MATHCCES

Department of Mathematics

RWTH Aachen University

Schinkelstr. 2

D-52062 Aachen

Germany

Office: 229 (Rogowski building, 2nd floor)

Phone: +49 (0) 241 80 98 671

Email:Muhammad Hassan

I'm a Phd student at the MathCCES working under the supverision of Prof. Dr. Benjamin Stamm. I dabbled a bit in a range of mathematical sub-fields during my graduate studies including fluid dynamics (super fancy simulations!) and stochastic differential equations (still gives me nightmares!) before joining Dr. Stamm's research group. While I continue to study PDEs, the equations usually arise from (or have applications in) electrostatic phenomena in Chemistry and Physics.

I'm usually in my office after 10:00 am. Feel free to drop by if you have a general question, or just want to discuss interesting mathematical problems!

**06/2016 - 06/2020**: Ph.D. student at the MathCCES, RWTH Aachen University, Germany.

**09/2013 - 04/2016**: M.Sc. in Applied Mathematics, ETH Zürich, Switzerland.

- Broadly speaking, I work on the numerical analysis of elliptic partial differential equations that arise, for instance, in solvation models in Chemistry or electrostatics problems in Physics. Often these PDEs are posed on unbounded domains so we adopt a boundary integral equation approach, sometimes coupled with a domain decomposition strategy. The goal of my research is to analyse these formulations and answer questions about well-posedness, convergence of approximate solutions, and a priori error estimates.

- During my MS thesis, I studied shock instability and the so-called Carbuncle phenomenon in supersonic and hypersonic flows. My thesis presented the results of numerical simulations to explore the effectiveness of the entropy measure valued solution framework, which was developed by U. Fjordholm and S. Mishra, in resolving this instability phenomenon. This thesis was supervised by Prof. Dr. Siddhartha Mishra at the Seminar for Applied Mathematics at ETH.

**August 2020**Workshop on Implicit Solvation Models under the ERC Synergy project EMC2, Roscoff, Brittany.

**September 2019**2019 Annual Meeting of the European SIAM and GAMM Student Chapters, RWTH Aachen.

**June 2019**MAEFLAP 2019, Brunel University, London.

**February 2019**GAMM Annual Meeting 2019, TU Wien.

**October 2018**Annual Meeting of the `Modelling, Analysis and Simulation of Molecular Systems' GAMM activity Group, TU Berlin/ Zuse Institute.

**April 2018**2nd Edition of the GDR CORREL Mini-school on Mathematics in Electronic Structure Theory, Laboratoire Jacques-Louis Lions, UPMC, Paris.

**October 2017**Annual Meeting of the “Modelling, Analysis and Simulation of Molecular Systems” GAMM activity Group, RWTH Aachen.

**January 2017**GDR CORREL Mini-school on Mathematics in Electronic Structure Theory, Laboratoire Jacques-Louis Lions, UPMC, Paris.

**September 2019**Analysis of a Linear Scaling Algorithm for Calculating Electrostatic Interactions in $N$-body dielectric systems, 2019 Annual Meeting of the European SIAM and GAMM Student Chapters, RWTH Aachen.

**July 2019**On the scalability of the Schwarz method, MathCCES Seminar, RWTH Aachen.

**June 2019**Scalability Analysis of an Integral Equation Formulation of the Many-Body Dielectric Problem in Electrostatics, MAFELAP 2019, Brunel University, London.

**February 2019**Scalability Analysis of an Integral Equation Formulation of the Many-Body Dielectric Problem in Electrostatics, GAMM Annual Meeting 2019, TU Wien.

**October 2018**Scalability Analysis of an Integral Equation Formulation of the Many-Body Dielectric Problem in Electrostatics, Annual Meeting of the `Modelling, Analysis and Simulation of Molecular Systems' GAMM Activity Group, TU Berlin/ Zuse Institute.

**September 2018**On the Numerical Analysis of the Many-Body Dielectric Problem in Electrostatics, Universität Konstanz.

**September 2018**Numerical Analysis Results on the Scalability of the Many-Body Dielectric Problem in Electrostatics, Franco-German Workshop on Mathematical Aspects of Computational Chemistry, RWTH Aachen University.

**March 2018**On the numerical analysis of the ddCOSMO Algorithm, Universität Konstanz.

**January 2017**On the numerical analysis of the ddCOSMO Algorithm, Young Researchers Workshop on Mathematical Methods in Quantum Chemistry, Laboratoire Jacques-Louis Lions, UPMC, Paris.

**February 2016**Exploring the Carbuncle Phenomenon using the Framework of Entropy Measure Valued Solutions, MathCCES Seminar, RWTH Aachen.

**October 2018**, Two week visit to the Laboratoire Jacques-Louis Lions, UPMC, Paris for discussions with Prof. Xavier Claeys.

**March and September 2018**, Four day visits to Numerical Optimization Group at the Universität Konstanz for discussions with Dr. Gabriele Ciaramella.

