University, Civil Engineering ( Structural Engineering ), Faculty Member

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-Experienced Graduate Teaching and Research Assistant at Schulich School of Engineering, University of Calgary and Co-instructor at Faculty of Engineering, Ain Shams University; taught different courses of Structural design, Theory of structures, and Dynamics of structures.
-Have a wide knowledge in programming, finite element analysis, and structural design of bridges and other types of buildings.
-Worked for 3 years as a structural design engineer: Designed RC and steel bridges, factories, and residential & administrative buildings.
-Currently pursuing my PhD degree at Schulich School of Engineering, University of Calgary, Canada. (cGPA 4)
-Got my thesis-based MSc degree in Civil Engineering (Structural Engineering) from Ain Shams University. (cGPA 3.93)
-Graduated from Faculty of Engineering, Ain Shams University with a BSc degree in Civil Engineering. (ranked 1st out of 287 students)

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A new, fast method for solving finite-element equations iteratively based on Gauss–Seidel

Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics

Solving large equation systems is the most time-consuming part of finite-element modelling – iter... more Solving large equation systems is the most time-consuming part of finite-element modelling – iterative techniques are favoured for models with numerous degrees of freedom where direct techniques have high storage requirements. Classical iterative techniques such as Gauss–Seidel (GS) are robust due to guaranteed convergence and algorithmic simplicity. Performance of iterative techniques chiefly depends on system scale and stiffness matrix properties – which are influenced by structural configuration. However, it is possible to adjust an iterative algorithm such that its speed is greatly enhanced for a certain class of structural configurations. This paper presents an adjusted GS solver, ‘constrained Gauss–Seidel’ (CGS), which has been formulated to solve typical multi-storey structures with an enhanced speed. The innovation in CGS originates from the adoption of a diaphragmatic relaxation mechanism that results in dividing equations into two groups to optimally deal with the differen...

A New Modified Version Of Gauss-Seidel Iterative Method Using Grouping Relaxation Approach

INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH (ISSN 2277-8616), 2020

Systems of linear equations appear in many areas either directly as in modeling physical situatio... more Systems of linear equations appear in many areas either directly as in modeling physical situations or indirectly as in the numerical solutions of other mathematical models. The solution of the linear equations' system is probably the most important issue in numerical methods like the finite element method (FEM). Using the finite element method in modeling various structures, with either simple or complicated configuration of elements, in structural engineering became prevalent many years ago. There are two main types of solvers depending on whether the used method is direct or iterative (indirect) method. In contrast to the iterative techniques, the direct techniques provide almost exact solutions, however they are not convenient for some situations, including but not limited to huge systems of equations. In such situations, the iterative solvers are favored as they have privileges concerning solving speed and storage requirements. In addition, indirect solvers are simpler to program. This research focuses on using the Classical (Stationary) iterative techniques for solving linear systems of equations. The main objective of this research is to develop a new modified version of the well-known Gauss-Seidel (GS) iterative technique which is adapted to solving problems in structural engineering. The proposed technique remarkably outperforms GS technique regarding the required number of iterations and the convergence speed. In this paper, the differences between the direct and iterative approaches have been discussed, along with a quick overview of some of the methods underlying these two classes. Then, the idea and algorithm of the new proposed-Modified Gauss-Seidel‖ (MGS) technique have been elucidated. Afterward, the algorithm has been programmed and used to solve some 2D Practical Examples, besides using the conventional Jacobi and GS techniques. Finally, the obtained results have been compared to assess the proposed MGS; it outperformed both Jacobi and GS.

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An Overview of Iterative Techniques Used for Solving the Systems of Equations Resulting from the Finite Element Analysis

by Baher A . Haleem, Bahaa Tork, and Hisham El-Arabaty

IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE), 2020

The sophistication and size of the models of the finite element method are continually growing. H... more The sophistication and size of the models of the finite element method are continually growing. Hence, there is a rising need for faster solvers. The speed of any algorithm varies depending on the analyzed system's scale and the features of the coefficient matrix, that accordingly affect the selection of the proper solver depending on various standards, for instance, the required storage, the results' accuracy, and solving speed. However, these demands are, unfortunately, usually contradictory; there is no single procedure which outperforms the other techniques in all cases. The two main classes of solving techniques are Direct and Iterative (Indirect) solvers. Generally, direct methods tend to need many computations and large memory space, especially for significantly large problems, so a long time is elapsed during the analysis process. Consequently, an iterative solver, in such cases, is more desirable. Besides, such solvers are generally simpler to program. The main objective of this study is to provide a historical background in addition to shedding light on the latest research literature of several well-known classical and modern iterative techniques that have been used in solving myriad engineering problems. In this paper, the difference between both classes of the direct and iterative finite element solvers is explained; showing their strengths and weaknesses, besides mentioning the proper cases to use each class. Some examples of well-known direct and indirect techniques are mentioned. Then, attention is paid to the iterative techniques till the end of the paper; the eminent methods within the two main classes of iterative solvers, classical and modern methods, are mentioned with providing a historical background and literature review for them.

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A new, fast method for solving finite-element equations iteratively based on Gauss–Seidel

Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics

A New Modified Version Of Gauss-Seidel Iterative Method Using Grouping Relaxation Approach

INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH (ISSN 2277-8616), 2020

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An Overview of Iterative Techniques Used for Solving the Systems of Equations Resulting from the Finite Element Analysis

by Baher A . Haleem, Bahaa Tork, and Hisham El-Arabaty

IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE), 2020

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