Research INS Preprints

2024

  1. On the numerical approximation of the Karhunen-Loève expansion for random fields with random discrete data. M. Griebel, G. Li, and C. Rieger. Available as INS Preprint No. 2404, 2024. BibTeX PDF
  2. On multilevel energy-based fragmentation methods. J. Barker, M. Griebel, and J. Hamaekers. Available as INS Preprint No. 2403, 2024. BibTeX PDF
  3. Learning Lipschitz operators with respect to Gaussian measures with near-optimal sample complexity. B. Adcock, M. Griebel, and G. Maier. Available as INS Preprint No. 2402, 2024. BibTeX PDF
  4. Efficient solution of ill-posed integral equations through averaging. M. Griebel and T. Jahn. Available as INS Preprint No. 2401, 2024. BibTeX PDF

2023

  1. Convergence of generalized cross-validation for an ill-posed integral equation. T. Jahn. Available as INS Preprint No. 2303, 2023. BibTeX PDF
  2. Convergence analysis of online algorithms for vector-valued kernel regression. M. Griebel and P. Oswald. Available as INS Preprint No. 2302, 2023. BibTeX PDF
  3. On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction. B. Brown, M. Griebel, F. Y. Kuo, and I. H. Sloan. Bulletin of the Australian Mathematical Society, pages 1–13, 2023. Also available as INS Preprint No. 2301. BibTeX PDF DOI

2022

  1. A modified SimRank++ approach for searching crash simulation data. A. Pakiman, J. Garcke, and A. Schumacher. Applied Intelligence, 2024. accepted. BibTeX PDF
  2. A mass-conserving sparse grid combination technique with biorthogonal hierarchical basis functions for kinetic simulations. T. Pollinger, J. Rentrop, D. Pflüger, and K. Kormann. Available as INS Preprint No. 2209, 2022. BibTeX PDF arXiv
  3. Alignment of highly resolved time-dependent experimental and simulated crash test data. J. Garcke, S. Hahner, and R. Iza-Teran. International Journal of Crashworthiness, 29(1):1–15, 2024. also available as INS Preprint No. 2208. BibTeX PDF DOI
  4. Knowledge discovery assistants for crash simulations with graph algorithms and energy absorption features. A. Pakiman, J. Garcke, and A. Schumacher. Applied Intelligence, 53:19217–19236, 2023. earlier version under title "Crash Simulation Exploration with Energy Absorption Features and Graph Algorithms" available as V1, also available as INS Preprint No. 2207. BibTeX PDF V1 DOI
  5. A note on source term representation for control-and-state-constrained parabolic control problems with purely time-dependent control. I. Neitzel. Technical Report, Institute for Numerical Simulation, Bonn University, 2022. Available as INS Preprint No. 2206. BibTeX PDF
  6. A dimension-adaptive combination technique for uncertainty quantification. M. Griebel and U. Seidler. International Journal for Uncertainty Quantification, 14(2):21–43, 2024. Also available as INS Preprint No. 2205. BibTeX PDF DOI
  7. In-situ estimation of time-averaging uncertainties in turbulent flow simulations. S. Rezaeiravesh, C. Gscheidle, A. Peplinski, J. Garcke, and P. Schlatter. Computer Methods in Applied Mechanics and Engineering, 433:117511, 2025. BibTeX PDF DOI arXiv
  8. Low-rank approximation of continuous functions in Sobolev spaces with dominating mixed smoothness. M. Griebel, H. Harbrecht, and R. Schneider. Mathematics of Computation, 92(342):1729–1746, 2023. Also available as INS Preprint No. 2203. BibTeX PDF DOI
  9. Sparse optimal control of a quasilinear elliptic PDE in measure spaces. F. Hoppe. Submitted. Available as INS Preprint No. 2202, 2022. BibTeX PDF
  10. Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization. F. Hoppe and I. Neitzel. ESAIM: COCV, 2022. also available as INS Preprint No. 2201. BibTeX PDF DOI

2021

  1. On the numerical approximation of the Karhunen-Loève expansion for random fields with random discrete data. M. Griebel, G. Li, and C. Rieger. Available as INS Preprint No. 2106, 2021. BibTeX PDF
  2. A dimension-oblivious domain decomposition method based on space-filling curves. M. Griebel, M. A. Schweitzer, and L. Troska. SIAM Journal on Scientific Computing, 45(2):A369–A396, 2023. Also available as INS Preprint No. 2105. BibTeX PDF DOI
  3. Multi-resolution DynamicMode decomposition for early damage detection in wind turbine gearboxes. P. Climaco, J. Garcke, and R. Iza-Teran. Available as INS Preprint No. 2103, 2021. BibTeX PDF
  4. Deep neural networks and PIDE discretizations. B. Bohn, M. Griebel, and D. Kannan. SIAM Journal on Mathematics of Data Science, 4(3):1145–1170, 2022. Also available as INS Preprint No. 2102. BibTeX PDF Supplement DOI
  5. A fault-tolerant domain decomposition method based on space-filling curves. M. Griebel, M. A. Schweitzer, and L. Troska. Available as INS Preprint No. 2101, 2021. BibTeX PDF

