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Numerical Analysis Group

Office
Kollegiengebäude Mathematik (20.30)
Room 3.002 (3rd floor)

Address
Karlsruhe Institute of Technology
Institute for Applied and Numerical Mathematics 1
Englerstr. 2
76131 Karlsruhe
Germany

Office hours:

Mon. - Fri.

9 - 12 o'clock

Mon. - Thu.

13 - 16 o'clock

Contact:

Phone: +49 721 608-42061
Fax: +49 721 608-43767
Email:na-sek@math.kit.edu

GRK1294 - Publications

The following lists contain only publications coauthored by PhD students or PostDocs of the GRK 1294.

Preprints

[1] M. Hochbruck and A. Sturm
Error analysis of a second order locally implicit method for linear Maxwell's equations
CRC-Preprint, no. 2015/1 (2015)
Preprint, Paper, BibTex

[2] M. Hochbruck and T. Pažur
Implicit Runge—Kutta methods and discontinuous Galerkin, discretizations for linear Maxwell's equations
preprint SIAM J. Numer. Anal., to appear, vol. 0000 (2014)
Preprint, Paper, BibTex

[3] A. Khrabustovskyi and M. Plum
Spectral properties of elliptic operator with double-contrast coefficients near a hyperplane
preprint (2014)
Preprint, Paper, BibTex

[4] A. Demirel, J. Niegemann, K. Busch and M. Hochbruck
Efficient Multiple Time-Stepping Algorithms of Higher Order
preprint (2014)
Preprint, Paper, BibTex

[5] M. Hochbruck and T. Pažur
Implicit Runge—Kutta methods and discontinuous Galerkin, discretizations for linear Maxwell's equations
preprint SIAM J. Numer. Anal., to appear (2014)
Preprint, Paper, BibTex

[6] A. Schneck
Constrained Hardy Space Approximation II: Numerics
(2009)
Preprint, Paper, BibTex

[7] A. Schneck
HOPT — A MATLAB Package for Constrained Optimization in Hardy Spaces
preprint (2009)
Preprint, Paper, BibTex

Papers

[1] G. Cardone and A. Khrabustovskyi
Neumann spectral problem in a domain with very corrugated boundary
Journal of Differential Equations (2015)
Preprint, Paper, BibTex

[2] P. Exner and A. Khrabustovskyi
On the spectrum of narrow Neumann waveguide with periodically distributed $\delta'$ traps
Journal of Physics A: Mathematical and Theoretical, vol. 48, no. 31 (2015)
Preprint, Paper, BibTex

[3] S. Findeisen and W. Dörfler
Numerical optimization of a waveguide transition using finite element beam propagation
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields (published online Apr 3, 2014), vol. 28, no. 2, pp. 201—212 (2015)
Preprint, Paper, BibTex

[4] M. Hochbruck, T. Pažur, A. Schulz, E. Thawinan and C. Wieners
Efficient time integration for discontinuous Galerkin approximations of linear wave equations
ZAMM, vol. 95, no. 3, pp. 237—259 (2015)
Preprint, Paper, BibTex

[5] A. Khrabustovskyi and E. Khruslov
Gaps in the spectrum of the Neumann Laplacian generated by a system of periodically distributed trap
Math. Meth. Appl. Sci., vol. 38, pp. 11-26 (2015)
Preprint, Paper, BibTex

[6] V. Hoang and M. Radosz
Absence of bound states for waveguides in 2D periodic structures
J. Math. Phys., vol. 55, pp. 033506 (2014)
Preprint, Paper, BibTex

[7] M. Hochbruck, T. Jahnke, and R. Schnaubelt
Convergence of an ADI splitting for Maxwell's equations
Numer. Math. online first, vol. 0000 (2014)
Preprint, Paper, BibTex

[8] P. J. McKenna, W. Reichel, and A. Verbitsky
Mesh-independent a priori bounds for nonlinear elliptic finite difference boundary value problems
J. Math. Anal. Appl., vol. 419, no. 1, pp. 496—524 (2014)
Preprint, Paper, BibTex

