# Kareem Taha ElgindyKing Fahd University of Petroleum and Minerals | KFUPM · Department of Mathematics

Kareem Taha Elgindy

PhD in Applied and Computational Mathematics

## About

27

Publications

12,831

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

275

Citations

Citations since 2016

Introduction

My research area is concerned with numerical analysis, optimal control theory, and nonlinear optimization.

Additional affiliations

June 2019 - present

August 2017 - present

November 2013 - August 2017

Education

August 2009 - June 2013

November 2004 - November 2008

September 2000 - June 2004

## Publications

Publications (27)

We present a novel direct integral pseudospectral (PS) method (a direct IPS method) for solving a class of continuous-time infinite-horizon optimal control problems (IHOCs). The method transforms the IHOCs into finite-horizon optimal control problems in their integral forms by means of certain parametric mappings, which are then approximated by fin...

This paper presents a Fourier integral pseudospectral (FIPS) method for a general class of nonlinear, periodic optimal control (OC) problems with equality and/or inequality constraints and sufficiently smooth solutions. In this scheme, the integral form of the problem is collocated at an equispaced set of nodes, and all necessary integrals are appr...

We present a novel direct integral pseudospectral (PS) method (a direct IPS method) for solving a class of continuous-time infinite-horizon optimal control problems (IHOCs). The method transforms the IHOCs into finite-horizon optimal control problems (FHOCs) in their integral forms by means of certain parametric mappings, which are then approximate...

In its simplest form, the chemostat consists of microorganisms or cells which grow continually in a specific phase of growth while competing for a single limiting nutrient. Under certain conditions on the cells' growth rate, substrate concentration, and dilution rate, the theory predicts and numerical experiments confirm that a periodically operate...

This paper presents an extension to the Cole-Hopf barycentric Gegenbauer integral pseudospectral (PS) method (CHBGPM) presented in [Elgindy, Kareem T., and Sayed A. Dahy. "High‐order numerical solution of viscous Burgers' equation using a Cole‐Hopf barycentric Gegenbauer integral pseudospectral method." Mathematical Methods in the Applied Sciences...

We propose a high-order adaptive spectral element method based on Gegenbauer polynomial basis for solving singularly perturbed differential equations with Dirichlet boundary conditions and a boundary layer at one end. The method reduces the singularly perturbed boundary value problem into a single system of linear algebraic equations when the solut...

We developed a novel direct optimization method to solve distributed optimal control of viscous Burgers' equation over a finite‐time horizon by minimizing the distance between the state function and a desired target state profile along with the energy of the control. Through a novel linearization strategy, well‐conditioned integral reformulations,...

Partial differential equations (PDEs) arise naturally in a wide variety of scientific areas and applications, and their numerical solutions are highly indispensable in many cases. Typical spectral/pseudospectral (PS) methods for solving PDEs work well only for regular domains such as rectangles or disks; however, the application of these methods to...

We developed a novel direct optimization method to solve distributed optimal control (OC) of viscous Burgers' equation over a finite time horizon by minimizing the distance between the state function and a desired target state profile along with the energy of the control. Through a novel linearization strategy, well conditioned integral reformulati...

We present a high-order integral nodal discontinuous Galerkin (DG) method to solve Burgers' equation. The method lays the first stone of a novel class of integral nodal DG methods exhibiting exponential convergence rates in both spatial and temporal directions; thus, producing highly accurate approximations using a significantly small number of col...

We present a novel, high-order, efficient, and exponentially convergent shifted Gegenbauer integral pseudo-spectral method (SGIPSM) to solve numerically Lane-Emden equations provided with some mixed Neumann and Robin boundary conditions. The framework of the proposed method includes: (i) recasting the problem into its integral formulation, (ii) col...

We present a novel, high-order numerical method to solve viscous Burger's equation with smooth initial and boundary data. The proposed method combines Cole-Hopf transformation with well conditioned integral reformulations to reduce the problem into either a single easy-to-solve integral equation with no constraints, or an integral equation provided...

In this paper, we introduce a novel fully exponentially convergent direct integral pseudospectral method for the numerical solution of optimal control problems governed by a parabolic distributed parameter system. The proposed method combines the superior advantages possessed by the family of pseudospectral methods with the well-conditioning of int...

This paper presents for the first time a robust exact line-search method based on a full pseudospectral (PS) numerical scheme employing orthogonal polynomials. The proposed method takes on an adaptive search procedure and combines the superior accuracy of Chebyshev PS approximations with the high-order approximations obtained through Chebyshev PS d...

In this work, we propose an adaptive spectral element algorithm for solving non-linear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable numerical quadratures to fully discretize the multiple-phase integral form of the optimal control problem. The propos...

The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models. The proposed numerical scheme exploits the stability and the well-conditioning of the numerical integration operators to produce well-conditioned systems of algebraic equations,...

We present a high-order shifted Gegenbauer pseudospectral method (SGPM) to
solve numerically the second-order one-dimensional hyperbolic telegraph
equation provided with some initial and Dirichlet boundary conditions. The
framework of the numerical scheme involves the recast of the problem into its
integral formulation followed by its discretizatio...

