Jean-Luc Guermond, Matthias Maier, Eric J. Tovar
A high-order explicit Runge-Kutta approximation technique for the
Shallow Water Equations
Submitted, 2024
Matthias Maier, Dennis Corraliza-Rodriguez, Dionisios Margetis
Dyakonov-Shur instability of electronic fluid: Spectral effect of
weak magnetic field
Submitted, 2024
(arXiv preprint)
Martin Kronbichler, Matthias Maier, Ignacio Tomas
Graph-based methods for hyperbolic systems of conservation laws using
discontinuous space discretizations, Part I: building blocks
Submitted, 2024
(arXiv preprint)
Jean-Luc Guermond, Matthias Maier, Bojan Popov, Laura Saavedra, Ignacio Tomas
Greedy invariant-domain preserving approximation for hyperbolic systems
Submitted, 2023
(arXiv preprint)
Manaswinee Bezbaruah, Matthias Maier, Winnifried Wollner
Shape optimization of optical microscale inclusions
SIAM Journal on Scientific Computing, accepted, 2024
(arXiv preprint)
Daniel Arndt, Wolfgang Bangerth, Maximilian Bergbauer, Marco Feder,
Marc Fehling, Johannes Heinz, Timo Heister, Luca Heltai, Martin
Kronbichler, Matthias Maier, Peter Munch, Jean-Paul Pelteret, Bruno
Turcksin, David Wells, Stefano Zampini
The deal.II Library, Version 9.5
Journal of Numerical Mathematics, Vol. 31, 2023
(preprint)
DOI 10.1515/jnma-2023-0089
Matthias Maier, John Shadid, Ignacio Tomas
Structure-preserving finite-element schemes for the Euler-Poisson equations
Communications in Computational Physics, Vol. 33, 2023
(arXiv preprint)
DOI 10.4208/cicp.OA-2022-0205
Bennett Clayton, Jean-Luc Guermond, Matthias Maier, Bojan Popov, Eric J. Tovar
Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state
Journal of Computational Physics, Vol. 478, 2023
arXiv preprint)
DOI 10.1016/j.jcp.2023.111926
Daniel Arndt, Wolfgang Bangerth, Marco Feder, Marc Fehling, Rene Gassmöller, Timo Heister,
Luca Heltai, Martin Kronbichler, Matthias Maier, Peter Munch, Jean-Paul Pelteret, Simon Sticko,
Bruno Turcksin, David Wells
The deal.II Library, Version 9.4
Journal of Numerical Mathematics, Vol. 30, 2022
(preprint)
DOI 10.1515/jnma-2022-0054
Jean-Luc Guermond, Martin Kronbichler, Matthias Maier, Bojan Popov, Ignacio Tomas
On the implementation of a robust and efficient finite element-based
parallel solver for the compressible Navier-Stokes equations
Computer Methods in Applied Mechanics and Engineering, Vol. 389, 2022
(arXiv preprint)
DOI
10.1016/j.cma.2021.114250
Wei Li, Robert Lipton, Matthias Maier
Lorentz Resonance in the Homogenization of Plasmonic Crystals
Proceedings of the Royal Society of London A, Vol. 477, 2021
(arXiv preprint)
DOI 10.1098/rspa.2021.0609
Daniel Arndt, Wolfgang Bangerth, Bruno Blais, Marc Fehling, Rene
Gassmöller, Timo Heister, Luca Heltai, Uwe Köcher, Martin Kronbichler,
Matthias Maier, Peter Munch, Jean-Paul Pelteret, Sebastian Proell, Konrad
Simon and Bruno Turcksin, David Wells, Jiaqi Zhang
The deal.II Library, Version 9.3
Journal of Numerical Mathematics, Vol. 29, 2021
(preprint)
DOI 10.1515/jnma-2021-0081
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, Vol. 8, 2021
(arXiv preprint)
DOI 10.1145/3470637
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
Manaswinee Bezbaruah, Matthias Maier, Winnifried Wollner
InverseHomogenization: shape optimization for optical metamaterials
with low-dimensional interfaces
DOI 10.5281/zenodo.10459309
, 2024
Ignacio Tomas, John Shadid, Matthias Maier, Abner Salgado
Final report of activities for the LDRD-CIS project 226834 titled:
Asymptotic preserving methods for fluid electron-fluid models in the
large magnetic field limit with mathematically guaranteed
properties
Sandia National Laboratory, 2022
(preprint)
DOI
10.2172/1872178
Manaswinee Bezbaruah, Matthias Maier
deal.II step-81: A time-harmonic Maxwell solver for lower-dimensional inclusions
DOI 10.5281/zenodo.7268246
, 2022
Ignacio Tomas, John Shadid, Michael Crockatt, Roger Pawlowski, Matthias Maier, Jean-Luc Guermond
Final report of activities for the LDRD-express project 223796 titled: Fluid models of charged species transport: numerical methods with mathematically guaranteed properties
Sandia National Laboratory, 2021
(preprint)
DOI
10.2172/1822320
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
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)