Lambert Theisen

M.Sc.
→ Computational Engineer, PhD Student, Digital Creator.
@ RWTH Aachen University / University of Stuttgart
Picture of the author
# Researching PDE eigenvalue problems, asymptotic analysis of expanding domains, directional homogenization, preconditioners for eigenvalue algorithms, preconditioners for linear solvers, spectral coarse spaces for domain decomposition, and Galerkin methods for moment models in rarefied gas modelling.
👋 CV

Blog

Research Interest & Projects

Journal Publications

A Quasi-Optimal Factorization Preconditioner for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains
SIAM Journal on Numerical Analysis Vol. 60, Iss. 5 (2022)
09/2022Lambert TheisenBenjamin Stamm

Picture of the authorPicture of the authorPicture of the authorThis paper provides a provably quasi-optimal preconditioning strategy of the linear Schrödinger eigenvalue problem with periodic potentials for a possibly nonuniform spatial expansion of the domain. The quasi-optimality is achieved by having the iterative eigenvalue algorithms converge in a constant number of iterations for different domain sizes. In the analysis, we derive an analytic factorization of the spectrum and asymptotically describe it using concepts from the homogenization theory. This decomposition allows us to express the eigenpair as an easy-to-calculate cell problem solution combined with an asymptotically vanishing remainder. We then prove that the easy-to-calculate limit eigenvalue can be used in a shift-and-invert preconditioning strategy to bound the number of eigensolver iterations uniformly. Several numerical examples illustrate the effectiveness of this quasi-optimal preconditioning strategy.

Keywords: # periodic Schrödinger equation# iterative eigenvalue solvers# preconditioner# asymptotic eigenvalue analysis# factorization principle# directional homogenization
fenicsR13: A Tensorial Mixed Finite Element Solver for theLinear R13 Equations Using the FEniCS Computing Platform
ACM Trans. Math. Softw. 47, 2, Article 17 (April 2021)
04/2021Lambert TheisenManuel Torrilhon

Picture of the authorPicture of the authorPicture of the authorWe present a mixed finite element solver for the linearized regularized 13-moment equations of non-equilibrium gas dynamics. The Python implementation builds upon the software tools provided by the FEniCS computing platform. We describe a new tensorial approach utilizing the extension capabilities of FEniCS’ Unified Form Language to define required differential operators for tensors above second degree. The presented solver serves as an example for implementing tensorial variational formulations in FEniCS, for which the documentation and literature seem to be very sparse. Using the software abstraction levels provided by the Unified Form Language allows an almost one-to-one correspondence between the underlying mathematics and the resulting source code. Test cases support the correctness of the proposed method using validation with exact solutions. To justify the usage of extended gas flow models, we discuss typical application cases involving rarefaction effects. We provide the documented and validated solver publicly.

Keywords: # tensorial mixed finite element method# R13 equations# FEniCS project# continuous interior penalty

Talks

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Software

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Miscellaneous

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Theses

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Teaching

You can find most of my teaching activity in the Github repository @lamBOOO/teaching.[TODO Add all other teaching with PDF previews.]

Selected classes

Vortragsübung Höhere Mathematik 1 für Ingenieure
(global exercise higher mathematics 1 for engineers)
WS22~1000Unversity of Stuttgart

The class is about the basic concepts of linear algebra. For example:

  • logics
  • numbers, sets, inequalities
  • euclidian vectorspace
  • linear systems of equations
  • transformations and transformation groups
  • principal axis transformations
Course notesLINK
[TODO: Add all other classes from ACOM website]

Selected Projects

The tool gradescaler.com provides a graphical overveiw of exam grading schemes.[TODO: Add grammarly script, latex templates, check Git repos, ...]

Contact

E-Mail

You can contact me directly via the e-mail address Maillmbrt∂thsn.dev or Maillambert.theisen∂rwth-aachen.de preferrable using PGP encryption. My PGP key can be found on the keyserver keys.openpgp.org or you can directlty download it here using the link lt-pgpkey.asc. The corresponding sigature reads 9C32 B2D9 E59B 09C1 72AB C577 F2C2 52C0 F331 EB87.

Profiles

I am part of the major science and networking sites, for example:

Also have a look at my institute webpages:

Impressum

Applied and Computational Mathematics (ACoM)
RWTH Aachen University
Schinkelstr. 2, Room 229 (Rogowski Building, 2nd floor)
D-52062 Aachen
Germany
Office Phone: +49 241 80-98671
Mobile Phone: +49 241 80-98686

Institut für Angewandte Analysis und Numerische Simulation (IANS)
Lehrstuhl Numerische Mathematik für Höchstleistungsrechner (NMH)
Universität Stuttgart
Pfaffenwaldring 57, Raum 7.154
70569 Stuttgart
Germany
Phone: 0049 711 685 65522