Thesis Topic: The Finite Element Treatment of Maxwell’s Equations in Polygonal domains.
Dr. Jake Leonard Nkeck, AIMS-Cameroon alumnus of the 2013/2014 batch and Assistant Lecturer at the University of Buea, has successfully earned a Ph.D. in Mathematics, specifically in the field of Numerical Analysis and Computation.
This success was possible after he carried out a 6-year-long research aimed at proposing an adaptation of the standard nodal finite element method for the treatment of the Time-harmonic Maxwell’s equations in polygonal domains with corner singularities.
His research, done under the supervision of Prof. Boniface Nkemzi, proposes an adaptation of the standard nodal finite element method for the treatment of the Time-harmonic Maxwell’s equations in polygonal domains with corner singularities by coupling a Fourier decomposition of the solution with a predictor-corrector algorithm. The research work also analyses the stability and convergence of the new algorithm and develops a software in Python that can implement the algorithm on polygonal domains.
During his defense on July 15, 2020, Jake was proud to divulge that some numerical experiments reveal the robustness, accuracy, and efficiency of the new algorithm. A comparison with the edge Finite Element Method, suitable for Maxwell’s equations was equally done, together with a comparison of some other nodal adaptive methods.
“This work has partly been supported by the government of Canada’s International Development Research Centre (IDRC) within the framework of the AIMS Research for Africa Project in 2016. Many thanks to the African Institute for Mathematical Sciences, Cameroon, and the University of Buea for their unwavering support”, he said, in acknowledgment of all entities that contributed to his triumph.
The fresh Ph.D. holder, who plans to further pursue a postdoc position, is now the 9th AIMS-Cameroon alumni to complete a Ph.D. His research interests include Numerical Methods for Partial Differential Equations and Mathematical Modelling.