2020

  1. Sparse tensor product approximation for a class of generalized method of moments estimators. A. Gilch, M. Griebel, and J. Oettershagen. International Journal for Uncertainty Quantification, 12(2):53–79, 2022. Also available as INS Preprint No. 2006. BibTeX PDF DOI
  2. A-posteriori reduced basis error-estimates for a semi-discrete in space quasilinear parabolic PDE. F. Hoppe and I. Neitzel. Comput. Optim. Appl., 2021. BibTeX PDF DOI
  3. Optimal Control of Quasilinear Parabolic PDEs with State-Constraints. F. Hoppe and I. Neitzel. SIAM J. Control Optim., 60(1):330–354, 2022. BibTeX PDF DOI
  4. Note on 1D quarklet approximation. P. Oswald. Available as INS Preprint No. 2003, 2020. BibTeX PDF
  5. Multivariate Haar systems in Besov function spaces. P. Oswald. Submitted to Mat. Sbornik. Available as INS Preprint No. 2002, 2020. BibTeX PDF arXiv
  6. EXAHD: A massively parallel fault tolerant sparse grid approach for high-dimensional turbulent plasma simulations. R. Lago, M. Obersteiner, T. Pollinger, J. Rentrop, H.-J. Bungartz, T. Dannert, M. Griebel, F. Jenko, and D. Pflüger. In H.-J. Bungartz, S. Reiz, B. Uekermann, P. Neumann, and W. E. Nagel, editors, Software for Exascale Computing - SPPEXA 2016-2019, 301–329. Cham, 2020. Springer International Publishing. Also available as INS Preprint No. 2001. BibTeX PDF DOI

2019

  1. Convergence of the SQP method for quasilinear parabolic optimal control problems. F. Hoppe and I. Neitzel. Optim. Eng., 2020. BibTeX PDF DOI
  2. Finite differences on sparse grids for continuous time heterogeneous agent models. J. Garcke and S. Ruttscheidt. Available as INS Preprint No. 1906., 2019. BibTeX PDF
  3. Maximum approximated likelihood estimation. M. Griebel, F. Heiss, J. Oettershagen, and C. Weiser. Submitted to Econometric Theory. Available as INS Preprint No. 1905, 2019. BibTeX PDF
  4. On the numerical approximation of the Karhunen-Loève expansion for lognormal random fields. M. Griebel and G. Li. Available as INS Preprint No. 1904, 2019. BibTeX PDF
  5. Analysis of tensor approximation schemes for continuous functions. M. Griebel and H. Harbrecht. Foundations of Computational Mathematics, 23:219–240, 2023. Also available as INS Preprint No. 1903. BibTeX PDF DOI
  6. Generalized sparse grid interpolation based on the fast discrete Fourier transform. M. Griebel and J. Hamaekers. In Sparse Grids and Applications - Munich 2018, volume 144 of Lecture Notes in Computational Science and Engineering, pages 53–68. Springer International Publishing, 2022. BibTeX PDF DOI
  7. Simplex stochastic collocation for piecewise smooth functions with kinks. B. Fuchs and J. Garcke. International Journal for Uncertainty Quantification, 10(1):1–24, 2020. BibTeX PDF DOI arXiv

2018

  1. Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations. M. Griebel, C. Rieger, and P. Zaspel. International Journal for Uncertainty Quantification, 9(5):471–492, 2019. Also available as INS Preprint No. 1813. BibTeX PDF DOI
  2. Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids. B. Bohn, M. Griebel, and J. Oettershagen. In Proceedings of the 2019 SIAM International Conference on Data Mining, 163–171. 2019. Also available as INS Preprint No. 1812. BibTeX PDF DOI
  3. Simulation of micron-scale drop impact. M. Griebel and M. Klitz. Computers & Mathematics with Applications, 78(9):3027–3043, 2019. Also available as INS Preprint No. 1811. BibTeX PDF DOI
  4. Haar system as Schauder basis in Besov spaces: the limiting cases for 0 < p ≤ 1. P. Oswald. Available as INS Preprint No. 1810, 2018. BibTeX PDF arXiv
  5. Stochastic subspace correction methods and fault tolerance. M. Griebel and P. Oswald. Math. Comp., 89(321):279–312, 2020. Also available as INS Preprint No. 1809. BibTeX PDF DOI arXiv
  6. Incremental kernel based approximations for Bayesian inverse problems. C. Rieger. Available as INS Preprint No. 1807., 2018. BibTeX PDF
  7. Iterated Landweber method for radial basis functions interpolation with finite accuracy. C. Rieger. Available as INS Preprint No. 1806., 2018. BibTeX PDF
  8. Sampling inequalities for anisotropic tensor product grids. C. Rieger and H. Wendland. IMA Journal of Numerical Analysis, 2019. Online first. Also available as INS Preprint No. 1805. BibTeX PDF DOI
  9. Kernel-based reconstructions for parametric PDEs. R. Kempf, H. Wendland, and C. Rieger. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations IX, volume 129 of Lecture Notes in Computational Science and Engineering, 53–71. Springer, 2019. Also available as INS Preprint No. 1804. BibTeX PDF DOI
  10. Estimates for generalized sparse grid hierarchical basis preconditioners. P. Oswald. Available as INS Preprint No. 1803, 2018. BibTeX PDF arXiv
  11. Stability of low-rank tensor representations and structured multilevel preconditioning for elliptic PDEs. M. Bachmayr and V. Kazeev. arXiv:1802.09062, 2018. Also available as INS Preprint No. 1802. BibTeX arXiv
  12. Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces. C. Kacwin, J. Oettershagen, M. Ullrich, and T. Ullrich. Preprint Uni Bonn, pages 1–40, 2018. INS Preprint No. 1801. BibTeX PDF

