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Submitted Articles

  1. A splitting-based KPIK method for eddy current optimal control problems in an all-at-once approach, Min-Li Zeng, Martin Stoll, Submitted 2024

  2. Efficient training of Gaussian processes with tensor product structure, Josie Koenig, Max Pfeffer, Martin Stoll, Submitted 2023

  3. A Preconditioned Interior Point Method for Support Vector Machines Using an ANOVA-Decomposition and NFFT-Based Matrix-Vector Products, Theresa Wagner, John Pearson, Martin Stoll, Submitted 2023

  4. A nonlinear spectral core-periphery detection method for multiplex networks, Kai Bergermann, Martin Stoll, Francesco Tudisco, Submitted 2023

  5. Uncertainty Propagation of Initial Conditions in Thermal Models, Alexandra Bünger, Roland Herzog, Andreas Naumann, Martin Stoll, Submitted 2023

  6. A weighted subspace exponential kernel for support tensor machines,Kirandeep Kour, Sergey Dolgov, Peter Benner, Martin Stoll, Max Pfeffer, Submitted 2023

  7. A comparison of PINN approaches for drift-diffusion equations on metric graphs, Jan Blechschmidt, Jan-Frederik Pietschman, Tom-Christian Riemer, Martin Stoll, Max Winkler, Submitted 2022

  8. A low-rank tensor method to reconstruct sparse initial states for PDEs with Isogeometric Analysis, Alexandra Buenger, Martin Stoll, Submitted 2021

Peer-Reviewed Publications

  1. Second-order Partial Outer Convexification for Switched Dynamical Systems,Christoph Plate, Sebastian Sager, Martin Stoll, Manuel Tetschke, IEEE Transactions on Automatic Control. 2024

  2. Adaptive rational Krylov methods for exponential Runge--Kutta integrators, Kai Bergermann, Martin Stoll, SIAM Journal on Matrix Analysis and Applications, 2024

  3. Gibbs-Helmholtz Graph Neural Network: capturing the temperature dependency of activity coefficients at infinite dilution, Edgar Ivan Sanchez Medina, Steffen Linke, Martin Stoll, Kai Sundmacher,Digital Discovery, 2023

  4. Preconditioning for a phase-field model with application to morphology evolution in organic semiconductors, Kai Bergermann, Carsten Deibel, Roland Herzog, Roderick C. I. MacKenzie, Jan-Frederik Pietschmann, Martin Stoll, Accepted Communications in Computational Physics, 2023

  5. Efficient Structure-preserving Support Tensor Train Machine Kirandeep Kour, Sergey Dolgov, Martin Stoll, Peter Benner, JMLR 2023

  6. An Improved Penalty Algorithm using Model Order Reduction for MIPDECO problems with partial observations, Dominik Garmatter, Margherita Porcelli, Francesco Rinaldi, Martin Stoll, Computational Optimization and Applications, 2022

  7. Learning in High-Dimensional Feature Spaces Using ANOVA-Based Fast Matrix-Vector Multiplication, Franziska Nestler, Martin Stoll, Theresa Wagner, Foundations of Data Science (FoDS), doi: 10.3934/fods.2022012, 2022

  8. Fast computation of matrix function-based centrality measures for layer-coupled multiplex networks, Kai Bergermann, Martin Stoll, Physical Review E, Vol. 105 (3), https://doi.org/10.1103/PhysRevE.105.034305, 2022

  9. Graph Neural Networks for the prediction of infinite dilution activity coefficients, Edgar Ivan Sanchez Medina, Steffen Linke, Martin Stoll and Kai Sundmacher, Digital Discovery, https://doi.org/10.1039/D1DD00037C, 2022

  10. An Emperical Study of Graph-Based Approaches for Semi-Supervised Time Series Classification, Dominik Buenger, Miriam Gondos, Lucile Peroche, Martin Stoll, Frontiers: Mathematics of Computation and Data Science, Vol 3,  https://doi.org/10.3389/fams.2021.784855, 2022

  11. Improved Penalty Algorithm for Mixed Integer PDE Constrained Optimization (MIPDECO) Problems, Dominik Garmatter, Margherita Porcelli, Francesco Rinaldi, Martin Stoll, Computers and Mathematics with Applications, Vol 116, pp 2-14, https://doi.org/10.1016/j.camwa.2021.11.004, 2022

  12. Orientations and matrix function-based centralities in multiplex network analysis of urban public transport, Kai Bergermann, Martin Stoll, Applied Network Science, https://doi.org/10.1007/s41109-021-00429-9, 2021