[9] J. Ott
Domain Optimization for an Acoustic Waveguide Scattering Problem
Applied Mathematics & Optimization, vol. 0000, pp. 1-46 (2014)
Preprint, Paper, BibTex

[10] A. Khrabustovskyi
Opening up and control of spectral gaps of the Laplacian in periodic domains
Journal of Mathematical Physics, vol. 55 (2014)
Preprint, Paper, BibTex

[11] T. Arens, K. Sandfort and S. Schmitt
Analysing Ewald's Method for the Evaluation of Green's Functions for Periodic Media
IMA J. Appl. Math., vol. 78, pp. 405—431 (2013)
Preprint, Paper, BibTex

[12] M. Bürg
Convergence of an Automatic $hp$-Adaptive Finite Element Strategy for Maxwell's Equations.
Appl. Numer. Math., vol. 72, pp. 188—206 (2013)
Preprint, Paper, BibTex

[13] T. Dohnal and W. Dörfler
Coupled mode equations modeling for out-of-plane gap solitons in 2D photonic crystals
SIAM Multiscale Model. Simul., vol. 11, pp. 162—191 (2013)
Preprint, Paper, BibTex

[14] T. Dohnal, K. Nagatou, M. Plum and W. Reichel
Interfaces Supporting Surface Gap Soliton Ground States in the 1D Nonlinear Schrödinger Equation
J. Math. Anal. Appl., vol. 407, pp. 425—435 (2013)
Preprint, Paper, BibTex

[15] R. Mandel and W. Reichel
Distributional solutions of the stationary nonlinear Schrödinger equation: singularities, regularity and exponential decay
ZAA, vol. 32, pp. 55—82 (2013)
Preprint, Paper, BibTex

[16] C. Wieners and J. Xin
Boundary element approximation for Maxwell's eigenvalue problem
Math. Methods Appl. Sci., vol. 36, pp. 2524—2539 (2013)
Preprint, Paper, BibTex

[17] T. Dohnal and D. Pelinovsky
Vortex families near a spectral edge in the Gross-Pitaevskii equation with a two-dimensional periodic potential
Phys. Rev. E, vol. 85, pp. 026605 (2012)
Preprint, Paper, BibTex

[18] C. Blank, M. Chirilus-Bruckner, V. Lescarret and G. Schneider
Breather solutions in periodic media
Comm. Math. Phys., vol. 302, pp. 815—841 (2011)
Preprint, Paper, BibTex

[19] E. Blank and T. Dohnal
Families of Surface Gap Solitons and their Stability via the Numerical Evans Function Method
SIAM J. Appl. Dyn. Syst., vol. 10, pp. 667—706 (2011)
Preprint, Paper, BibTex

[20] M. Bürg
An $hp$-Efficient Residual-Based A Posteriori Error Estimator for Maxwell's Equations
Proc. Appl. Math. Mech., vol. 11, pp. 869—870 (2011)
Preprint, Paper, BibTex

[21] M. Bürg and W. Dörfler
Convergence of an adaptive $hp$ finite element strategy in higher space-dimensions
Appl. Numer. Math., vol. 61, pp. 1132—1146 (2011)
Preprint, Paper, BibTex

[22] C. Chong and D. E. Pelinovsky
Variational approximations of bifurcations of asymmetric solitons in cubic-quintic nonlinear Schrödinger lattices
Discrete and Continuous Dynamical Systems, Series S, vol. 4, pp. 1019—1031 (2011)
Preprint, Paper, BibTex

[23] T. Dohnal, M. Plum and W. Reichel
Surface gap soliton ground states for the nonlinear Schrödinger equation
Comm. Math. Phys., vol. 308, pp. 511—542 (2011)
Preprint, Paper, BibTex

[24] K. R. Hiremath, J. Niegeman and K. Busch
Analysis of light propagation in slotted resonator based systems via coupled-mode theory
Opt. Express, vol. 19, pp. 8641—8655 (2011)
Preprint, Paper, BibTex

[25] V. Hoang
The Limiting Absorption Principle in a semi-infinite periodic waveguide
SIAM J. Appl. Math., vol. 71, pp. 791—810 (2011)
Preprint, Paper, BibTex