2017

  1. On the degree of ill-posedness of multi-dimensional magnetic particle imaging. T. Kluth, B. Jin, and G. Li. Inverse Problems, 2018. Also available as INS preprint No. 1718. BibTeX PDF DOI
  2. Stochastic subspace correction in Hilbert space. M. Griebel and P. Oswald. Constructive Approximation, 48(3):501–521, 2018. Also available as INS Preprint No. 1717. BibTeX PDF DOI
  3. Upscaled HDG methods for Brinkman equations with high-contrast heterogeneous coefficient. G. Li and K. Shi. INS preprint No. 1716., 2017. BibTeX PDF
  4. Tangent and normal cones for low-rank matrices. S. Hosseini, D. R. Luke, and A. Uschmajew. INS Preprint No. 1715, oct 2017. BibTeX PDF
  5. A representer theorem for deep kernel learning. B. Bohn, M. Griebel, and C. Rieger. Journal of Machine Learning Research, 20(64):1–32, 2019. Also available as INS Preprint No. 1714. BibTeX PDF JMLR
  6. A collection of nonsmooth Riemannian optimization problems. P.-A. Absil and S. Hosseini. INS Preprint No. 1713, sep 2017. BibTeX PDF
  7. Alternating least squares as moving subspace correction. I. V. Oseledets, M. V. Rakhuba, and A. Uschmajew. INS Preprint No. 1712, sep 2017. BibTeX
  8. On the convergence rate of sparse grid least squares regression. B. Bohn. In J. Garcke, D. Pflüger, C. Webster, and G. Zhang, editors, Sparse Grids and Applications - Miami 2016, volume 123 of Lecture Notes in Computational Science and Engineering, pages 19–41. Springer, 2018. BibTeX PDF
  9. Efficient higher order time discretization schemes for Hamilton-Jacobi-Bellman equations based on diagonally implicit symplectic Runge-Kutta methods. J. Garcke and I. Kalmykov. In D. Kalise, K. Kunisch, and Z. Rao, editors, Hamilton-Jacobi-Bellman Equations: Numerical Methods and Applications in Optimal Control, pages 97–128. De Gruyter, 2018. BibTeX PDF DOI
  10. Projection methods for dynamical low-rank approximation of high-dimensional problems. E. Kieri and B. Vandereycken. INS Preprint No. 1709, jul 2017. BibTeX
  11. Singular value decomposition versus sparse grids: Refined complexity estimates. M. Griebel and H. Harbrecht. IMA Journal of Numerical Analysis, 39(4):1652–1671, 2019. Also available as INS Preprint No. 1708. BibTeX PDF DOI
  12. On orthogonal tensors and best rank-one approximation ratio. Z. Li, Y. Nakatsukasa, T. Soma, and A. Uschmajew. INS Preprint No. 1707, jul 2017. BibTeX arXiv
  13. On the expected uniform error of geometric Brownian motion approximated by the Lévy-Ciesielski construction. B. Brown, M. Griebel, F. Y. Kuo, and I. H. Sloan. Available as INS Preprint No. 1706., 2017. BibTeX PDF
  14. Second order optimality conditions for optimal control of quasilinear parabolic pdes. L. Bonifacius and I. Neitzel. Mathematical Control and Related Fields, 8(1):1–34, 2018. Preprint version available as INS Preprint No. 1705. BibTeX PDF DOI
  15. Low-rank approximation to heterogeneous elliptic problems. G. Li. INS preprint No. 1704., 2017. BibTeX PDF
  16. ε\varepsilon -dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs. D. Dũng, M. Griebel, V. N. Huy, and C. Rieger. Journal of Complexity, 46:66–89, 2018. Also available as INS Preprint No. 1703. BibTeX PDF DOI arXiv
  17. On the decay rate of the singular values of bivariate functions. M. Griebel and G. Li. SIAM J. Numer. Anal., 56(2):974–993, 2018. Also available as INS preprint No. 1702. BibTeX PDF DOI
  18. Numerical stochastic homogenization by quasi-local effective diffusion tensors. D. Gallistl and D. Peterseim. INS Preprint No. 1701, 2017. BibTeX PDF arXiv