**December 2017**, Two week visit to the Laboratoire Jacques-Louis Lions, UPMC, Paris for discussions with Prof. Yvon Maday and Prof. Xavier Claeys.

Teaching assistant for

- Partial Differential Equations (WS 2019) RWTH Aachen.

- Gewöhnliche Differentialgleichungen (SS 2019) RWTH Aachen.

- Mathematical Aspects of Computational Chemistry (SS 2019) RWTH Aachen.

- Partielle Differentialgleichungen (WS 2018) RWTH Aachen.

- Mathematical Aspects of Computational Chemistry (SS 2018) RWTH Aachen.

- Analysis für Informatiker (WS 2017-2018) RWTH Aachen.

- Mathematical Aspects of Computational Chemistry (SS 2017) RWTH Aachen.

- Mathematische Grundlagen I (WS 2016-2017) RWTH Aachen.

- Mathematical Aspects of Computational Chemistry (June-July 2017) RWTH Aachen.

- Mathematische Grundlagen II (June-July 2016) RWTH Aachen.

Part-Time Teaching assistant for

- Topics in Mathematical and Computational Fluid Dynamics (February-May 2016) ETH Zürich.

- Computational Methods for Engineering Applications II (WS 2015-16) ETH Zürich.

Additionally, I was a Tutor for CAMMP Week Pro during the Summer Semesters 2017, 2018, and 2019.

**Mathematical analysis of boundary integral equations and domain decomposition methods with applications in polarisable electrostatics**, Phd Dissertation, M. Hassan, RWTH Aachen, 2020 (Available Here).

**Exploring the Carbuncle Phenomenon in Hypersonic flows using the Framework of Entropy Measure Valued Solutions**, Master thesis, M. Hassan, ETH Zürich, 2016.

**The Girsanov Transformation Theorem Revisited**, Semester Project in the Numerical Analysis of Stochastic Ordinary Differential Equations, ETH Zürich, 2015.

**Entropy Stable Schemes for Hyperbolic Conservations Laws**, Semester Project in the Numerical Analysis of Hyperbolic Partial Differential Equations, ETH Zürich, 2015.

**Minkowski's Theorem and Ideal Class Groups**, Semester Project in Algebraic Number Theory, LUMS Pakistan, 2012.

**The Crystallisation Conjecture**, Semester Project of Mario Drevers, RWTH Aachen, 2020.

**Application of Grassmann Manifold Interpolation and Model Order Reduction to Eigenvalue Problems in Computational Chemistry**, Bachelor Thesis of Pawel Bittner, RWTH Aachen, 2019.

**The Alternating Schwarz Method for solving Eigenvalue Problems by Inverse Power Iteration and Steepest Descent**, Semester Project of Hendrik Borchardt, RWTH Aachen, 2019.

**Continuum Solvation Models**, Semester Project of Lucia Baltz, RWTH Aachen, 2019.

**Variational Markov-Chain Monte-Carlo Methods in the context of Computational Chemistry**, Semester Project of Lucia Baltz, RWTH Aachen, 2018.

**Efficient solvers for computing the scalar magnetic potential for multiple spheres**, MS Thesis of Christian Bauer- Co-supervised with Prof. Benjamin Stamm, RWTH Aachen, 2017.

- M. Hassan and B. Stamm.
**An Integral Equation Formulation of the N-Body Dielectric Spheres Problem. Part I: Numerical Analysis**, ESAIM:M2AN, 2020, (https://doi.org/10.1051/m2an/2020030).

- B. Bramas, M. Hassan and B. Stamm.
**An Integral Equation Formulation of the N-Body Dielectric Spheres Problem. Part II: Complexity Analysis**, ESAIM:M2AN, 2020, (https://doi.org/10.1051/m2an/2020055).

- M. Hassan and B. Stamm.
**A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the N-Body Dielectric Spheres Problem**, accepted in Communications in Computational Physics (2020), arXiv prepint arXiv:2002.01579. - G. Ciaramella, M. Hassan and B. Stamm.
**On the Scalability of the Schwarz Method**, The SMAI Journal of Computational Mathematics, Volume 6 (2020), pp. 33-68, (https://doi.org/10.5802/smai-jcm.61).

- G. Ciaramella, M. Hassan and B. Stamm.
**On the Scalability of the Parallel Schwarz Method in One Dimension**, to appear in The Proceedings of the 25th International Domain Decomposition Conference.

- A. Khan, M. Hassan and M. Imran.
**Estimating the basic reproduction number for single- strain dengue fever epidemics.**Infectious diseases of poverty 3.1 (2014): 12.

- M. Imran, M. Hassan, M. Dur-E-Ahmad and A. Khan.
**A comparison of a deterministic and stochastic model for Hepatitis C with an isolation stage.**Journal of biological dynamics 7.1 (2014): 276-301.