[26] A. Lechleiter
Imaging of Periodic Dielectrics
BIT Numerical Mathematics, vol. 50, pp. 59—83 (2010)
Preprint, Paper, BibTex

[27] V. Lescarret
Intermediate model for spatial evolution in nonlinear optics
Math. Models Methods Appl. Sci., vol. 20, pp. 1209—1249 (2010)
Preprint, Paper, BibTex

[28] A. Schneck
Constrained Hardy Space Approximation
J. Approx. Theory, vol. 162, pp. 1466—1483 (2010)
Preprint, Paper, BibTex

[29] T. Arens and A. Lechleiter
The Linear Sampling Method Revisited
J. Int. Eq. Appl., vol. 21, pp. 179—202 (2009)
Preprint, Paper, BibTex

[30] T. Arens, A. Lechleiter and D. R. Luke
MUSIC for Extended Scatterers as an Instance of the Factorization Method
SIAM J. Appl. Math., vol. 70, pp. 1283—1304 (2009)
Preprint, Paper, BibTex

[31] C. Chong, R. Carretero-González and B. A. Malomed and P. G. Kevrekidis
Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices
Physica D, vol. 238, pp. 126—136 (2009)
Preprint, Paper, BibTex

[32] T. Dohnal
Perfectly Matched Layers for Coupled Nonlinear Schrödinger Equations with Mixed Derivatives
J. Comput. Phys., vol. 228, pp. 8752—8765 (2009)
Preprint, Paper, BibTex

[33] T. Dohnal, D. Pelinovsky and G. Schneider
Coupled-mode equations and gap solitons for a two-dimensional nonlinear elliptic problem with a separable periodic potential
J. Nonlin. Sci., vol. 19, pp. 95—131 (2009)
Preprint, Paper, BibTex

[34] T. Dohnal, M. Plum and W. Reichel
Localized Modes of the Linear Periodic Schrödinger Operator with a Nonlocal Perturbation
SIAM J. Math. Anal., vol. 41, pp. 1967—1993 (2009)
Preprint, Paper, BibTex

[35] T. Dohnal and H. Uecker
Coupled Mode Equations and Gap Solitons for the 2D Gross-Pitaevskii equation with a non-separable periodic potential
Physica D, vol. 238, pp. 860—879 (2009)
Preprint, Paper, BibTex

[36] C. Engström, C. Hafner and K. Schmidt
Computations of lossy Bloch waves in two-dimensional photonic crystals
J. Comput. Theor. Nanosci., vol. 6, pp. 775—783 (2009)
Preprint, Paper, BibTex

[37] C. Engström and M. Richter
On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials
SIAM J. Appl. Math., vol. 70, pp. 231—247 (2009)
Preprint, Paper, BibTex

[38] V. Hoang, M. Plum and C. Wieners
A computer-assisted proof for photonic band gaps
Z. Angew. Math. Phys., vol. 60, pp. 1035—1052 (2009)
Preprint, Paper, BibTex

[39] A. Kirsch and A. Lechleiter
The operator equations of Lippmann-Schwinger type for acoustic and electromagnetic scattering problems in $L^2$
Appl. Anal., vol. 88, pp. 807—830 (2009)
Preprint, Paper, BibTex

[40] A. Lechleiter
The factorization method is independent of transmission eigenvalues
Inv. Prob. Imag., vol. 3, pp. 123—138 (2009)
Preprint, Paper, BibTex

[41] V. Lescarret, C. Blank, M. Chirilus-Bruckner and C. Chong and G. Schneider
Standing generalized modulating pulse solutions for a nonlinear wave equation in periodic media
Nonlinearity, vol. 22, pp. 1869—1898 (2009)
Preprint, Paper, BibTex

[42] A. Peleg, Y. Chung, T. Dohnal and Q. M. Nguyen
Diverging probability density functions for flat-top solitary waves
Phys. Rev. E, vol. 80, pp. 026602 (2009)
Preprint, Paper, BibTex

[43] M. Brown, V. Hoang, M. Plum and I. Wood
On Spectral Bounds for Photonic Crystal Waveguides
in Inequalities and Applications , edited by C. Bandle, A. Gilanyi, L. Losonczi, Z. Pales and M. Plum , International Series of Numerical Mathematics , vol. 157 pp. 23—30 (2009)
Preprint, Paper, BibTex