2016

  1. Numerical verification of a bond-based softening peridynamic model for small displacements: deducing material parameters from classical linear theory. P. Diehl, R. Lipton, and M. A. Schweitzer. Technical Report, Institut für Numerische Simulation, 2016. BibTeX PDF
  2. Extraction of fragments and waves after impact damage in particle-based simulations. P. Diehl, M. Bußler, D. Pflüger, S. Frey, T. Ertl, F. Sadlo, and M. A. Schweitzer. In Meshfree Methods for Partial Differential Equations VIII, pages 17–34. Springer International Publishing, 2017. BibTeX Publisher
  3. Simulation of wave propagation and impact damage in brittle materials using peridynamics. P. Diehl and M. A. Schweitzer. In M. Mehl, M. Bischoff, and M. Schäfer, editors, Recent Trends in Computational Engineering – CE2014, Lecture Notes in Computational Science and Engineering, pages 251–265. Springer, 2015. BibTeX PDF Publisher
  4. Upwind schemes for scalar advection-dominated problems in the discrete exterior calculus. M. Griebel, C. Rieger, and A. Schier. In D. Bothe and A. Reusken, editors, Transport Processes at Fluidic Interfaces, pages 145–175. Springer International Publishing, 2017. BibTeX PDF DOI
  5. Line search algorithms for locally Lipschitz functions on Riemannian manifolds. S. Hosseini, W. Huang, and R. Yousefpour. INS Preprint No. 1626. Revised version, August 2017, nov 2016. BibTeX PDF
  6. Additive schwarz solvers for hphp-fem discretizations of pde-constrained optimzation problems. S. Beuchler and K. Hofer. Technical Report, INS, 2016. also avaiable as INS-Preprint 1625. BibTeX PDF
  7. A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization. S. Hosseini and A. Uschmajew. INS Preprint No. 1624. Extended and revised version, March 2017, oct 2016. BibTeX PDF
  8. Multiscale simulation of polymeric fluids using the sparse grid combination technique. A. Rüttgers and M. Griebel. Applied Mathematics and Computation, 319:425–443, 2018. also available as INS Preprint No. 1623. BibTeX PDF Publisher
  9. Numerical simulation of the temporal evolution of a three dimensional barchanoid dune and the corresponding sediment dynamics. M. Burkow and M. Griebel. Computers and Fluids, 166:275–285, 2018. Also available as INS Preprint No. 1622. BibTeX PDF DOI
  10. Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with disorder potentials. P. Henning and D. Peterseim. INS Preprint No. 1621, 2016. BibTeX PDF
  11. Multiscale sub-grid correction method for time-harmonic high-frequency elastodynamics with wavenumber explicit bounds. D. Brown and D. Gallistl. INS Preprint No. 1620, 2016. BibTeX arXiv
  12. Computation of local and quasi-local effective diffusion tensors in elliptic homogenization. D. Gallistl and D. Peterseim. INS Preprint No. 1619, 2016. BibTeX PDF arXiv
  13. Nonconforming p1 elements on distorted triangulations: lower bounds for the discrete energy norm error. P. Oswald. INS Preprint No. 1618, 2016. BibTeX PDF
  14. Stable splittings of Hilbert spaces of functions of infinitely many variables. M. Griebel and P. Oswald. Journal of Complexity, 41:126–151, 2017. Also available as INS Preprint No. 1617. BibTeX PDF DOI
  15. Perturbation of higher-order singular values. W. Hackbusch, D. Kressner, and A. Uschmajew. SIAM J. Appl. Algebra Geom., 1(1):374–387, 2017. INS Preprint No. 1616. BibTeX DOI
  16. Variational formulation and numerical analysis of linear elliptic equations in nondivergence form with Cordes coefficients. D. Gallistl. Siam J. Numer. Anal., 2017. Accepted for publication. BibTeX arXiv
  17. Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in 2d. G. Li, D. Peterseim, and M. Schedensack. ArXiv e-prints, 2016. Also available as INS Preprint No. 1612. BibTeX PDF arXiv
  18. Adaptive Mesh Refinement Strategies in Isogeometric Analysis - A Computational Comparison. P. Hennig, M. Kästner, P. Morgenstern, and D. Peterseim. Comp. Meth. Appl. Mech. Eng., 316:424––448, 2017. BibTeX PDF DOI arXiv
  19. Sampling inequalities for sparse grids. C. Rieger and H. Wendland. Numerische Mathematik, 2017. Also available as INS preprint no. 1609. BibTeX PDF DOI
  20. A-posteriori error estimation of discrete pod models for pde-constrained optimal control. M. Gubisch, I. Neitzel, and S. Volkwein. In Model reduction and approximation: theory and algorithms, volume of Computational Science and Engineering, pages. SIAM. BibTeX PDF
  21. A priori l2l^2-discretization error estimates for the state in elliptic optimization problems with pointwise inequality state constraints. I. Neitzel and W. Wollner. Numer. Math., 2017. also available as INS Preprint No. 1606. BibTeX PDF DOI
  22. A priori error estimates for state constrained semilinear parabolic optimal control problems. F. Ludovici, I. Neitzel, and W. Wollner. J. Optim. Theory Appl., 178(2):317–348, 2018. also available as INS Preprint No. 1605. BibTeX PDF DOI
  23. LC-GAP: Localized Coulomb descriptors for the Gaussian Approximation Potential. J. Barker, J. Bulin, J. Hamaekers, and S. Mathias. In M. Griebel, A. Schüller, and M. A. Schweitzer, editors, Scientific Computing and Algorithms in Industrial Simulations: Projects and Products of Fraunhofer SCAI, pages 25–42. Springer International Publishing, Cham, 2017. BibTeX PDF
  24. Robust numerical upscaling of elliptic multiscale problems at high contrast. D. Peterseim and R. Scheichl. Computational Methods in Applied Mathematics, 16:579–603, 2016. BibTeX PDF DOI arXiv
  25. Relaxing the CFL condition for the wave equation on adaptive meshes. D. Peterseim and M. Schedensack. J. Sci. Comput., 2017. Online First. BibTeX PDF DOI arXiv
  26. An adaptive multiscale approach for electronic structure methods. M. Griebel, J. Hamaekers, and R. Chinnamsetty. Multiscale Modeling & Simulation, 16(2):752–776, 2018. Also available as INS Preprint No. 1601. BibTeX PDF DOI