This paper reports a novel direct Gegenbauer (ultraspherical) transcription method (GTM) for solving continuous-time optimal control (OC) problems (CTOCPs) with linear/nonlinear dynamics and path constraints. In (Elgindy et al. 2012) [1], we presented a GTM for solving nonlinear CTOCPs directly for the state and the control variables, and the metho...

The analytic solutions of simple optimal control problems may be found using the classical tools such as the calculus of variations, dynamic programming, or the minimum principle. However, in practice, a closed form expression of the optimal control is difficult or even impossible to determine for general nonlinear optimal control problems. Therefo...

In this dissertation, I have developed some computational methods aimed at solving nonlinear optimal control problems. The bulk of the effort has involved the development of some efficient numerical
methods for solving boundary value problems, integral equations, and integro-differential equations. Chapters 1 and 2 provide an introduction to the ne...

This paper treats definite integrations numerically using Gegenbauer quadratures. The novel numerical scheme introduces the idea of exploiting the strengths of the Chebyshev, Legendre, and Gegenbauer polynomials through a unified approach, and using a unique numerical quadrature. In particular, the developed numerical scheme employs the Gegenbauer...

We introduce a hybrid Gegenbauer (ultraspherical) integration method (HGIM) for solving boundary value problems (BVPs), integral and integro-differential equations. The proposed approach recasts the original problems into their integral formulations, which are then discretized into linear systems of algebraic equations using Gegenbauer integration...

The theory of Gegenbauer (ultraspherical) polynomial approximation has received considerable attention in recent decades. In particular, the Gegenbauer polynomials have been applied extensively in the resolution of the Gibbs phenomenon, construction of numerical quadratures, solution of ordinary and partial differential equations, integral and inte...

In this paper we describe a novel direct optimization method using Gegenbauer-Gauss (GG) collocation for solving continuous-time optimal control (OC) problems (CTOCPs) with nonlinear dynamics, state and control constraints. The time domain is mapped onto the interval [0; 1], and the dynamical system formulated as a system of ordinary differential e...

A new explicit expression of the higher order pseudospectral integration matrices is presented using an explicit formula for computing iterated integrals of Chebyshev polynomials. Applications to initial value problems, boundary value problems, linear integral and integro-differential equations are presented. The present numerical results are in sa...

Newton’s method is an important and basic method for solving nonlinear, univariate and unconstrained optimization problems. In this study, a new line search technique based on Chebyshev polynomials is presented. The proposed method is adaptive where it determines a descent direction at each iteration and avoids convergence to a maximum point. Appro...

## Questions

Questions (9)

I know how to differentiate a vector function, say g, with respect to a vector, say x. But what if x was a vector function of some variable, say t? Is it possible to make such a differentiation then? Does it have a meaning?

SETs are largely used by university administrators in decisions about faculty hiring, promotions, and merit increases, so it is very crucial to learn whether SETs actually reflect the true performance of instructors or it is a biased, pointless, and misleading measure that may shape the faculty behavior and causes grade inflation.

I understand that we can produce that number in MATLAB by evaluating exp(1), or possibly using exp(sym(1)) for the exact representation. But e is a very common constant in mathematics and it is as important as pi to some scholars, so after all these many versions of MATLAB, why haven't they recognize this valuable constant yet and show some appreciation by defining it as an individual constant rather than having to use the exp function for that?

Publication in a high-impact journal has been viewed for many years as an indirect form of evaluation of quality. However, is the two-year window provided by Clarivate Analytics (the most famous company in this direction) enough for significant papers to receive most of their citations? Isn't it possible that IFs of journals be manipulated by Editors and Publishers? Recall that the IF is calculated by dividing the number of citations in the JCR year, say x, by the total number of articles published in the two previous years, say y. Therefore, an easy way to increase the IF is to decrease y(!) On the other hand, should we expect a paper published in a high IF journal to be of better quality than that of a lower one? Let's assume for the sake of argument that the IF is a reliable measure of "average quality," does it confirm the high quality of "any single paper" published in the journal in a specific year? In fact, IFs in its current form should not be taken as a reliable measure for the quality of papers by any means not to mention that it does not distinguish between various disciplines of science! That's why we see journals in one discipline with very large IFs, and many other eminent journals with relatively low IFs in other disciplines! One of my concerns also about this matter is with the obsession of academic researchers and institutions nowadays with IFs. What's the fate of emerging journals in this case which has no IFs if researchers all over the world continued to submit their manuscripts only to journals with IFs to get hired and promoted? What's the fate of journals indexed by big citation databases of peer-reviewed literature, like Scopus for example, when they are not indexed by Web of Science; therefore, have no IFs? They can only be measured by other metrics, like CiteScore for example, but alas, most of the academic institutions do not authorize such a metric-- take the top institutions in the middle east as a very clear case. I'm one of those who largely feel that IFs may seriously harm the very essence of research. Editors may favor only those articles or publications that can elevate the IF of the journal. I support the saying that 'science must break the tyranny of the luxury journals'; cf. https://www.theguardian.com/science/2013/dec/09/nobel-winner-boycott-science-journals.