[44] T. Arens, D. Gintides and A. Lechleiter
Variational Formulations for Scattering in a Three-Dimensional Acoustic Waveguide
Math. Meth. Appl. Sci., vol. 31, pp. 821—847 (2008)
Preprint, Paper, BibTex

[45] C. Blank, M. Chirilus-Bruckner, C. Chong, V. Lescarret, G. Schneider and H. Uecker
A remark about the justification of the nonlinear Schrödinger equation in quadratic spatially periodic media
ZAMP, vol. 59, pp. 554—557 (2008)
Preprint, Paper, BibTex

[46] M. Chirilus-Bruckner, C. Chong, G. Schneider and H. Uecker
Seperation of internal and interaction dynamics for NLS-described wave packets with different carrier waves
J. Math. Anal. Appl., vol. 347, pp. 304—314 (2008)
Preprint, Paper, BibTex

[47] A. Lechleiter and A. Rieder
Newton regularizations for impedance tomography: Convergence by local injectivity
Inverse Probl., vol. 24, pp. 065009 (2008)
Preprint, Paper, BibTex

[48] M. Chirilus-Bruckner, G. Schneider and H. Uecker
On the interaction of NLS-described modulating pulses with different carrier waves
Math. Meth. Appl. Sci., vol. 30, pp. 1965—1978 (2007)
Preprint, Paper, BibTex

[49] A. Lechleiter, N. Hyvönen and H. Hakula
The Factorization Method Applied to the Complete Electrode Model of Impedance Tomography
SIAM J. Appl. Math., vol. 68, pp. 1097—1121 (2007)
Preprint, Paper, BibTex

[50] A. Rieder and A. Schneck
Optimality of the fully discrete filtered backprojection algorithm for tomographic inversion
Numer. Math., vol. 108, pp. 151—175 (2007)
Preprint, Paper, BibTex

[51] A. Lechleiter, N. Hyvönen and H. Hakula
Regularization of the factorization method and an application in impedance tomography
in Inverse Problems in Wave Scattering , Oberwolfach Reports , vol. 13 pp. 14—16 (2007)
Preprint, Paper, BibTex

[52] R. Carretero-Gonzáles, J. D. Talley and C. Chong and B. A. Malomed
Multistable solitons in the cubic-quintic discrete nonlinear Schrödinger equation
Physica D, vol. 216, pp. 77—89 (2006)
Preprint, Paper, BibTex

[53] A. Lechleiter
A regularization technique for the factorization method
Inverse Probl., vol. 22, pp. 1605—1625 (2006)
Preprint, Paper, BibTex

[54] A. Lechleiter and A. Rieder
Newton regularizations for impedance tomography: A numerical study
Inverse Probl., vol. 22, pp. 1967—1987 (2006)
Preprint, Paper, BibTex

PhD thesis

[1] A. Demirel
Eine flexible Klasse von local time stepping Verfahren
Karlsruhe Institute of Technology (2014)
Preprint, Paper, BibTex

[2] D. Müller
Well-posedness for a general class of quasilinear evolution equations with applications to Maxwell's equations
Karlsruhe Institute of Technology (2014)
Preprint, Paper, BibTex

[3] A. Verbitsky
Positive Solutions for the Discrete Nonlinear Schrödinger Equation: A Priori Estimates and Convergence
Karlsruhe Institute of Technology (2014)
Preprint, Paper, BibTex

[4] B. Anić
The Fourier-Galerkin Method for Band Structure Computations of 2D and 3D Photonic Crystals
Karlsruhe Institute of Technology (2013)
Preprint, Paper, BibTex

[5] B. Barth
The Bloch Transform on $L^p$-Spaces
Karlsruhe Institute of Technology (2013)
Preprint, Paper, BibTex

[6] E. Blank
Die unstetige Galerkinmethode für die Maxwell-Gleichungen: Anwendung auf Rotationskörper und Kerr-Nichtlinearitäten
Karlsruhe Institute of Technology (2013)
Preprint, Paper, BibTex