2015

  1. Stable splitting of polyharmonic operators by generalized Stokes systems. D. Gallistl. Math. Comp., 2016. Accepted for publication. Also available INS Preprint No. 1529. BibTeX PDF
  2. A new discretization for mmth-Laplace equations with arbitrary polynomial degrees. M. Schedensack. SIAM J. Numer. Anal., 54(4):2138–2162, july 2016. Also available as INS Preprint No. 1528 and arXiv e-print 1512.06513. BibTeX PDF DOI arXiv
  3. On the stability of the Rayleigh-Ritz method for eigenvalues. D. Gallistl, P. Huber, and D. Peterseim. Accepted for publication in Numerische Mathematik. Available as INS Preprint No. 1527, 2017. BibTeX PDF
  4. Multiscale Petrov-Galerkin method for high-frequency heterogeneous Helmholtz equations. D. Brown, D. Gallistl, and D. Peterseim. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations VII, Lecture Notes in Computational Science and Engineering. 2016. BibTeX PDF arXiv
  5. A multilevel approach to the evolutionary generation of polycrystalline structures. J. Barker, G. Bollerhey, and J. Hamaekers. Computational Materials Science, 114:54–63, 2016. Also available as INS Preprint No. 1525. BibTeX PDF
  6. Operator based multi-scale analysis of simulation bundles. R. Iza-Teran and J. Garcke. Submitted, also available as INS Preprint No. 1524, 2015. BibTeX PDF
  7. Convergence of nonsmooth descent methods via Kurdyka–Łojasiewicz inequality on Riemannian manifolds. S. Hosseini. INS Preprint No. 1523. Revised version, July 2017, nov 2015. BibTeX PDF
  8. Generalized finite element methods for quadratic eigenvalue problems. A. Målqvist and D. Peterseim. ESAIM Math. Model. Numer. Anal., 51(1):147–163, 2017. BibTeX PDF DOI arXiv
  9. Multilevel quadrature for elliptic parametric partial differential equations in case of polygonal approximations of curved domains. M. Griebel, H. Harbrecht, and M. Multerer. SIAM J. Numer. Anal., 58(1):684–705, 2020. Also available as INS Preprint No. 1521. BibTeX PDF DOI
  10. On the interconnection between the higher-order singular values of real tensors. W. Hackbusch and A. Uschmajew. Numer. Math., 135(3):875–894, 2017. INS Preprint No. 1520. BibTeX DOI
  11. Complexity of hierarchical refinement for a class of admissible mesh configurations. A. Buffa, C. Giannelli, P. Morgenstern, and D. Peterseim. Computer Aided Geometric Design, 47:83–92, 2016. BibTeX PDF DOI
  12. Suboptimal Feedback Control of PDEs by Solving HJB Equations on Adaptive Sparse Grids. J. Garcke and A. Kröner. Journal of Scientific Computing, 70(1):1–28, 2017. also available as INS Preprint No. 1518. BibTeX PDF DOI Link
  13. Regularized kernel-based reconstruction in generalized Besov spaces. M. Griebel, C. Rieger, and B. Zwicknagl. Foundations of Computational Mathematics, 18(2):459–508, 2018. Also available as INS Preprint No. 1517. BibTeX PDF DOI
  14. A generalized multiscale finite element method for poroelasticity problems I: linear problems. D. L. Brown and M. Vasilyeva. Journal of Computational and Applied Mathematics, 294(C):372–388, 2016. Also available as INS Preprint No. 1516. BibTeX PDF
  15. CLSVOF as a fast and mass-conserving extension of the level-set method for the simulation of two-phase flow problems. M. Griebel and M. Klitz. Numer. Heat Transfer, Part B, 71(1):1–36, 2017. Also available as INS Preprint No. 1515. BibTeX PDF DOI
  16. A sparse grid based method for generative dimensionality reduction of high-dimensional data. B. Bohn, J. Garcke, and M. Griebel. Journal of Computational Physics, 309:1–17, 2016. also available as INS Preprint No. 1514. BibTeX PDF DOI
  17. Note on ”The smoothing effect of integration in Rd\mathbb {R}^d and the ANOVA decomposition”. M. Griebel, F. Y. Kuo, and I. H. Sloan. Mathematics of Compuation, 86:1855–1876, 2017. Also available as INS preprint No. 1513. BibTeX PDF
  18. On tensor product approximation of analytic functions. M. Griebel and J. Oettershagen. Journal of Approximation Theory, 207:348–379, 2016. Also available as INS Preprint No. 1512. BibTeX PDF
  19. Reproducing kernel Hilbert spaces for parametric partial differential equations. M. Griebel and C. Rieger. SIAM/ASA J. Uncertainty Quantification, 5:111–137, 2017. also available as INS Preprint No. 1511. BibTeX PDF DOI
  20. Subspace correction methods in algebraic multi-level frames. P. Zaspel. INS Preprint No. 1510, submitted to Linear Algebra and its Applications., june 2015. BibTeX PDF
  21. Variational multiscale stabilization and the exponential decay of fine-scale correctors. D. Peterseim. In G. R. Barrenechea, F. Brezzi, A. Cangiani, and E. H. Georgoulis, editors, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, volume 114 of Lecture Notes in Computational Science and Engineering. Springer, may 2016. BibTeX PDF arXiv
  22. Globally structured three-dimensional analysis-suitable T-splines: definition, linear independence and mm-graded local refinement. P. Morgenstern. SIAM J. Numer. Anal., 54(4):2163–2186, may 2016. Also available as INS Preprint No. 1508. BibTeX PDF DOI arXiv
  23. A new generalization of the P1{P}_1 non-conforming FEM to higher polynomial degrees. M. Schedensack. Comput. Methods Appl. Math., 17(1):161–185, 2017. also available as INS Preprint No. 1507 and arXiv e-print 1505.02044. BibTeX PDF arXiv
  24. Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form. D. Boffi, D. Gallistl, F. Gardini, and L. Gastaldi. Math. Comp., 2016. Accepted for publication. BibTeX arXiv
  25. Finding a low-rank basis in a matrix subspace. Y. Nakatsukasa, T. Soma, and A. Uschmajew. Math. Program., 162(1-2, Ser. A):325–361, 2017. BibTeX DOI arXiv
  26. Stable multiscale Petrov-Galerkin finite element method for high frequency acoustic scattering. D. Gallistl and D. Peterseim. Comp. Meth. Appl. Mech. Eng., 295:1–17, march 2015. BibTeX PDF DOI arXiv
  27. A multiscale finite element method for Neumann problems in porous microstructures. D. L. Brown and V. Taralova. Disc. and Cont. Dyn. Sys., 2016. In press. Also available as INS Preprint No. 1503. BibTeX PDF
  28. Towards the three-dimensional numerical simulation of fluvial geomorphological processes. M. Burkow and M. Griebel. Zeitschrift für Geomorphologie, 58(3):15–32, 2015. also available as INS Preprint No. 1502. BibTeX DOI
  29. Hyperbolic cross approximation in infinite dimensions. D. Dũng and M. Griebel. Journal of Complexity, 33:55–88, 2016. Also available as INS Preprint No. 1501. BibTeX PDF DOI

