# Research INS Preprints

## 2022

1. Simrank-based prediction of crash simulation similarities. A. Pakiman, J. Garcke, and A. Schumacher. submitted, also available as INS Preprint No. 2210, 2022.
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.
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, 2022. also available as INS Preprint No. 2208.
4. Knowledge discovery assistants for crash simulations with graph algorithms and energy absorption features. A. Pakiman, J. Garcke, and A. Schumacher. Applied Intelligence, 2022. in press, earlier version under title "Crash Simulation Exploration with Energy Absorption Features and Graph Algorithms" available as V1, also available as INS Preprint No. 2207.
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. Submitted. Available as INS Preprint No. 2206.
6. A dimension-adaptive combination technique for uncertainty quantification. U. Seidler and M. Griebel. Available as INS Preprint No. 2205, 2022.
7. In-situ estimation of time-averaging uncertainties in turbulent flow simulations. C. Gscheidle, S. Rezaeiravesh, P. Schlatter, and J. Garcke. Available as INS Preprint No. 2204, 2022.
8. Low-rank approximation of continuous functions in Sobolev spaces with dominating mixed smoothness. M. Griebel, H. Harbrecht, and R. Schneider. Accepted by Mathematics of Computation. Available as INS Preprint No. 2203, 2022.
9. Sparse optimal control of a quasilinear elliptic PDE in measure spaces. F. Hoppe. Submitted. Available as INS Preprint No. 2202, 2022.
10. Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization. F. Hoppe and I. Neitzel. Submitted. Available as INS Preprint No. 2201, 2022.

## 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.
2. A dimension-oblivious domain decomposition method based on space-filling curves. M. Griebel, M. A. Schweitzer, and L. Troska. Accepted by SIAM SISC. Available as INS Preprint No. 2105, 2021.
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.
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.
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.

## 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.
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.
3. Optimal Control of Quasilinear Parabolic PDEs with State-Constraints. F. Hoppe and I. Neitzel. SIAM J. Control Optim., 60(1):330–354, 2022.
4. Note on 1D quarklet approximation. P. Oswald. Available as INS Preprint No. 2003, 2020.
5. Multivariate Haar systems in Besov function spaces. P. Oswald. Submitted to Mat. Sbornik. Available as INS Preprint No. 2002, 2020.
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.

## 2019

1. Convergence of the SQP method for quasilinear parabolic optimal control problems. F. Hoppe and I. Neitzel. Optim. Eng., 2020.
2. Finite differences on sparse grids for continuous time heterogeneous agent models. J. Garcke and S. Ruttscheidt. Available as INS Preprint No. 1906., 2019.
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.
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.
5. Analysis of tensor approximation schemes for continuous functions. M. Griebel and H. Harbrecht. Foundations of Computational Mathematics, 2021. Also available as INS Preprint No. 1903.
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.
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.

## 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.
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.
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.
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.
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.
6. Incremental kernel based approximations for Bayesian inverse problems. C. Rieger. Available as INS Preprint No. 1807., 2018.
7. Iterated Landweber method for radial basis functions interpolation with finite accuracy. C. Rieger. Available as INS Preprint No. 1806., 2018.
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.
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.
10. Estimates for generalized sparse grid hierarchical basis preconditioners. P. Oswald. Available as INS Preprint No. 1803, 2018.
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.
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.

## 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.
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.
3. Upscaled HDG methods for Brinkman equations with high-contrast heterogeneous coefficient. G. Li and K. Shi. INS preprint No. 1716., 2017.
4. Tangent and normal cones for low-rank matrices. S. Hosseini, D. R. Luke, and A. Uschmajew. INS Preprint No. 1715, oct 2017.
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.
6. A collection of nonsmooth Riemannian optimization problems. P.-A. Absil and S. Hosseini. INS Preprint No. 1713, sep 2017.
7. Alternating least squares as moving subspace correction. I. V. Oseledets, M. V. Rakhuba, and A. Uschmajew. INS Preprint No. 1712, sep 2017.
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.
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.
10. Projection methods for dynamical low-rank approximation of high-dimensional problems. E. Kieri and B. Vandereycken. INS Preprint No. 1709, jul 2017.
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.
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.
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.
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.
15. Low-rank approximation to heterogeneous elliptic problems. G. Li. INS preprint No. 1704., 2017.
16. $\varepsilon$-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.
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.
18. Numerical stochastic homogenization by quasi-local effective diffusion tensors. D. Gallistl and D. Peterseim. INS Preprint No. 1701, 2017.

## 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.
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.
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.
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.
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.
6. Additive schwarz solvers for $hp$-fem discretizations of pde-constrained optimzation problems. S. Beuchler and K. Hofer. Technical Report, INS, 2016. also avaiable as INS-Preprint 1625.
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.
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.
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.
10. Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with disorder potentials. P. Henning and D. Peterseim. INS Preprint No. 1621, 2016.
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.
12. Computation of local and quasi-local effective diffusion tensors in elliptic homogenization. D. Gallistl and D. Peterseim. INS Preprint No. 1619, 2016.
13. Nonconforming p1 elements on distorted triangulations: lower bounds for the discrete energy norm error. P. Oswald. INS Preprint No. 1618, 2016.
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.
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.
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.
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.
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.
19. Sampling inequalities for sparse grids. C. Rieger and H. Wendland. Numerische Mathematik, 2017. Also available as INS preprint no. 1609.
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.
21. A priori $l^2$-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.
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.
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.
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.
25. Relaxing the CFL condition for the wave equation on adaptive meshes. D. Peterseim and M. Schedensack. J. Sci. Comput., 2017. Online First.
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.

## 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.
2. A new discretization for $m$th-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.
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.
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.
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.
6. Operator based multi-scale analysis of simulation bundles. R. Iza-Teran and J. Garcke. Submitted, also available as INS Preprint No. 1524, 2015.
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.
8. Generalized finite element methods for quadratic eigenvalue problems. A. Målqvist and D. Peterseim. ESAIM Math. Model. Numer. Anal., 51(1):147–163, 2017.
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.
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.
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.
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.
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.
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.
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.
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.
17. Note on ”The smoothing effect of integration in $\mathbb {R}^d$ 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.
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.
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.
20. Subspace correction methods in algebraic multi-level frames. P. Zaspel. INS Preprint No. 1510, submitted to Linear Algebra and its Applications., june 2015.
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.
22. Globally structured three-dimensional analysis-suitable T-splines: definition, linear independence and $m$-graded local refinement. P. Morgenstern. SIAM J. Numer. Anal., 54(4):2163–2186, may 2016. Also available as INS Preprint No. 1508.
23. A new generalization of the ${P}_1$ 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.
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.
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.
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.
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.
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.
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.

## 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.
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.
3. Eliminating the pollution effect in Helmholtz problems by local subscale correction. D. Peterseim. Math. Comp., 86:1005–1036, 2017.
4. A multiscale method for porous microstructures. D. Brown and D. Peterseim. SIAM MMS, 14:1123–1152, 2016.
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.
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.
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.
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.
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.
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.
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.

## 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.

## 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.
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.
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.
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.
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.
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.
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.

## 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.
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.
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.
4. Schwarz type solvers for $hp$-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.
5. Inexact additive Schwarz solvers for $hp$-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.
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.
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.
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.

## 2010

1. The smoothing effect of integration in $\mathbb {R}^d$ 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.
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.

## 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.
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.

## 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.
2. Principal manifold learning by sparse grids. Chr. Feuersänger and M. Griebel. Computing, 2009. Also available as INS Preprint no 0801.

## 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.
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.
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.
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.

## 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.

## 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.
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.
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.
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.

## 2002

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