This is a very serious question that any Academic should know its answer, but unfortunately, most academic institutions and universities in the globe do not provide any rules or even some useful guidelines to follow.

In fact, I recently had a very controversial conversation with an academic person about this topic, and it was clear to me that we had some serious conflicting viewpoints. He belongs to those academics who believe that a supervisor must be an author of all of the student's works; not just that, but he also believes that it is his judicious right to put his name before the student's name in the order of authors of any published works. On the other hand, I support those academics who refrain from putting their names on students' works unless they have somehow participated/contributed to the work; moreover, the ordering of authors should not be based on the seniority of supervisors, but rather on how much contribution each individual made. That is, if someone did not add any sort of contribution to some finished work, he should not by any means insert his name on that work.

Let me summarize the full arguments that took place during the conversation I had with that Academic in the following lines:

* The Other Academic Arguments:

1- His master and doctorate supervisors put their names first on his works, even when some of them did not contribute to the work. Therefore, this is the customary thing to do and he must put his name in any published works.

2- He needs to get promoted, and he cannot get promoted without publications.

3- When I gave him examples of good Academics who did not put their names on their students' works, he argued that they have already got promotions, so they do not need this.

4- He wasted his time reading his students' works, therefore, he must put his name.

5- He finds no problem at all to put his name on all his students' works, even if he did nothing.

* My Arguments:

1- It is fair for a supervisor to put his name based on how much contribution he did.

2- My main M.Sc. Supervisor, Prof. Salah El-Gendi did not put his name on my published works given the fact that he read them beforehand. I do respect him much because of this.

3- My Ph.D. Co-Supervisor's name did occur only once out of five published works, and that was because he only suggested the problem that we are going to work on. But even with this suggestion, his name appeared last in the published article, because his contribution was much less than what the other participants did.

4- In Egypt, we follow some points system to get promoted. A single author of some published work gets the full share of the total number of points assigned to this particular work. However, the number of points decreases monotonically for published works having an increasing number of authors. For instance, a paper having two authors would credit both of them 0.8% of the total number of points assigned to this particular work. For three authors, each gets 0.7%, and so on. So, it seems to me that it is very unfair to put my name as a supervisor on some work accomplished by my student and his co-supervisor just because I am a supervisor and read the work! The insertion of my name will simply reduce the share of points of the co-supervisor, when he should have taken more weight of points.

5- According to [1, Page 2], and I am quoting, `According to the International Committee of ..., an author is a person who has made substantive intellectual

contribution to the work reported in the paper. The committee has set three conditions that must be met before a person qualifies as an author. These are:

a) An author should have made substantial contribution in the conception and design, acquisition of data, analysis and interpretation of the results.

b) An author should have drafted the paper or critically revised it for important intellectual content.

c) An author should have approved the final version of the paper to be sent for publication.

With the above conditions in mind, one could easily disqualify people who masquerade as authors and fall into any one of the following categories:

a) Those who write the paper based on the work carried out by others due to their writing prowess.

b) Those who merely help in the collection of the data, such as technicians, laboratory assistants, field surveyors etc.

c) Those who have not read and approved the final draft of the manuscript.

d) Those who merely help in acquiring funding, providing research space, initiating collaboration, providing test samples and other non-intellectual contributions, e.g. heads of research groups, heads of departments, industrial partners etc.

People who have helped in the course of the research but do not qualify as authors should be duly acknowledged in the paper. It is unethical to include them as co-authors. As the academia rests upon honesty and integrity, breach of either of these in reporting research findings by people who do not qualify as authors is considered an act of academic dishonesty.'

Of course, it would be very beneficial for someone like me to put his name on any of his students' works, especially when he still works as a lecturer and needs to get promoted. Yet, under any circumstances, I cannot put my name on any of my students' works when I have made zero contribution in the course of having the works completed. Being simply a reader of my student's work does not give me the right to practice my influence as a supervisor and put my name by force.

I hope such a serious problem that may lead into a dispute between supervisors will be fixed in the near future by putting some global well-written rules and guidelines that can control authorship in all academic institutions and universities around the globe. This would surely mend this issue permanently.

**References.**

[1] Ratnam, Mani Maran . "Why the supervisor should be the corresponding author?" 25 Oct. 2010. Web. <http://mechanical.eng.usm.my/MMR/Why_the_supervisor_should_be_the_corresponding_author.pdf>. Date

accessed: 16 Dec. 2016.

In other words, would ETHNICITY, RELIGION, LOW-RANKED INSTITUTION, COUNTRY, etc. be some major causes for rejecting your research article?

## Projects

Projects (6)

This research project endeavors to take advantage of spectral and pseudospectral (PS) methods for solving PDEs in complex domains by introducing some novel, high-order numerical methods that bring into play domain embedding into a regular, square computational domain in combination with integral reformulation, fully exponentially convergent Fourier PS collocation, and Fourier extensions of arbitrary length (FE-AL) methods.

Provide a state of the art computational algorithm to provide a better control policy on many natural phenomena described by nonlinear PDEs.