2014

  1. Schwarz iterative methods: Infinite space splittings. M. Griebel and P. Oswald. Constructive Approximation, 44(1):121–139, 2016. Also available as INS Preprint No. 1413. BibTeX PDF DOI
  2. Error estimates for multivariate regression on discretized function spaces. B. Bohn and M. Griebel. SIAM Journal on Numerical Analysis, 55(4):1843–1866, 2017. Also available as INS Preprint No. 1412. BibTeX PDF DOI
  3. Eliminating the pollution effect in Helmholtz problems by local subscale correction. D. Peterseim. Math. Comp., 86:1005–1036, 2017. BibTeX PDF DOI arXiv
  4. A multiscale method for porous microstructures. D. Brown and D. Peterseim. SIAM MMS, 14:1123–1152, 2016. BibTeX PDF arXiv
  5. Analysis-suitable adaptive T-mesh refinement with linear complexity. P. Morgenstern and D. Peterseim. Computer Aided Geometric Design, 34:50–66, 2015. Also available as INS Preprint No. 1409. BibTeX PDF DOI
  6. Non-intrusive uncertainty quantification with sparse grids for multivariate peridynamic simulations. F. Franzelin, P. Diehl, and D. Pflüger. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations VII, volume 100 of Lecture Notes in Computational Science and Engineering, pages 115–143. Springer, 2014. BibTeX PDF Publisher
  7. Efficient neighbor search for particle methods on GPUs. P. Diehl and M. A. Schweitzer. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations VII, volume 100 of Lecture Notes in Computational Science and Engineering, pages 81–95. Springer, 2014. BibTeX PDF Publisher
  8. Simulation of the oil storage process in the scopa of specialized bees. A. Rüttgers, M. Griebel, L. Pastrik, H. Schmied, D. Wittmann, A. Scherrieble, A. Dinkelmann, and T. Stegmaier. Computers & Fluids, 119:115–130, 2015. Also available as INS Preprint No. 1404. BibTeX PDF Publisher
  9. The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth. M. Griebel, F. Y. Kuo, and I. H. Sloan. Mathematics of Computation, 86:1855–1876, 2017. Also available as INS preprint No. 1403. BibTeX PDF
  10. A bond order dissection ANOVA approach for efficient electronic structure calculations. M. Griebel, J. Hamaekers, and F. Heber. In Extraction of Quantifiable Information from Complex Systems, volume 102 of Lecture Notes in Computational Science and Engineering, pages 211–235. Springer, 2014. BibTeX PDF
  11. 3D incompressible two-phase flow benchmark computations for rising droplets. J. Adelsberger, P. Esser, M. Griebel, S. Groß, M. Klitz, and A. Rüttgers. In Proceedings of the 11th World Congress on Computational Mechanics (WCCM XI), Barcelona, Spain. 2014. Also available as INS Preprint No. 1401 and as IGPM Preprint No. 393. BibTeX PDF