  13. Power-to-Syngas: a PARAREAL optimal control approach , Andrea Maggi, Dominik Garmatter, Sebastian Sager, Martin Stoll and Kai Sundmacher, Frontiers in Energy Research, https://doi.org/10.3389/fenrg.2021.720489, 2021

  14. A low-rank matrix equation method for solving PDE-constrained optimization problems Alexandra Buenger, Valeria Simoncini, Martin Stoll, SIAM J. Sci. Comput., Vol. 43, No. 5, pp. 637-654, https://doi.org/10.1137/20M1341210, 2021

  15. Optimization of a partial differential equation on a complex network , Martin Stoll, Max Winkler, Accepted ETNA, 2021

  16. Pseudoinverse Graph Convolutional Networks: Fast Filters Tailored for Large Eigengaps of Dense Graphs and Hypergraphs Dominik Alfke, Martin Stoll, Data Mining and Knowledge Discovery, Vol 35, pp 1318–1341, https://doi.org/10.1007/s10618-021-00752-w, 2021

  17. Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix Vector Products , Kai Bergermann, Martin Stoll, Toni Volkmer, SIAM Journal on Mathematics of Data Science, 3(2):758-785, https://doi.org/10.1137/20M1352028, 2021, Code

  18. Tomographic X-ray scattering based on invariant reconstruction - analysis of the 3D nanostructure of bovine bone, Paolino De Falco, Richard Weinkamer, Wolfgang Wagermaier*, Chenghao Li, Tim Snow, Nicholas J. Terrill, Himadri S. Gupta, Pawan Goyal, Martin Stoll, Peter Benner and Peter Fratzl , Journal of Applied Crystallography, Vol 54, pp 486-497,  https://doi.org/10.1107/S1600576721000881, 2021

  19. A literature survey of matrix methods for data science, Martin Stoll, GAMM Mitteilungen 2020, https://doi.org/10.1002/gamm.202000013

  20. Efficient Numerical Methods for Gas Network Modeling and Simulation, Yue Qiu, Sara Grundel, Martin Stoll, Peter Benner, Networks & Heterogeneous Media, doi: 10.3934/nhm.2020018, 2020

  21. Solving differential Riccati equations: A nonlinear space-time method using tensor trains , Tobias Breiten, Sergey Dolgov, Martin Stoll, Numerical Algebra, Control & Optimization, doi: 10.3934/naco.2020034, 2020

  22. Power-to-Chemicals: A Superstructure Problem for Sustainable Syngas Production Andrea Maggi, Dominik Garmatter, Marcus Wenzel, Shaimaa Monem, Mirko Hahn, Martin Stoll, Sebastian Sager, Peter Benner, and Kai Sundmacher, Mathematics in Industry, vol 34. Springer, Cham., https://doi.org/10.1007/978-3-030-62732-4_7, 2021

  23. Solving optimal control problems governed by random Navier-Stokes equations using low rank methods, Peter Benner, Sergey Dolgov, Akwum Onwunta, Martin Stoll, Int J Numer Meth Fluids, doi.org/10.1002/fld.4843, 2020

  24. Interior Point Methods for PDE-Constrained Optimization with Sparsity Constraints, John W. Pearson, Margherita Porcelli, Martin Stoll, Numer Linear Algebra Appl., doi.org/10.1002/nla.2276, 2020

  25. A low-rank tensor method for PDE-constrained optimization with isogeometric analysis, Alexandra Buenger, Sergey Dolgov, Martin Stoll, SIAM J. Sci. Comput., 42(1), A140–A161, 2020

  26. Node classification for signed networks using diffuse interface methods, Jessica Bosch, Pedro Mercado, Martin Stoll, ECML PKDD 2019: Machine Learning and Knowledge Discovery in Databases pp 524-540, 2019

  27. NFFT meets Krylov methods: Fast matrix-vector products for the graph Laplacian of fully connected networks, Dominik Alfke, Daniel Potts, Martin Stoll, Toni Volkmer. Frontiers: Mathematics of Computation and Data Science, 4:61, 2018.

  28. Adaptive Discontinuous Galerkin Approximation of Optimal Control Problems Governed by Transient Convection-Diffusion Equations . Hamdullah Yücel and Martin Stoll and Peter Benner, Electronic Transactions on Numerical Analysis. Volume 48, pp. 407–434, 2018.