[7] H. J. Freisinger
Grenzflächenprobleme bei der nichtlinearen Schrödingergleichung
Karlsruhe Institute of Technology (2013)
Preprint, Paper, BibTex

[8] H. Gerner
Stetige Galerkinverfahren für zeitabhängige Maxwellgleichungen mit Kerr-Nichtlinearität
Karlsruhe Institute of Technology (2013)
Preprint, Paper, BibTex

[9] R. Mandel
Grundzustände, Verzweigungen und singuläre Lösungen nichtlinearer Schrödingersysteme
Karlsruhe Institute of Technology (2013)
Preprint, Paper, BibTex

[10] T. Pažur
Error analysis of implicit and exponential time integration of linear Maxwell's equations
Karlsruhe Institute of Technology (2013)
Preprint, Paper, BibTex

[11] P. Schmalkoke
On the Spectral Properties of Dispersive Photonic Crystals
Karlsruhe Institute of Technology (2013)
Preprint, Paper, BibTex

[12] M. Bürg
A Fully Automatic $hp$-Adaptive Refinement Strategy
Karlsruhe Institute of Technology (2012)
Preprint, Paper, BibTex

[13] S. Ronnas
$hp$-FEM for Two-component Flows with Applications in Optofluidics
Karlsruhe Institute of Technology (2012)
Preprint, Paper, BibTex

[14] T. Bulovyatova
Numerical methods of localization of Wannier Functions in the modeling of Photonic Crystals
Karlsruhe Institute of Technology (2011)
Preprint, Paper, BibTex

[15] A. Krämer
Adaptivity in Bandstructure Calculations of Photonic Crystals
Karlsruhe Institute of Technology (2011)
Preprint, Paper, BibTex

[16] H. Li
Numerical Simulation of a Micro-ring Resonator with Adaptive Wavelet Collocation Method
Karlsruhe Institute of Technology (2011)
Preprint, Paper, BibTex

[17] M. Reimers
Nichtlineare photonische Kristalle: Computerunterstützter Beweis einer spektralen Bandlücke
Karlsruhe Institute of Technology (2011)
Preprint, Paper, BibTex

[18] J. Xin
Boundary Element Approximation for Maxwell's Eigenvalue Problem
Karlsruhe Institute of Technology (2011)
Preprint, Paper, BibTex

[19] C. Blank
On the Existence of Breathers Solutions in non-linear Klein-Gordon equations with periodic coefficients
Karlsruhe Institute of Technology (2010)
Preprint, Paper, BibTex

[20] A. Bulovyatov
Parallel multigrid methods for the band structure computation of 3D photonic crystals with higher order finite elements
Karlsruhe Institute of Technology (2010)
Preprint, Paper, BibTex

[21] T. Gauss
Floquet Theory for a Class of Periodic Evolution Equations in an $L_p$-Setting
Karlsruhe Institute of Technology (2010)
Preprint, Paper, BibTex

[22] M. Radosz
The Principles of Limit Absorption and Limit Amplitude for Periodic Operators
Karlsruhe Institute of Technology (2010)
Preprint, Paper, BibTex

[23] M. Richter
Optimization of photonic band structures
Karlsruhe Institute of Technology (2010)
Preprint, Paper, BibTex

[24] K. Sandfort
The factorization method for inverse scattering from periodic inhomogeneous media
Karlsruhe Institute of Technology (2010)
Preprint, Paper, BibTex

[25] M. Chirilus-Bruckner
Nonlinear Interaction of Pulses
Karlsruhe Institute of Technology (2009)
Preprint, Paper, BibTex

[26] C. Chong
Modeling optical technologies with continuous and discrete Nonlinear Schrödinger equations
Karlsruhe Institute of Technology (2009)
Preprint, Paper, BibTex

[27] A. Schneck
Bounds for optimization of the reflection coefficient by constrained optimization in Hardy spaces
Karlsruhe Institute of Technology (2009)
Preprint, Paper, BibTex

[28] A. Lechleiter
Factorization methods for photonics and rough surfaces
Karlsruhe Institute of Technology (2008)
Preprint, Paper, BibTex