EPFL SB MATH-GE
Martin Licht
MA A1 364, Bât. MA
Station 8
1015 Lausanne
Switzerland
martin.licht [at] epfl [dot] ch
https://martinlicht.github.io
PUBLISHED OR ACCEPTED
Complexes of discrete distributional differential forms and their homology theory, Found Comput Math (2017) 17: 1085-1122. [Arxiv] [Journal]
Smoothed projections over weakly Lipschitz domains. Math. Comp. 88 (315), 179-210 [Arxiv] [Journal]
Smoothed projections and mixed boundary conditions. Math. Comp. 88 (316), 607-635 [Arxiv] [Journal]
Poincaré-Friedrichs inequalities for complexes of distributional differential forms. With Snorre Christiansen. Bit Numer Math 60, 345-371. [Journal]
A divergence-conforming finite element method for the surface Stokes equation. With Andrea Bonito and Alan Demlow. SIAM J. Numer. Anal., 58(5), 2764–2798. [Arxiv] [Journal]
Local finite element approximation of Sobolev differential forms. With Michael Holst and Evan Gawlik. Submitted. [Arxiv]
On basis constructions in finite element exterior calculus. Adv Comput Math 48, 14 (2022) [Arxiv]
Symmetry and invariant bases in finite element exterior calculus.
Found Comput Math. (2023) [Arxiv] [Journal]
Geometric transformation of finite element methods: theory and applications.
With Michael Holst. Applied Numerical Mathematics 192, 389-413. [Arxiv] [Journal]
Higher-order chain rules for tensor fields, generalized Bell polynomials, and estimates in Sobolev-Slobodeckij and bounded variation spaces. Journal of Mathematical Analysis and Applications 534 (1). [Arxiv] [Journal]
On Lipschitz partitions of unity and the Assouad–Nagata dimension
Topology and its Applications 348. [Arxiv] [Journal]
PREPRINT
Averaging-based local projections in finite element exterior calculus. Submitted. [Arxiv]
Constructing collars in paracompact spaces and Lipschitz estimates in metric spaces
Submitted. [Arxiv]
Newest vertex bisection over general triangulations. With Michael Holst and Zhao Lyu. Submitted. [Download]
Higher-order finite element de Rham complexes, partially localized flux reconstructions, and applications. Submitted. [Download]
Finite Element Methods for Linear Maxwell's Equations in Bianisotropic Media Permitting Polarization Fields and Magnetic Currents. With Tharindu Fernando and Michael Holst. Submitted. [Arxiv]
THESES AND OTHER WORK
On the A Priori and A Posteriori Error Analysis in Finite Element Exterior Calculus. PhD Thesis. [Download]
Smoothed Analysis of Linear Programming. Diplom thesis in Computer Science. [Download]
Discrete distributional differential forms and their applications. Diplom thesis in Mathematics.
Domain Distribution for parallel Modeling of Root Water Uptake. Proceedings 2010, JSC Guest Student Programme on Scientific Computing, 2010. [Link]
Finite element methods, Finite element exterior calculus
Structure-preserving numerical methods for partial differential equations
Partial differential equations over manifolds, geometric analysis
Numerical linear algebra
Algorithms and approximation theory of artificial neural networks
Numerical Methods for Conservation Laws — EPFL, Math-459, Winter Semester 2023
Analysis III (for Life Sciences and Microtechnology) — EPFL, Math-202(c), Winter Semester 2023
Numerical Approximation for Partial Differential Equations, Math-451, Summer Semester 2022
Numerical Methods for Conservation Laws — EPFL, MATH-459, Winter Semester 2022
Analysis IV (for Life Sciences and Microtechnology) — EPFL, MATH-207, Summer Semester 2022
Numerical Methods for Conservation Laws — EPFL, MATH-459, Winter Semester 2021
Numerical Methods for Partial Differential Equations — UCSD, MATH175/275, Spring Quarter 2021
Numerical Methods for Physical Modeling — UCSD, MATH174/274, Winter Quarter 2021
Calculus for Science and Engineering II — UCSD, MATH20B, Winter Quarter 2021
Introduction to Numerical Analysis: Ordinary Differential Equations — UCSD, MATH170C, Spring 2020
Linear Algebra — UCSD, MATH18, Spring 2020
Introduction to Numerical Analysis: Approximation and Nonlinear Equations — UCSD, MATH170B, Spring 2020
Linear Algebra — UCSD, MATH18, Winter 2020
Introduction to Numerical Analysis: Linear Algebra — UCSD, MATH170A, Winter Quarter 2019
Introduction to Numerical Analysis: Approximation and Nonlinear Equations — UCSD, MATH170B, Winter Quarter 2019
Numerical Linear Algebra — UCSD, MATH270A, Fall Quarter 2018
Calculus III — UCSD, MATH10C, Spring Quarter 2018
Mathematical Reasoning — UCSD, MATH 109, Winter Quarter 2018
Applied Linear Algebra — UCSD, MATH 102, Fall Quarter 2017