2013

  1. Multiscale partition of unity. P. Henning, P. Morgenstern, and D. Peterseim. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations VII, volume 100 of Lecture Notes in Computational Science and Engineering, pages 185–204. Springer International Publishing, 2015. BibTeX PDF DOI
  2. Optimal scaling parameters for sparse grid discretizations. M. Griebel, A. Hullmann, and P. Oswald. Numerical Linear Algebra with Applications, 22(1):76–100, 2015. Also available as INS Preprint No. 1314. BibTeX PDF DOI
  3. Multiscale simulations of three-dimensional viscoelastic flows in a square-square contraction. M. Griebel and A. Rüttgers. Journal of non-Newtonian Fluid Mechanics, 205:41–63, 2014. also available as INS Preprint No. 1313. BibTeX PDF Publisher
  4. Multiscale approximation and reproducing kernel Hilbert space methods. M. Griebel, C. Rieger, and B. Zwicknagl. SIAM Journal on Numerical Analysis, 53(2):852–873, 2015. Also available as INS Preprint No. 1312. BibTeX PDF DOI
  5. Dimensionality reduction of high-dimensional data with a nonlinear principal component aligned generative topographic mapping. M. Griebel and A. Hullmann. SIAM Journal on Scientific Computing, 36(3):A1027–A1047, 2014. Also available as INS Preprint No. 1311. BibTeX PDF DOI
  6. Dimension-adaptive sparse grid quadrature for integrals with boundary singularities. M. Griebel and J. Oettershagen. In Sparse grids and Applications, volume 97 of Lecture Notes in Computational Science and Engineering, pages 109–136. Springer, 2014. BibTeX PDF
  7. Simulation of dilute polymeric fluids in a three-dimensional contraction using a multiscale FENE model. M. Griebel and A. Rüttgers. In AIP Conference Proceedings, volume 1593, 539–543. 2014. Proceedings of PPS-29: The 29th International Conference of the Polymer Processing Society, Nuremberg, Germany, also available as INS Preprint No. 1308. BibTeX PDF DOI
  8. A full three dimensional numerical simulation of the sediment transport and the scouring at a rectangular obstacle. M. Burkow and M. Griebel. Computer and Fluids, 125:1–10, 2016. Also available as INS Preprint No. 1307. BibTeX PDF DOI
  9. Fast discrete Fourier transform on generalized sparse grids. M. Griebel and J. Hamaekers. In Sparse grids and Applications, volume 97 of Lecture Notes in Computational Science and Engineering, pages 75–108. Springer, 2014. BibTeX PDF
  10. On the convergence of the combination technique. M. Griebel and H. Harbrecht. In Sparse grids and Applications, volume 97 of Lecture Notes in Computational Science and Engineering, pages 55–74. Springer, 2014. BibTeX PDF
  11. Simulation of droplet impact with dynamic contact angle boundary conditions. M. Griebel and M. Klitz. In Singular Phenomena and Scaling in Mathematical Models, pages 297–325. Springer International Publishing Switzerland, 2013. BibTeX PDF
  12. On a multilevel preconditioner and its condition numbers for the discretized Laplacian on full and sparse grids in higher dimensions. M. Griebel and A. Hullmann. In Singular Phenomena and Scaling in Mathematical Models, pages 263–296. Springer International Publishing Switzerland, 2014. BibTeX PDF

2012

  1. Multiscale simulation of ion migration for battery systems. C. Neuen, M. Griebel, and J. Hamaekers. MRS Online Proceedings Library, 2013. Also available as INS Preprint no. 1208. BibTeX PDF DOI
  2. An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations. O. Bokanowski, J. Garcke, M. Griebel, and I. Klompmaker. Journal of Scientific Computing, 55(3):575–605, 2013. also available as INS Preprint No. 1207. BibTeX PDF DOI
  3. A sparse grid based generative topographic mapping for the dimensionality reduction of high-dimensional data. M. Griebel and A. Hullmann. In H. Bock, X. Hoang, R. Rannacher, and J. Schlöder, editors, Modeling, Simulation and Optimization of Complex Processes - HPSC 2012, pages 51–62. Springer International Publishing, 2014. BibTeX PDF DOI
  4. A note on the construction of L-fold sparse tensor product spaces. M. Griebel and H. Harbrecht. Constructive Approximation, 38(2):235–251, 2013. Also available as INS Preprint No. 1205. BibTeX PDF
  5. Computational 3D simulation of calcium leaching in cement matrices. J.J. Gaitero, J.S. Dolado, C. Neuen, F. Heber, and E. Koenders. In Proceedings of the Second International Conference on Microstructural-related Durability of Cementitious Composites, RILEM. 2012. Also available as INS Preprint no 1203. BibTeX PDF
  6. An efficient sparse grid Galerkin approach for the numerical valuation of basket options under Kou's jump-diffusion model. M. Griebel and A. Hullmann. In Sparse grids and Applications, Lecture Notes in Computational Science and Engineering, 121–150. Springer, 2013. Also available as INS Preprint No. 1202. BibTeX PDF
  7. An adaptive sparse grid approach for time series predictions. B. Bohn and M. Griebel. In J. Garcke and M. Griebel, editors, Sparse grids and Applications, volume 88 of Lecture Notes in Computational Science and Engineering, pages 1–30. Springer, 2012. BibTeX PDF DOI

2011

  1. Solving incompressible two-phase flows on multi-GPU clusters. P. Zaspel and M. Griebel. Computers &amp; Fluids, 80(0):356 – 364, 2013. Selected contributions of the 23rd International Conference on Parallel Fluid Dynamics ParCFD2011, also available as INS Preprint no. 1113. BibTeX PDF DOI
  2. Fast approximation of the discrete Gauss transform in higher dimensions. M. Griebel and D. Wissel. Journal of Scientific Computing, 55(1):149–172, 2013. Also available as INS Preprint No. 1111, 2011. BibTeX PDF DOI
  3. Approximation of two-variate functions: singular value decomposition versus sparse grids. M. Griebel and H. Harbrecht. IMA Journal of Numerical Analysis, 34(1):28–54, 2014. Also available as INS Preprint No. 1109. BibTeX PDF DOI
  4. Schwarz type solvers for hphp-FEM discretizations of mixed problems. S. Beuchler and M. Purrucker. Comput. Methods Appl. Math., 12(4):369–390, 2012. also avaiable as INS-Preprint 1108. BibTeX PDF DOI
  5. Inexact additive Schwarz solvers for hphp-FEM discretizations in three dimensions. S. Beuchler. In Advanced finite element methods and applications, volume 66 of Lect. Notes Appl. Comput. Mech., pages 91–108. Springer, Heidelberg, 2013. BibTeX PDF DOI
  6. Coupling molecular dynamics and continua with weak constraints. K. Fackeldey, D. Krause, R. Krause, and C. Lenzen. Multiscale Model. Simul., 9(4):1459–1494, 2011. Available as INS Preprint 1106. Also available as ICS preprint 2009-03 and as ZIB preprint. BibTeX PDF
  7. Greedy and randomized versions of the multiplicative Schwarz method. M. Griebel and P. Oswald. Linear Algebra Appl., 437:1596–1610, 2012. also available as INS Preprint No. 1105. BibTeX PDF DOI
  8. On the construction of sparse tensor product spaces. M. Griebel and H. Harbrecht. Mathematics of Computations, 82(282):975–994, apr 2013. Also available as INS Preprint No. 1104, 2011. BibTeX PDF

