Doctorate Nicholas Mueller: PhD student at Monash University, Australia
Nicholas Mueller is a dedicated mathematician and engineer who combines a strong theoretical foundation with a practical focus on real-world applications. His work spans multiple disciplines, from mathematical modeling and numerical methods to high-performance computing, particularly in fluid dynamics and structural mechanics. Currently a PhD candidate at Monash University, Nicholas is focused on enhancing the computational efficiency of simulations for complex, unsteady physical systems. His passion lies in solving challenging problems through collaboration, deep theoretical analysis, and cutting-edge computational techniques, positioning him as a future leader in applied mathematics and scientific computing.
Online Profiles
Education
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Monash University (Australia), 2022-2025
Pursuing a Doctorate in Applied Mathematics, Nicholas is focusing on the development of linear reduced order models to solve complex, unsteady parameterized partial differential equations. His research integrates both theoretical and computational approaches to optimize the performance of high-dimensional simulations in fluid dynamics, structural mechanics, and other fields. -
Ecole Polytechnique Fédérale de Lausanne (Switzerland), 2019-2021
Master’s degree with distinction, specializing in reduced modeling of unsteady Stokes flow. During this time, Nicholas developed novel methods to reduce computational complexity in fluid flow simulations while maintaining high accuracy, particularly in applications related to arterial blood flow. -
Politecnico di Milano (Italy), 2016-2019
Bachelor of Science in Mathematical Engineering, focusing on numerical methods for partial differential equations. His undergraduate thesis, on the development of solvers for the Bidomain model of the human heart, showcased his early interest in applying mathematical techniques to biological and medical problems.
Research Focus
Nicholas’s research centers on developing efficient computational methods to solve parameterized, unsteady partial differential equations (PDEs) using reduced order models (ROMs). These techniques enable simulations of complex systems, such as fluid dynamics and structural mechanics, to be carried out with significantly lower computational costs. His work particularly addresses the challenges of unsteady flow in systems where traditional methods are computationally expensive, and focuses on the application of these models to a wide range of scientific and engineering problems, including cardiovascular modeling and aerospace engineering.
Experience
In addition to his academic experience, Nicholas gained hands-on expertise at CSEM, Switzerland, where he worked as an intern on a research project involving topology optimization for aerospace applications. This experience enhanced his skills in numerical analysis, solver development, and validation, providing him with practical insights into applying mathematical theory to real-world engineering problems. Nicholas is also proficient in a variety of programming languages and tools, including Julia, Python, Matlab, C++, and Comsol, making him versatile in his computational research.
Research Timeline
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2022-Present: PhD research at Monash University, focusing on linear reduced order models for unsteady parameterized PDEs, aiming to improve the efficiency and accuracy of simulations.
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2019-2021: Master’s thesis research at EPFL, creating a space-time reduced model to solve unsteady Stokes equations for hæmodynamic simulations, significantly reducing computational time while retaining accuracy.
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2016-2019: Undergraduate research at Politecnico di Milano, focusing on developing numerical solvers for cardiac electrophysiology through finite element methods for the Bidomain model.
Awards & Honors
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Monash University PhD Fellowship: Awarded a prestigious fellowship to support Nicholas’s doctoral research in Applied Mathematics, providing funding for his extensive computational and theoretical work.
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EPFL Excellence in Research Award: Nicholas received this award for his outstanding contributions to the field of computational fluid dynamics and reduced order modeling.
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Best Master’s Thesis Award: Recognized for the exceptional quality and impact of his master’s thesis, which advanced the field of space-time reduced modeling in fluid mechanics.
These awards highlight Nicholas’s dedication to research excellence and his ability to contribute significantly to cutting-edge scientific fields.
Top-Noted Publication
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Space-Time Reduced Basis Methods for Parametrized Unsteady Stokes Equations, SIAM Journal on Scientific Computing (2024).
This publication presents innovative space-time reduced basis methods to efficiently solve parameterized unsteady Stokes equations, with applications in bioengineering, particularly in modeling blood flow dynamics. The work has contributed to advancing the understanding and application of reduced-order modeling techniques in computational fluid dynamics, helping to bridge the gap between high-fidelity simulations and real-time, practical applications.
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A Tensor-Train Reduced Basis Solver for Parameterized Partial Differential Equations on Cartesian Grids
Journal of Computational and Applied Mathematics, 2025
DOI: 10.1016/j.cam.2025.116790-
In this paper, Nicholas Mueller and his collaborators introduce a novel tensor-train reduced basis solver to address the computational challenges of parameterized partial differential equations on Cartesian grids. The method enhances the efficiency of solving high-dimensional problems by using tensor rank-reduction techniques, which significantly reduce computational costs while maintaining the solution’s accuracy. This work is instrumental for applications where large-scale simulations of complex systems are required.
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Model Order Reduction with Novel Discrete Empirical Interpolation Methods in Space–Time
Journal of Computational and Applied Mathematics, 2024
DOI: 10.1016/j.cam.2024.115767-
This paper presents an innovative hyper-reduction strategy for parameterized partial differential equations, focusing on space-time methods. Nicholas Mueller and Santiago Badia propose a discrete empirical interpolation method that efficiently approximates space- and time-dependent operators, enabling faster simulations of complex physical systems. The paper highlights the effectiveness of the method in reducing the computational burden while improving accuracy.
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Space-Time Reduced Basis Methods for Parametrized Unsteady Stokes Equations
SIAM Journal on Scientific Computing, 2024
DOI: 10.1137/22M1509114-
This work presents a comprehensive analysis of space-time reduced basis methods for the efficient simulation of unsteady Stokes equations, particularly applied to hæmodynamic problems. In collaboration with Riccardo Tenderini and Simone Deparis, Nicholas Mueller contributes significantly to the development of these methods, demonstrating their utility in reducing the complexity of time-dependent simulations without compromising accuracy.
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