About
Computational science engineer with a PhD in mathematics interested in research, technical software development and new technologies, with experience in numerical methods, algorithms for simulation, scientific product development and leadership
Industry Experience
Plexim GmbH
Zurich, Switzerland
Head of Scientific Software Development 2024 - ongoing
Team Lead Research Scientist 2023 - 2024
Scientific Software Developer 2022 - 2023
- Core Technology: R&D in high-performance differential algebraic equations (DAEs) solvers for the simulation of multi-physics, mixed-formulations, mixed-signals circuits and power electronics systems
Keywords: sparse & dense linear algebra, KLU, QR and SVD decompositions, multi-threading, automatic differentiation, ExprTk, Netlist parsing, graph algorithms, Runge-Kutta time-stepping, BDFs, interpolation, error estimation, nonlinear optimization, voltage limiting
- Product Development: Building a state-of-the-art SPICE solver with innovative technology (multiyear roadmap); created a native fuzzy-search command-launcher/model-finder tool to improve UI/UX and discoverability of features in our flagship software PLECS; deployed a Python package (thermal-network) using JAX and Optax for surrogate thermal modeling of semiconductor devices (gradient-based fitting, model identification)
- Real-Time Systems: Development and stability analysis of new numerical schemes for real-time simulation on FPGAs (RT box)
- Leadership: Lead a team of 6 research scientists and engineers; code reviews; supervised Bachelor and Master's theses in collaboration with ETH Zurich; travelled internationally to give workshops to research institutes, engineering firms and manufacturers of semiconductors.
- Tooling & Tech Stack: C++ with Qt, embedded Lua, CMake, Gitlab, Git (version control), testing pipeline, Python, MATLAB, Octave (for initialization scripts), Modelica, circuit schematic editors
Mitsubishi Electric Research Laboratories (MERL)
Cambridge, USA
Research Intern May 2017 - Aug 2017
- Modeling & Optimization: Simulation and optimization of large-scale HVAC systems with surrogate models; built a Levenberg-Marquardt optimizer (least-squares) with geodesic acceleration (using SUNDIALS for transients) to fit physically-based models to temperature data (MATLAB); simulated DAEs arising from a robot arm model
- Tooling & Tech Stack: MATLAB, Modelica, Mercurial (version control)
Montreal University Hospital Center (CHUM)
Montreal, Canada
Research Assistant May 2012 - Aug 2012
- Conducted literature review on motor learning (brain processes involved in imitation games)
MEEIR
Montreal, Canada
Laboratory Thechnician part-time, 2010-2011
- Processed and graded ruthenium powder by particle size through multi-stage sieving
Academic Experience
ETH Zurich
Zurich, Switzerland
Scientific Assistant 2018 - 2022
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Research at the interface of numerical analysis and differential geometry (PDEs on manifolds), leading to multiple publications in top-tier journals and presentations at international conferences
Keywords: numerical analysis, PDEs, manifolds, electromagnetism, scattering, domain decompositions, boundary and finite element methods (FEM & BEM), exterior calculus, clifford algebras, resonant frequencies, Hilbert complexes, conservative methods
McGill University
Montreal, Canada
Research Assistant 2014 - 2016
- Scientific Computing: Developed a Lattice Gauge Theory solver in C for the Yang-Mills equation, implement gradient descent and line search on Principal Fiber bundles
- Algorithm Implementation: Implemented an algorithm in C to study Copulas and measures of statistical correlation
Teaching Experience
ETH Zurich
Organizer & T.A. 2018 - 2022
- Contributed in developing the curriculum, exercises and exams for Numerical Methods for PDEs; mentored and supervised teaching assistants; led weekly exercise sessions and prepared examinations for large classes
- Weekly exercise sessions: Numerical Methods for Application in Engineering II
F.A.C.E.
Montreal, Canada
Teacher Assistant part-time, 2013 - 2015
- Led biweekly exercise sessions for elementary and high school students, focusing on mathematics and science
Activities & Leadership
NPDECODES Project
Project Co-Lead 2018 - 2022
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Led a team of student developers in creating NPDECODES, a C++ repository of ~65 physical simulation and optimization algorithms, now the standard framework for the course
Keywords: wave propagation, convection-diffusion, conservation laws, electrostatics, force calculations, error estimators, convergence analysis, polynomial fitting, method of lines and much more; C++, Python
Seminars in Undergraduate Mathematics in Montreal (SUMM)
VP Finance 2015 - 2016
Oranizing Committee Member 2014 - 2015
- SUMM is an annual conference organized in collaboration by students of all four universities in Montreal, QC, Canada. Of provincial scale, it is the largest event of the type in Quebec. It benefits to undergraduate students from universities of both Quebec and Ontario.
McGill CodeJam - Artificial Intelligence
Hackathon (48h) 2014
- Design and implementation of a facial recognition algorithm based on PCA
Publications
- Schulz, E., Hiptmair, R., & Kurz, S. (2025). Boundary integral exterior calculus. Journal of the European Mathematical Society.
- Schulz, E., & Wan, A. T. S. (2025). Minimal $ \ell^2 $ norm discrete multiplier method. Journal of Computational Dynamics, 12(2), 212-238.
- Hiptmair, R., Pauly, D., & Schulz, E. (2023). Traces for Hilbert complexes. Journal of Functional Analysis, 284(10).
- Schulz, E., & Hiptmair, R. (2022). First-kind boundary integral equations for the Dirac operator in 3-dimensional Lipschitz domains. SIAM Journal on Mathematical Analysis, 54(1), 616-648.
- Schulz, E., & Hiptmair, R. (2022). Spurious resonances in coupled domain-boundary variational formulations... Computational Methods in Applied Mathematics, 22(4), 971-985.
- Schulz, E., & Hiptmair, R. (2022). Coupled domain-boundary variational formulations for Hodge--Helmholtz operators. Integral Equations and Operator Theory, 94(1).
- Kirchhart, M., & Schulz, E. (2022). Div--curl problems and H1-regular stream functions in 3D Lipschitz domains. Mathematical Methods in the Applied Sciences, 45(3), 1097-1117.
- Schulz, E., & Tsogtgerel, G. (2020). Convergence of discrete exterior calculus approximations for Poisson problems. Discrete & Computational Geometry, 63, 346-376.
- Hiptmair, R., & Schulz, E. (in progress). Boundary element exterior calculus. TBD.
Multiple intenational conference presentations in Canada, Germany, Switzerland and UK.