2010

  1. The smoothing effect of integration in Rd\mathbb {R}^d and the ANOVA decomposition. M. Griebel, F. Y. Kuo, and I. H. Sloan. Math. Comp., 82:383–400, 2013. Also available as INS preprint No. 1007, 2010. BibTeX PDF
  2. Intraday foreign exchange rate forecasting using sparse grids. J. Garcke, T. Gerstner, and M. Griebel. In J. Garcke and M. Griebel, editors, Sparse grids and applications, volume 88 of Lecture Notes in Computational Science and Engineering, pages 81–105. Springer, 2013. BibTeX PDF DOI

2009

  1. A molecular dynamics study on fullerene–implanted carbon nanotori as electronmagnetic sensing and emitting devices. M. Griebel and F. Heber. INS Preprint no 0912, 2009. BibTeX PDF
  2. Tensor product multiscale many-particle spaces with finite-order weights for the electronic Schrödinger equation. M. Griebel and J. Hamaekers. Zeitschrift für Physikalische Chemie, 224:527–543, 2010. Also available as INS Preprint no 0911. BibTeX PDF

2008

  1. Dimension-wise integration of high-dimensional functions with applications to finance. M. Griebel and M. Holtz. J. Complexity, 26:455–489, 2010. Also available as INS Preprint 0809. BibTeX PDF
  2. Principal manifold learning by sparse grids. Chr. Feuersänger and M. Griebel. Computing, 2009. Also available as INS Preprint no 0801. BibTeX PDF DOI

2007

  1. A molecular dynamics study of the aluminosilicate chains structure in Al-rich calcium silicate hydrated (C-S-H) gels. H. Manzano, J. Dolado, M. Griebel, and J. Hamaekers. physica status solidi (a) - applications and materials science, 205(6):1324–1329, 2008. Also as INS Preprint No. 0707. BibTeX PDF DOI
  2. A molecular dynamics study on the impact of defects and functionalization on the Young modulus of boron-nitride nanotubes. M. Griebel, J. Hamaekers, and F. Heber. Computational Materials Science, 45(4):1097–1103, 2009. BibTeX PDF
  3. BOSSANOVA: A bond order dissection approach for efficient electronic structure calculations. M. Griebel, J. Hamaekers, and F. Heber. INS Preprint 0704, Institut für Numerische Simulation, Universität Bonn, 2008. BibTeX PDF
  4. A molecular dynamics study of cementitious silicate hydrate (C-S-H) gels. J. S. Dolado, M. Griebel, and J. Hamaekers. Journal of the American Ceramic Society, 90(12):3938–3942, 2007. Also as INS Preprint No. 0701. BibTeX PostScript PDF

2006

  1. A wavelet based sparse grid method for the electronic Schrödinger equation. M. Griebel and J. Hamaekers. In M. Sanz-Solé, J. Soria, J. Varona, and J. Verdera, editors, Proceedings of the International Congress of Mathematicians, volume III, 1473–1506. Madrid, Spain, August 22–30 2006. European Mathematical Society. Also as INS Preprint No. 0603. BibTeX PDF

2005

  1. Sparse grids for the Schrödinger equation. M. Griebel and J. Hamaekers. Mathematical Modelling and Numerical Analysis, 41(2):215–247, 2007. Special issue on Molecular Modelling. Also as INS Preprint No. 0504. BibTeX PostScript PDF
  2. Molecular dynamics simulations of the influence of chemical cross-links on the elastic moduli of polymer-carbon nanotube composites. M. Griebel, J. Hamaekers, and R. Wildenhues. In J. Sanchez, editor, Proceedings 1st Nanoc-Workshop. LABEIN, Bilbao, Spain, 2005. Also as INS Preprint No. 0503. BibTeX PDF
  3. Molecular dynamics simulations of the mechanical properties of polyethylene-carbon nanotube composites. M. Griebel and J. Hamaekers. In M. Rieth and W. Schommers, editors, Handbook of Theoretical and Computational Nanotechnology, volume 9, chapter 8, pages 409–454. American Scientific Publishers, 2006. BibTeX PostScript PDF Link
  4. Molecular dynamics simulations of boron-nitride nanotubes embedded in amorphous Si-B-N. M. Griebel and J. Hamaekers. Computational Materials Science, 39(3):502–517, 2007. Also as INS Preprint No. 0501. BibTeX PostScript PDF

2002

  1. Compression of anisotropic tensor–product discretizations. S. Knapek. INS Preprint 0200, Institut für Numerische Simulation, Universität Bonn, 2002. BibTeX PDF