Short Biography

I am currently a lecturer at the department of mathematics, Makerere University, Uganda and formerly a research scientist at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) , which is part of the Austrian Academy of Sciences. I have deep interests in mathematical modeling of industrial related problems and have participated in a number of activities such as the ECMI Modelling week in KongensLyngby, Copenhagen, Denmark in 2006, Philips medical systems modeling week at Technical University Eindhoven, the Netherlands, in March 2007 and the 19th European Conference on Mathematics for Industry which was held in Santiago de Compostela (Spain) on 13-17th June 2016. My research interests are areas of scientific computing, modeling using differential equations and optimization and optimal control of differential equations.

Education Background

2010-2014: Radon institute of computational and applied Mathematics Post- Doc
2007-2010: University Graz, Austria PhD
2005-2007: Johannes Kepler University, Linz, Austria and Eindhoven University of Technology-Netherlands MSc-Computational science and Engineering
2001-2004: Makerere University, Kampala, Uganda BSc/Educ

Publications
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18. R KATENDE, H KASUMBA, G KAKUBA, J. M MANGO.: On the Error Bounds for ReLU Neural Networks. IAENG International Journal of Applied Mathematics, Vol.54.No.12. Pages 2602-2611 (2024)
17. R KATENDE, H KASUMBA, G KAKUBA, J.M MANGO.: A proof of convergence and equivalence for 1D finite element methods and ReLU neural networks. Annals of Mathematics and Computer Science, Vol.25.Pages 97-111 (2024)
16. J. NANYONDO, H. KASUMBA, J. MUGISHA.: Analysis of heterogeneous vehicular traffic: Using proportional densities. Physica A: Statistical Mechanics and its Applications. Vol.633. Pages 129387, (2024) DOI: https://doi.org/10.1016/j.physa.2023.129387
15. M. D. AROP, H. KASUMBA, J. KASOZI, F. BERNTSSON .Optimal actuator design for control of vibrations induced by pedestrian-bridge interactions. Mathematics in Applied Sciences and Engineering, Vol. 5, No. 2. 85-184. DOI: https://doi.org/10.5206/mase/16958 . (2024).
14. M. D. AROP, H. KASUMBA, J. KASOZI, F. BERNTSSON, Optimal actuator placement for control of vibrations induced by pedestrian-bridge interactions. Mathematics in Applied Sciences and Engineering, Vol. 4 No. 3 (2023): pp.154-248 . DOI: https://doi.org/10.5206/mase/15949
13. C. ANGUZU, C. ENGSTROM, H. KASUMBA, J. M. MANGO, S. SILVESTROV.: Algorithms for Recalculating Alpha and Eigenvector Centrality Measures using Graph Partitioning Techniques. In: A. Malyarenko, Y. Ni, M. Rancic, S. Silvestrov. (eds), Stochastic Processes, Statistical Methods, and Engineering Mathematics, Springer, (2022)
12. F. MUGABI, J.Y.T. MUGISHA, B. NANNYONGA, H. KASUMBA, M.TUSIIME.: Parameter dependent transmission dynamics and optimal control of foot and mouth disease in a contaminated environment. Journal of the Egyptian Mathematical Society. Volume 27, Number 53 (2019).
11. H. KASUMBA, J. MANGO: Boundary Control of a Bernoulli Free Boundary Problem. International Journal of Mathematics and Computation. Volume 28, Number 2 ( 2017) pp. 40-56.
10. J. NYENDE, I. ENYOGOI, J. MANGO, H. KASUMBA. Numerical Simulation of a Two-Dimensional Groundwater Pollute Transport Problem Using Incompressible Steady-State Navier-Stokes Equations and Diffusion-Convection Equations. Modelling and Simulation in Engineering. Volume 2022, Article ID 7419502, 20 pages, DOI: 10.1155/2022/7419502.
9. H. KASUMBA, G. KAKUBA, J. MANGO: A second order fixed domain approach to a shape optimization problem. In Quintela, P., Barral, P., Gomez, D., Pena, F.J., Rodriguez, J., Salgado, P.,Vazquez-Mendez, M.E. (Eds.): Progress in Industrial Mathematics at ECMI 2016, Springer Mathematics in Industry Series, Vol. 26 (2017).
8. H. KASUMBA, K. KUNISCH, A. LAURAIN: A Bilevel shape optimization problem for the exterior Bernoulli free boundary problem. Interfaces and Free boundaries, Volume 16, Issue 4, 2014, pp. 459–487 DOI: 10.4171/IFB/326.
7. H. KASUMBA: Shape optimization approaches to free surface problems. International Journal of Numerical Methods in Fluids, Volume 74, Number 11 (2014), pp. 818-845.
6. H. KASUMBA, K. KUNISCH: On computation of shape Hessian of the cost functional without shape sensitivity of the state variable. Journal of Optimization theory and Appl., Volume 162, Issue 3(2014), pp. 779-804.
5. E. F. CARA, T. HORSINY, H. KASUMBA: Some inverse and control problems for fluids. Annales mathématiques Blaise Pascal 20 no. 1 (2013), pp. 101-138.
4. H. KASUMBA, K. KUNISCH: Vortex control of instationary channel flows using translation invariant cost functionals. Computational Optimization and Applications (2013) 55, pp.227-263
3. H. KASUMBA, K. KUNISCH: On a free surface PDE constrained shape optimization problem. Applied Mathematics and Computation 218 (2012) pp. 11429-11450
2. H. KASUMBA, K. KUNISCH: Vortex control in channel flows using translation invariant cost functionals. Computational Optimization and Applications, Volume 52, Number 3 (2012), pp.691-717.
1. H. KASUMBA, K. KUNISCH: On shape sensitivity analysis of the cost functional without shape sensitivity of the state variable. Control and Cybernectics. Vol 40(4) (2011), pp. 989-1017.

Projects /Grants
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None at the moment

Mentorship / Supervision
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PHD STUDENTS: COMPLETED
Anguzu Collins 2016/HD13/4313U Mathematical Methods for Updating Centrality Measures Based on Powersof the Adjacency Matrix for Changing Networks
Arop Martin 2016/HD13/3401U Optimal Control of a wave Equation Using Actuator Design and Placement

PHD STUDENTS: : ONGOING
Name Reg. No Title Status
Nanyondo Josephine 2016/HD13/18999U Mathematical modeling of heterogeneous traffic flow on an urban road network Ongoing
Katende Ronald Deep Learning Methods for Free Boundary Problems Ongoing

MSC STUDENTS: COMPLETED

Isaac Enyogoi 2014/HD13/185U Numerical Simulation of a Two Dimensional Groundwater Pollute Transport Problem Using Incompressible Steady State Navier-Stokes Equations and a Diffusion-Convection Equation
Francis Mugabi 2016/HD13/485U Modelling Environmental Transmission of Foot and Mouth Disease with Emergency Vaccination and Physical Barriers
Okello Oun Lawrence 2019/HD13/897U On a constitutive error cost functional for a Bernoulli Free Boundary Problem
Musisi Pascal 2020/HD13/17393U Lotka-Voltera –Prey Model with Spatial Effects, Population Diffusion Phenomenon and Seasonal Migration
Mugabi Muhmadi 2021/HD13/2568U Dividend Maximisation In an Insurance-Investment
Model Using Runge-Kutta Scheme

The detailed CV can be accessed here;