Publications and Preprints


Submitted

Wei Li, Robert Lipton, Matthias Maier
Lorentz Resonance in the Homogenization of Plasmonic Crystals
submitted, 2020
(arXiv preprint)


Journal publications

Matthias Maier, Martin Kronbichler
Efficient parallel 3D computation of the compressible Euler equations with an invariant-domain preserving second-order finite-element scheme
ACM Transactions on Parallel Computing, accepted, 2021
(arXiv preprint)

Jean-Luc Guermond, Matthias Maier, Bojan Popov, Ignacio Tomas
Second-order invariant domain preserving approximation of the compressible Navier--Stokes equations
Computer Methods in Applied Mechanics and Engineering, Vol. 375, 2021
(arXiv preprint) DOI 10.1016/j.cma.2020.113608

Daniel Arndt, Wolfgang Bangerth, Denis Davydov, Timo Heister, Luca Heltai, Martin Kronbichler, Matthias Maier, Jean-Paul Pelteret, Bruno Turcksin, David Wells
The deal.II finite element library: design, features, and insights
Computers and Mathematics with Applications, Vol. 81, 2021
(arXiv preprint) 10.1016/j.camwa.2020.02.022

Jung Heon Song, Matthias Maier, Mitchell Luskin
Nonlinear eigenvalue problems for coupled Helmholtz equations modeling gradient-index graphene waveguides
Journal of Computational Physics, Vol. 423, 2020
(arXiv preprint) DOI 10.1016/j.jcp.2020.109871

Matthias Maier, Mitchell Luskin, Dionisios Margetis
Finite-size effects in wave transmission through plasmonic crystals: A tale of two scales
Physical Review B, Vol. 102, 2020
(arXiv preprint) DOI 10.1103/PhysRevB.102.075308

Daniel Arndt, Wolfgang Bangerth, Bruno Blais, Thomas C. Clevenger, Marc Fehling, Alexander V. Grayver, Timo Heister, Luca Heltai, Martin Kronbichler, Peter Munch, Matthias Maier, Jean-Paul Pelteret, Reza Rastak, Bruno Turcksin, Zhuoran Wang, David Wells
The deal.II Library, Version 9.2
Journal of Numerical Mathematics, Vol. 28, 2020
(preprint) DOI 10.1515/jnma-2020-0043

Matthias Maier, Dionisios Margetis, Antoine Mellet
Homogenization of time-harmonic Maxwell's equations in nonhomogeneous plasmonic structures
Journal of Computational and Applied Mathematics, Vol. 377, 2020
(arXiv preprint) DOI 10.1016/j.cam.2020.112909

Dionisios Margetis, Matthias Maier, Tobias Stauber, Tony Low, Mitchell Luskin
Nonretarded edge plasmon-polaritons in anisotropic two-dimensional materials
Journal of Physics A: Mathematical and Theoretical, Vol. 53, 2020
(arXiv preprint) DOI 10.1088/1751-8121/ab5ff9

Matthias Maier, Marios Mattheakis, Efthimios Kaxiras, Mitchell Luskin, Dionisios Margetis
Homogenization of plasmonic crystals: Seeking the epsilon-near-zero effect
Proceedings of the Royal Society of London A, Vol. 475, 2019
(arXiv preprint) DOI 10.1098/rspa.2019.0220

Marios Mattheakis, Matthias Maier, Wei Xi Boo, Efthimios Kaxiras
Graphene epsilon-near-zero plasmonic crystals
Proceedings of the Sixth Annual ACM International Conference on Nanoscale Computing and Communication, NANOCOM '19, 2019
(arXiv preprint) DOI 10.1145/3345312.3345496

Daniel Arndt, Wolfgang Bangerth, Thomas C. Clevenger, Denis Davydov, Marc Fehling, Daniel Garcia-Sanchez, Graham Harper, Timo Heister, Luca Heltai, Martin Kronbichler, Ross Maguire Kynch, Matthias Maier, Jean-Paul Pelteret, Bruno Turcksin, David Wells
The deal.II Library, Version 9.1
Journal of Numerical Mathematics, Vol. 27, 2019
(preprint) DOI 10.1515/jnma-2019-0064

Jung Heon Song, Matthias Maier, Mitchell Luskin
Adaptive finite element simulations of waveguide configurations involving parallel 2D material sheets
Computer Methods in Applied Mechanics and Engineering, Vol. 351, 2019
(arXiv preprint) DOI 10.1016/j.cma.2019.03.039

Giovanni Alzetta, Daniel Arndt, Wolfgang Bangerth, Vishal Boddu, Benjamin Brands, Denis Davydov, Rene Gassmöller, Timo Heister, Luca Heltai, Katharina Kormann, Martin Kronbichler, Matthias Maier, Jean-Paul Pelteret, Bruno Turcksin, David Wells
The deal.II Library, Version 9.0
Journal of Numerical Mathematics, Vol. 26, 2018
(preprint) DOI 10.1515/jnma-2018-0054

Matthias Maier, Dionisios Margetis, Mitchell Luskin
Generation of surface plasmon-polaritons by edge effects
Communications in Mathematical Sciences, Vol. 16, 2018
(arXiv preprint) DOI 10.4310/CMS.2018.v16.n1.a4