  29. Numerical simulations of nonlocal phase-field and hyperbolic nonlocal phase-field models via localized radial basis functions-based pseudo-spectral method (LRBF-PSM), Wei Zhao, Y.C. Hon, Martin Stoll, Applied Mathematics and Computation Volume 337, 2018

  30. Fast iterative solvers for an optimal transport problem, Roland Herzog, John W. Pearson, Martin Stoll, Advances in Computational Mathematics volume 45, pages495–517, 2019

  31. An inexact Newton-Krylov method for stochastic eigenvalue problems, Peter Benner, Akwum Onwunta, Martin, Stoll, Computational Methods in Applied Mathematics | Volume 19: Issue 1, 2018,

  32. Low-Rank Eigenvector Compression of Posterior Covariance Matrices for Linear Gaussian Inverse Problems . Peter Benner, Yue Qiu, Martin Stoll, SIAM/ASA J. UNCERTAINTY QUANTIFICATION Vol. 6, No. 2, pp. 965–989 , 2018

  33. Symmetric Interior Penalty Galerkin Method For Fractional-In-Space Allen-Cahn Equations . Martin Stoll and Hamdullah Yücel, AIMS Mathematics, 3(1): 66–95 , 2018

  34. Generalizing diffuse interface methods on graphs: non-smooth potentials and hypergraphs . Jessica Bosch, Steffen Klamt, Martin Stoll, SIAM J. Appl. Math., 78(3), 1350–1377, 2018

  35. Localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for nonlocal diffusion problems . Wei Zhao, Yiuchung Hon, Martin Stoll, Computers and Mathematics with Applications Volume 75, Issue 5, 1 March 2018

  36. Preconditioning of a coupled Cahn--Hilliard Navier--Stokes system . Jessica Bosch, Christian Kahle, Martin Stoll, Commun. Comput. Phys., 23 (2018), pp. 603-628.

  37. Preconditioning PDE-constrained optimization with $\rm L^1$-sparsity and control constraints . Margherita Porcelli, Valeria Simoncini, Martin Stoll, Computers and Mathematics with Applications 74 (2017) pp. 1059-1075, 2017

  38. Stability on interpolation of scattered data via kernels. Wei Zhao, Martin Stoll, Neural, Parallel, and Scientific Computations 25 (2017) 45-60, 2017

  39. Low-rank solutions to an optimization problem constrained by the Navier-Stokes equations . Sergey Dolgov, Martin Stoll, SIAM J. SCI. COMPUT. Vol. 39, No. 1, pp. A255–A280, 2017

  40. Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs. Peter Benner, Akwum Onwunta, and Martin Stoll, SIAM. J. Matrix Anal. & Appl. , 37(2), 491–518, 2016

  41. Low-rank solvers for unsteady Stokes-Brinkman optimal control problem with random data . Peter Benner, Sergey Dolgov, Akwum Onwunta, and Martin Stoll, CMAME, Volume 304, 1 June 2016, Pages 26–54 2016 Matlab Codes and precomputed 3D matrices (41 MB)

  42. Low-rank solvers for fractional differential equations. Tobias Breiten, Valeria Simoncini, and Martin Stoll, ETNA, Volume 45, pp. 107-132, 2016. Matlab files

  43. Fast Solvers for Optimal Control Problems from Pattern Formation. Martin Stoll, John W. Pearson, and Philip K. Maini, Volume 304, 1 January 2016, Pages 27-45
  44. Fast tensor product solvers for optimization problems with fractional differential equations as constraints, Sergey Dolgov, John W. Pearson, Dmitry V. Savostyanov, Martin Stoll, Applied Mathematics and Computation,Volume 273, Pages 604–623, 2016, Matlab files
  45. A Discontinous Galerkin Method for Optimal Control Problems Governed by a System of Convection-Diffusion PDEs with Nonlinear Reaction Terms, Hamdullah Yücel, Martin Stoll, Peter Benner, Computers and Mathematics with Applications, Volume 70, Issue 10, Pages 2414–2431, 2015
  46. Domain Decomposition in time for PDE-constrained optimization, Barker, Andrew T., and Stoll, Martin, Computer Physics Communications, Volume 197, Pages 136–143 2015
  47. A fractional inpainting model based on the vector-valued Cahn--Hilliard equation. Jessica Bosch and Martin Stoll,SIAM Journal on Imaging Sciences, Vol. 37, No. 5, pp. S216–S243, 2015, Matlab Files

