Publications NDS Group

Submitted Articles

1. Localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for nonlocal diffusion problems . Wei Zhao, Yiuchung Hon, Martin Stoll, Submitted 2017

2. Solving optimal control problems governed by random Navier-Stokes equations using low rank methods . Peter Benner, Sergey Dolgov, Akwum Onwunta, Martin Stoll, Submitted 2017

3. Low-rank computation of posterior covariance matrices in Bayesian inverse problems . Peter Benner, Yue Qiu, Martin Stoll, Submitted 2017

4. Generalizing diffuse interface methods on graphs: non-smooth potentials and hypergraphs . Jessica Bosch, Steffen Klamt, Martin Stoll, Submitted 2016

5. A Fast Multipole Method based on Band-limited Approximations for Radial Basis Functions . Wei Zhao, Martin Stoll, Under Revision, 2016

6. Adaptive Discontinuous Galerkin Approximation of Optimal Control Problems Governed by Transient Convection-Diffusion Equations . Hamdullah Yücel and Martin Stoll and Peter Benner, Submitted 2015

7. Symmetric Interior Penalty Galerkin Method For Fractional-In-Space Allen-Cahn Equations . Martin Stoll and Hamdullah Yücel, Submitted 2015

Journal Publications

1. Preconditioning of a coupled Cahn--Hilliard Navier--Stokes system . Jessica Bosch, Christian Kahle, Martin Stoll, Accepted Communications in Computational Physics 2017

2. Preconditioning PDE-constrained optimization with $\rm L^1$-sparsity and control constraints . Margherita Porcelli, Valeria Simoncini, Martin Stoll, Accepted Computers and Mathematics with Applications, 2017

3. Stability on interpolation of scattered data via kernels. Wei Zhao, Martin Stoll, Accepted NPSC 2016

4. Low-rank solutions to an optimization problem constrained by the Navier-Stokes equations . Sergey Dolgov, Martin Stoll, Accepted SISC 2016

5. 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

6. 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)

7. Low-rank solvers for fractional differential equations. Tobias Breiten, Valeria Simoncini, and Martin Stoll, Accepted ETNA, 2016 Matlab files

8. Fast Solvers for Optimal Control Problems from Pattern Formation. Martin Stoll, John W. Pearson, and Philip K. Maini, Accepted Journal of Computational Physics 2014
9. 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
10. 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
11. Domain Decomposition in time for PDE-constrained optimization, Barker, Andrew T., and Stoll, Martin, Computer Physics Communications, Volume 197,  Pages 136–143 2015

12. 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

13. 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
14. 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
15. Preconditioning for vector-valued Cahn-Hilliard equations. Jessica Bosch, Martin Stoll, SIAM Journal on Scientific Computing,Vol. 37, No. 5, pp. S216–S243, 2015
16. A low-rank in time approach to PDE-constrained optimization, M Stoll, T Breiten, SIAM Journal on Scientific Computing, 2015
17. 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
18. Fast Solvers for Cahn-Hilliard Inpainting; Jessica Bosch, David Kay, Martin Stoll, Andy Wathen; SIAM Journal on Imaging Sciences; 7(1),67-97,2014.
19. 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.
20. 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
21. 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.
22. All-at-once solution of time-dependent Stokes control; Martin Stoll, Andy Wathen; Journal of Computational Physics,232 (2013), pp. 498-515; 2013.
23. 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
24. 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
25. 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.
26. 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.
27. 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.
28. Preconditioning for partial differential equation constrained optimization with control constraints; Martin Stoll; Andy Wathen; Numerical Linear Algebra with Applications  :  19:53–71;  2012.
29. 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.
30. 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.
31. 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.
32. All-at-once preconditioning in PDE-constrained optimization; Tyrone Rees; Martin Stoll; Andy Wathen; Kybernetika  :  Vol. 46 (2); 2010.
33. 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.
34. Approximation of the scattering amplitude and linear systems; Gene H. Golub; Martin Stoll; Andy Wathen; Electronic Transactions on Numerical Analysis, Vol. 31; 2008.
35. 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

• Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems; John W. Pearson, Martin Stoll, and Andrew J.Wathen; PAMM 2012  :  PAMM 2012; 2012.
• Preconditioning for Allen-Cahn variational inequalities with non-local constraints; Luise Blank; Lavinia Sarbu; Martin Stoll; Oberwolfach report; 2010.
• Efficient Solvers for Large-Scale Saddle Point Systems Arising in Feedback Stabilization of Multi-field Flow Problems, Peter Benner, Jens Saak, Martin Stoll, Heiko K. Weichelt, IFIP Advances in Information and Communication Technology Volume 443, 2014, pp 11-20

Technical Reports

• All-at-once solution of time-dependent PDE-constrained optimization problems; Martin Stoll; Andy Wathen; Technical Report  ; 2010.

Thesis

• Locking and purging for the Hamiltonian Lanczos process (In German),Diploma Thesis, TU Chemnitz, 2005
• Solving Linear Systems using the Adjoint, DPhil, University of Oxford, 2009
• Fast iterative solvers for time-dependent PDE-constrained optimization problems, kumulative Habilitation, 2016