Professur Wissenschaftliches Rechnen
Publikationen

Submitted Articles

  1. Gradient flow-based modularity maximization for community detection in multiplex networks, Kai Bergermann, Martin Stoll, Submitted 2024

  2. IETI-based Low-Rank method for PDE-constrained optimization, Alexandra Buenger, Tom-Christian Riemer, Martin Stoll, Submitted 2024

  3. Fast Evaluation of Additive Kernels: Feature Arrangement, Fourier Methods, and Kernel Derivatives, Theresa Wagner, Franziska Nestler, Martin Stoll, Submitted 2024

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

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

  6. 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

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

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

  9. 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

  10. 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. A nonlinear spectral core-periphery detection method for multiplex networks, Kai Bergermann, Martin Stoll, Francesco Tudisco, Proceedings of the Royal Society A, 2024

  2. Second-order Partial Outer Convexification for Switched Dynamical Systems,Christoph Plate, Sebastian Sager, Martin Stoll, Manuel Tetschke, IEEE Transactions on Automatic Control., Vol 69 (7), pp 4643 - 4656, DOI: 10.1109/TAC.2024.3351567, 2024

  3. Adaptive rational Krylov methods for exponential Runge--Kutta integrators, Kai Bergermann, Martin Stoll, SIAM Journal on Matrix Analysis and Applications, Vol 45 (1), https://doi.org/10.1137/23M1559439, 2024

  4. 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, Vol 3, 2023

  5. 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, Communications in Computational Physics, Vol 34, pp 1-17, DOI: 10.4208/cicp.OA-2022-0115, 2023

  6. Efficient Structure-preserving Support Tensor Train Machine Kirandeep Kour, Sergey Dolgov, Martin Stoll, Peter Benner, JMLR, Vol 24 (4), pp 1-22, 2023

  7. 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, Vol 84, pp 191–223, 2022

  8. Learning in High-Dimensional Feature Spaces Using ANOVA-Based Fast Matrix-Vector Multiplication, Franziska Nestler, Martin Stoll, Theresa Wagner, Foundations of Data Science (FoDS), Vol 4 (3), pp 423-440, doi: 10.3934/fods.2022012, 2022

  9. 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

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

  11. 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

  12. 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

  13. Orientations and matrix function-based centralities in multiplex network analysis of urban public transport, Kai Bergermann, Martin Stoll, Applied Network Science, Vol 6, https://doi.org/10.1007/s41109-021-00429-9, 2021

  14. Power-to-Syngas: a PARAREAL optimal control approach, Andrea Maggi, Dominik Garmatter, Sebastian Sager, Martin Stoll, Kai Sundmacher, Frontiers in Energy Research, Vol 9, https://doi.org/10.3389/fenrg.2021.720489, 2021

  15. A low-rank matrix equation method for solving PDE-constrained optimization problems, Alexandra Buenger, Valeria Simoncini, Martin Stoll, SIAM J. Sci. Comput., Vol 43 (5), pp 637-654, https://doi.org/10.1137/20M1341210, 2021

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

  17. 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

  18. 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, Vol 3 (2), pp 758-785, https://doi.org/10.1137/20M1352028, Code, 2021

  19. 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, Peter Fratzl, Journal of Applied Crystallography, Vol 54 (2), pp 486-497, https://doi.org/10.1107/S1600576721000881, 2021

  20. A literature survey of matrix methods for data science, Martin Stoll, GAMM Mitteilungen, Vol 23 (3), https://doi.org/10.1002/gamm.202000013, 2020

  21. Efficient Numerical Methods for Gas Network Modeling and Simulation, Yue Qiu, Sara Grundel, Martin Stoll, Peter Benner, Networks & Heterogeneous Media, Vol 15 (4), pp 653-679, doi: 10.3934/nhm.2020018, 2020

  22. Solving differential Riccati equations: A nonlinear space-time method using tensor trains, Tobias Breiten, Sergey Dolgov, Martin Stoll, Numerical Algebra, Control & Optimization, Vol 11 (3), pp 407-429, doi: 10.3934/naco.2020034, 2020

  23. 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, Kai Sundmacher, Mathematics in Industry, Springer, Cham., Vol 34, pp pp 145–168, https://doi.org/10.1007/978-3-030-62732-4_7, 2021

  24. 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, Vol 92 (11), pp 1653-1678, doi.org/10.1002/fld.4843, 2020

  25. Interior Point Methods for PDE-Constrained Optimization with Sparsity Constraints, John W. Pearson, Margherita Porcelli, Martin Stoll, Numer Linear Algebra Appl., Vol 27 (2), doi.org/10.1002/nla.2276, 2020

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

  27. 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

  28. 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, Vol 4 (61), 2018

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

  30. 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, Vol 337, pp 514-534, 2018

  31. Fast iterative solvers for an optimal transport problem, Roland Herzog, John W. Pearson, Martin Stoll, Advances in Computational Mathematics, Vol 45, pp 495-517, 2019

  32. An inexact Newton-Krylov method for stochastic eigenvalue problems, Peter Benner, Akwum Onwunta, Martin Stoll, Computational Methods in Applied Mathematics, Vol 19 (1), 2018

  33. 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 (2), pp 965-989, 2018

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

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

  36. 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, Vol 75 (5), pp 1685-1704, 2018

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

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

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

  40. Low-rank solutions to an optimization problem constrained by the Navier-Stokes equations, Sergey Dolgov, Martin Stoll, SIAM J. SCI. COMPUT., Vol 39 (1), pp A255-A280, 2017