Matthias Maier, Rolf Rannacher
A duality-based optimization approach for model adaptivity in heterogeneous multiscale problems
SIAM Multiscale Modeling and Simulation, Vol. 16, 2018
(arXiv preprint) DOI 10.1137/16M1105670

Matthias Maier, Andrei Nemilentsau, Tony Low, Mitchell Luskin
Ultracompact amplitude modulator by coupling hyperbolic polaritons over a graphene-covered gap
ACS Photonics, Vol. 5, 2018
(arXiv preprint) DOI 10.1021/acsphotonics.7b01094

Matthias Maier, Marios Mattheakis, Efthimios Kaxiras, Mitchell Luskin, Dionisios Margetis
Universal behavior of dispersive Dirac cone in gradient-index plasmonic metamaterials
Physical Review B, Vol. 97, 2018
(arXiv preprint) DOI 10.1103/PhysRevB.97.035307

Dionisios Margetis, Matthias Maier, Mitchell Luskin
On the Wiener-Hopf method for surface plasmons: Diffraction from semi-infinite metamaterial sheet
Studies in Applied Mathematics, Vol. 139, 2017
(arXiv preprint) DOI 10.1111/sapm.12180

Daniel Arndt, Wolfgang Bangerth, Denis Davydov, Timo Heister, Luca Heltai, Martin Kronbichler, Matthias Maier, Jean-Paul Pelteret, Bruno Turcksin, David Wells
The deal.II Library, Version 8.5
Journal of Numerical Mathematics, Vol. 25, 2017
(preprint) DOI 10.1515/jnma-2017-0058

Matthias Maier, Dionisios Margetis, Mitchell Luskin
Dipole excitation of surface plasmon on a conducting sheet: finite element approximation and validation
Journal of Computational Physics, Vol. 339, 2017
(arXiv preprint) DOI 10.1016/j.jcp.2017.03.014

Matthias Maier, Rolf Rannacher
Duality-based adaptivity in finite element discretization of heterogeneous multiscale problems
Journal of Numerical Mathematics, Vol. 24, 2016
(preprint) DOI 10.1515/jnma-2014-0074

Matthias Maier, Mauro Bardelloni, Luca Heltai
LinearOperator - A generic, high-level expression syntax for linear algebra
Computers and Mathematics with Applications, Vol. 72, 2016
(preprint) DOI 10.1016/j.camwa.2016.04.024

Wolfgang Bangerth, Denis Davydov, Timo Heister, Luca Heltai, Guido Kanschat, Martin Kronbichler, Matthias Maier, Bruno Turcksin, David Wells
The deal.II Library, Version 8.4
Journal of Numerical Mathematics, Vol. 24, 2016
(preprint) DOI 10.1515/jnma-2016-1045

Wolfgang Bangerth, Timo Heister, Luca Heltai, Guido Kanschat, Martin Kronbichler, Matthias Maier, Bruno Turcksin
The deal.II Library, Version 8.3
Archive of Numerical Software, Vol. 4, 2016
(preprint) DOI 10.11588/ans.2016.100.23122

Wolfgang Bangerth, Timo Heister, Luca Heltai, Guido Kanschat, Martin Kronbichler, Matthias Maier, Bruno Turcksin, Toby D. Young
The deal.II Library, Version 8.2
Archive of Numerical Software, Vol. 3, 2015
(preprint) DOI 10.11588/ans.2015.100.18031


Preprints and Software

Matthias Maier, Martin Kronbichler
Ryujin: High-performance second-order colocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes
DOI 10.5281/zenodo.3924365 , 2020

Matthias Maier, Ignacio Tomas
deal.II step-69: A first-order hydrodynamics code for the compressible Euler equations
DOI 10.5281/zenodo.3634929 , 2020

Martin Licht, Matthias Maier
Flux Reconstruction for Goal-Oriented A Posteriori Error Estimation
arXiv preprint, 2017

Matthias Maier, Mauro Bardelloni, Luca Heltai
LinearOperator Benchmarks, Version 1.0.0
DOI 10.5281/zenodo.47202 , 2016

Wolfgang Bangerth, Timo Heister, Luca Heltai, Guido Kanschat, Martin Kronbichler, Matthias Maier, Bruno Turcksin, Toby D. Young
The deal.II Library, Version 8.1
arXiv preprint, 2013

Wolfgang Bangerth, Timo Heister, Luca Heltai, Guido Kanschat, Martin Kronbichler, Matthias Maier, Bruno Turcksin, Toby D. Young
The deal.II Library, Version 8.0
arXiv preprint, 2013


Theses

Matthias Maier
Duality-based adaptivity of model and discretization in multiscale finite-element methods
Doctoral Thesis, Ruprecht-Karls-Universität Heidelberg, 2015
urn:nbn:de:bsz:16-heidok-188898

Matthias Maier
Simulation von Grenzschichtströmungen über Ribletstrukturen
Diplom Thesis, Ruprecht-Karls-Universität Heidelberg, 2011
pdf (in German)