  48. Low Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients, Peter Benner, and Akwum Onwunta, and Martin Stoll, SIAM/ASA J. UNCERTAINTY QUANTIFICATION, Vol. 3, pp. 622–649, 2015
  49. A fast solver for an H1 regularized optimal control problem, Barker, Andrew T., and Rees, Tyrone and Stoll, Martin, Communications in Computational Physic,19(1), 143-167, 2016
  50. Preconditioning for vector-valued Cahn-Hilliard equations. Jessica Bosch, Martin Stoll, SIAM Journal on Scientific Computing,Vol. 37, No. 5, pp. S216–S243, 2015
  51. A low-rank in time approach to PDE-constrained optimization, M Stoll, T Breiten, SIAM Journal on Scientific Computing, 2015, Matlab files
  52. Fast solution of Cahn-Hilliard Variational Inequalities using Implicit Time Discretization and Finite Elements, Bosch, Jessica, and Stoll, Martin, and Benner, Peter, Volume 262, 1 April 2014, Pages 38–57, Journal of Computational Physics, 2014
  53. Fast Solvers for Cahn-Hilliard Inpainting; Jessica Bosch, David Kay, Martin Stoll, Andy Wathen; SIAM Journal on Imaging Sciences; 7(1),67-97,2014.
  54. One-shot solution of a time-dependent time-periodic PDE-constrained optimization problem; Martin Stoll; IMA Journal of Numerical Analysis; 34 (4): 1554-1577, 2014.
  55. Preconditioners for state constrained optimal control problems with Moreau-Yosida penalty function; John W. Pearson, Martin Stoll; Andy Wathen; Volume 21, Issue 1, pages 81–97,Numerical Linear Algebra with Applications, 2014
  56. Discontinuous Galerkin Finite Element Methods with Shock-Capturing for Nonlinear Convection Dominated Models; Hamdullah Yücel, Martin Stoll, Peter Benner; Computers & Chemical Engineering, : Vol. 58, pp. 278 - 287; 2013.
  57. All-at-once solution of time-dependent Stokes control; Martin Stoll, Andy Wathen; Journal of Computational Physics,232 (2013), pp. 498-515; 2013.
  58. Efficient Solution of Large-Scale Saddle Point Systems Arising in Riccati-Based Boundary Feedback Stabilization of Incompressible Stokes Flow; Benner, Peter; Saak, Jens; Stoll, Martin; Weichelt, Heiko; SIAM J. Sci. Comput., 35(5), S150–S170. 2013
  59. Fast Iterative Solution of Reaction-Diffusion Control Problems Arising from Chemical Processes; John W. Pearson, Martin Stoll;2013, Vol. 35, No. 5, pp. B987-B1009, SIAM J. Sci. Comput., 2013
  60. Regularization-robust preconditioners for time-dependent PDE constrained optimization problems; John W. Pearson, Martin Stoll, Andy Wathen; SIAM Journal on Matrix Analysis and Applications : Vol. 33, No. 4, pp. 1126-1152; SIAM; 2012.
  61. Preconditioning for Allen-Cahn variational inequalities with non-local constraints; Luise Blank; Lavinia Sarbu; Martin Stoll; Journal of Computational Physics, 231, 5406-5420; 2012. http://dx.doi.org/10.1016/j.jcp.2012.04.035.
  62. A Krylov-Schur approach to the truncated SVD; Martin Stoll; Linear Algebra and its Applications, Volume 436, Issue 8, 15 April 2012, Pages 2795–2806; 2012.
  63. Preconditioning for partial differential equation constrained optimization with control constraints; Martin Stoll; Andy Wathen; Numerical Linear Algebra with Applications : 19:53–71; 2012.
  64. A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process; Peter Benner; Heike Faßbender; Martin Stoll; Linear Algebra and its Applications Volume 435, Issue 3, 1 August 2011, Pages 578-600; 2011.
  65. Preconditioning saddle point problems with applications in optimization; N.I.M. Gould; H.S. Dollar; Martin Stoll; Andy Wathen; SIAM Journal of Scientific Computing, 32(2010), pp. 249-270 : Vol. 31; 2010.
  66. Block triangular preconditioners for PDE constrained optimization; Tyrone Rees; Martin Stoll; Numerical Linear Algebra with Applications Volume 17, Issue 6, pages 977–996, December 2010; 2010.
  67. All-at-once preconditioning in PDE-constrained optimization; Tyrone Rees; Martin Stoll; Andy Wathen; Kybernetika : Vol. 46 (2); 2010.
  68. Solving Large-Scale Quadratic Eigenvalue Problems with Hamiltonian Eigenstructure using a Structure-Preserving Krylov Subspace Method; Benner, Peter; Faßbender, Heike;; Stoll, Martin; Electronic Transactions on Numerical Analysis ; 2008.
  69. Approximation of the scattering amplitude and linear systems; Gene H. Golub; Martin Stoll; Andy Wathen; Electronic Transactions on Numerical Analysis, Vol. 31; 2008.
  70. Combination preconditioning and the Bramble-Pasciak+ preconditioner; Martin Stoll; Andy Wathen; SIAM. J. Matrix Anal. & Appl. 30, pp. 582-608 : Vol. 30; 2008.

Articles in Conference Proceedings

Technical Reports