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

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

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

  44. Fast Solvers for Optimal Control Problems from Pattern Formation, Martin Stoll, John W. Pearson, Philip K. Maini, Vol 304, pp 27-45, 2016
  45. 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, Vol 273, pp 604-623, Matlab files, 2016
  46. 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, Vol 70 (10), pp 2414-2431, 2015
  47. Domain Decomposition in time for PDE-constrained optimization, Andrew T. Barker, Martin Stoll, Computer Physics Communications, Vol 197, pp 136-143, 2015

  48. A fractional inpainting model based on the vector-valued Cahn--Hilliard equation. Jessica Bosch and Martin Stoll, SIAM Journal on Imaging Sciences, Vol 37 (5), pp S216-S243, Matlab Files, 2015

  49. Low Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients, Peter Benner, Akwum Onwunta, Martin Stoll, SIAM/ASA J. Uncertainty Quantification, Vol 3, pp. 622-649, 2015
  50. A fast solver for an H1 regularized optimal control problem, Andrew Barker, Tyrone Rees, Martin Stoll, Communications in Computational Physic, Vol 19 (1), pp 143-167, 2016
  51. Preconditioning for vector-valued Cahn-Hilliard equations, Jessica Bosch, Martin Stoll, SIAM Journal on Scientific Computing, Vol 37 (5), pp S216-S243, https://doi.org/10.1137/14M0973633, 2015
  52. A low-rank in time approach to PDE-constrained optimization, Martin Stoll, Tobias Breiten, SIAM Journal on Scientific Computing, Vol 37 (1), Matlab files, https://doi.org/10.1137/130926365, 2015
  53. Fast solution of Cahn-Hilliard Variational Inequalities using Implicit Time Discretization and Finite Elements, Jessica Bosch, Martin Stoll, Peter Benner, Journal of Computational Physics, Vol 262, pp 38-57, 2014
  54. Fast Solvers for Cahn-Hilliard Inpainting, Jessica Bosch, David Kay, Martin Stoll, Andy Wathen, SIAM Journal on Imaging Sciences, Vol 7 (1), pp 67-97, 2014
  55. One-shot solution of a time-dependent time-periodic PDE-constrained optimization problem, Martin Stoll, IMA Journal of Numerical Analysis, Vol 34 (4), pp 1554-1577, 2014
  56. Preconditioners for state constrained optimal control problems with Moreau-Yosida penalty function, John W. Pearson, Martin Stoll, Andy Wathen, Numerical Linear Algebra with Applications, Vol 21 (1), pp 81-97, 2014
  57. 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.
  58. All-at-once solution of time-dependent Stokes control, Martin Stoll, Andy Wathen, Journal of Computational Physics, Vol 232, pp 498-515, 2013
  59. Efficient Solution of Large-Scale Saddle Point Systems Arising in Riccati-Based Boundary Feedback Stabilization of Incompressible Stokes Flow, Peter Benner, Jens Saak, Martin Stoll, Heiko Weichelt, SIAM J. Sci. Comput., Vol 35 (5), pp S150-S170, 2013
  60. Fast Iterative Solution of Reaction-Diffusion Control Problems Arising from Chemical Processes, John W. Pearson, Martin Stoll, Vol. 35 (5), pp B987-B1009, SIAM J. Sci. Comput., 2013
  61. 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 (4), pp. 1126-1152, 2012
  62. Preconditioning for Allen-Cahn variational inequalities with non-local constraints, Luise Blank, Lavinia Sarbu, Martin Stoll, Journal of Computational Physics, Vol 231, pp 5406-5420, http://dx.doi.org/10.1016/j.jcp.2012.04.035, 2012
  63. A Krylov-Schur approach to the truncated SVD, Martin Stoll, Linear Algebra and its Applications, Vol 436 (8), pp 2795-2806, 2012
  64. Preconditioning for partial differential equation constrained optimization with control constraints, Martin Stoll, Andy Wathen, Numerical Linear Algebra with Applications, Vol 19, pp 53–71, 2012
  65. A Hamiltonian Krylov-Schur-type method based on the symplectic Lanczos process, Peter Benner, Heike Faßbender, Martin Stoll, Linear Algebra and its Applications, Vol 435 (3), pp 578-600, 2011
  66. Preconditioning saddle point problems with applications in optimization, N.I.M. Gould, H.S. Dollar, Martin Stoll, Andy Wathen, SIAM Journal of Scientific Computing, Vol 32, pp. 249-270, 2010
  67. Block triangular preconditioners for PDE constrained optimization, Tyrone Rees, Martin Stoll, Numerical Linear Algebra with Applications, Vol 17 (6), pp 977–996, 2010
  68. All-at-once preconditioning in PDE-constrained optimization, Tyrone Rees, Martin Stoll, Andy Wathen,  Kybernetika Vol. 46 (2), 2010
  69. Solving Large-Scale Quadratic Eigenvalue Problems with Hamiltonian Eigenstructure using a Structure-Preserving Krylov Subspace Method, Peter Benner, Heike Faßbender, Martin Stoll, Electronic Transactions on Numerical Analysis, 2008
  70. Approximation of the scattering amplitude and linear systems, Gene H. Golub, Martin Stoll, Andy Wathen, Electronic Transactions on Numerical Analysis, Vol. 31, 2008
  71. Combination preconditioning and the Bramble-Pasciak+ preconditioner, Martin Stoll, Andy Wathen, SIAM. J. Matrix Anal. & Appl. Vol 30, pp. 582-608, 2008

Articles in Conference Proceedings

Technical Reports

Theses