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Griebel, Michael

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Author ID: griebel.michael Recent zbMATH articles by "Griebel, Michael"
Published as: Griebel, Michael; Griebel, M.
Homepage: http://wissrech.ins.uni-bonn.de/people/griebel.html
External Links: MGP · Wikidata · dblp · GND
Documents Indexed: 152 Publications since 1989, including 24 Books
all top 5

Co-Authors

15 single-authored
21 Schweitzer, Marc Alexander
11 Oswald, Peter
10 Zenger, Christoph
8 Bungartz, Hans-Joachim
8 Garcke, Jochen
8 Zumbusch, Gerhard W.
6 Hamaekers, Jan
6 Harbrecht, Helmut
6 Rieger, Christian
5 Knapek, Stephan
5 Neunhoeffer, Tilman
4 Gerstner, Thomas
4 Kuo, Frances Y.
4 Oeltz, Daniel
4 Sloan, Ian Hugh
3 Arndt, Marcel
3 Bohn, Bastian
3 Holtz, Markus
3 Hullmann, Alexander
3 Klitz, Margrit
3 Koster, Frank
3 Röschke, D.
2 Burkow, M.
2 Dinh Dũng
2 Dornseifer, Thomas
2 Engel, Martin
2 Hegland, Markus
2 Margenov, Svetozar D.
2 Oettershagen, Jens
2 Regler, Hans
2 Roubíček, Tomáš
2 Rüttgers, A.
2 Schiekofer, Thomas
2 Theß, Michael
2 Vassilevski, Panayot Spirov
2 Zaspel, Peter
2 Zimmer, Stefan
2 Zwicknagl, Barbara Maria
1 Babuška, Ivo
1 Bokanowski, Olivier
1 Braun, Jürgen
1 Caglar, Attila
1 Chinnamsetty, Sambasiva Rao
1 Croce, Roberto
1 Dahlke, Stephan
1 Dahmen, Wolfgang A.
1 Dinkelmann, A.
1 Farge, Marie
1 Faßbender, Heike
1 Feuersänger, Christian
1 Goschnick, Ralf
1 Grauschopf, Thomas
1 Hackbusch, Wolfgang
1 Haep, Marcus
1 Heber, Frederik
1 Holtz, Olga
1 Huy, Vu Nhat
1 Iliev, Oleg P.
1 Klompmaker, Irene
1 Li, Guanglian
1 Metsch, Bram
1 Multerer, Michael D.
1 Novák, Václav
1 Pastrik, L.
1 Pitkäranta, Juhani
1 Ritter, Klaus
1 Rüde, Ulrich
1 Scherer, Karl
1 Scherrieble, A.
1 Schier, Alexander
1 Schmied, H.
1 Schneider, Kai
1 Schneider, Michael
1 Schneider, Reinhold
1 Schüller, Anton
1 Schwab, Christoph
1 Šittner, Petr
1 Starke, Gerhard
1 Stegmaier, Tabea
1 Stewart, Gilbert Wright
1 Thurner, Veronika
1 Wissel, Daniel
1 Wittmann, Dominik M.
1 Woźniakowski, Henryk
1 Yalamov, P. Yu.
1 Yserentant, Harry
all top 5

Serials

11 Lecture Notes in Computational Science and Engineering
8 Mathematics of Computation
8 SIAM Journal on Scientific Computing
7 Computing
6 Journal of Complexity
5 SIAM Journal on Numerical Analysis
5 Constructive Approximation
4 Computers and Fluids
3 Computer Methods in Applied Mechanics and Engineering
3 International Journal for Numerical Methods in Fluids
3 Journal of Computational and Applied Mathematics
3 Numerische Mathematik
3 Multiscale Modeling & Simulation
2 IMA Journal of Numerical Analysis
2 Journal of Computational Physics
2 Insurance Mathematics & Economics
2 Journal of Scientific Computing
2 Linear Algebra and its Applications
2 Numerical Linear Algebra with Applications
2 Computing and Visualization in Science
1 Computers & Mathematics with Applications
1 International Journal of Plasticity
1 Applied Mathematics and Computation
1 International Journal for Numerical Methods in Engineering
1 Journal of Approximation Theory
1 Mathematics and Computers in Simulation
1 Parallel Computing
1 Applied Numerical Mathematics
1 Numerical Algorithms
1 Continuum Mechanics and Thermodynamics
1 International Journal of Numerical Methods for Heat & Fluid Flow
1 East-West Journal of Numerical Mathematics
1 Advances in Computational Mathematics
1
1 The ANZIAM Journal
1 Foundations of Computational Mathematics
1 Journal of Machine Learning Research (JMLR)
1 Acta Numerica
1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
1 SIAM Monographs on Mathematical Modeling and Computation
1 Texts in Computational Science and Engineering
1 SIAM/ASA Journal on Uncertainty Quantification

Publications by Year

Citations contained in zbMATH Open

125 Publications have been cited 1,953 times in 1,196 Documents Cited by Year
Sparse grids. Zbl 1118.65388
Bungartz, Hans-Joachim; Griebel, Michael
300
2004
Numerical integration using sparse grids. Zbl 0921.65022
Gerstner, Thomas; Griebel, Michael
170
1998
Dimension-adaptive tensor-product quadrature. Zbl 1030.65015
Gerstner, T.; Griebel, M.
111
2003
On the abstract theory of additive and multiplicative Schwarz algorithms. Zbl 0826.65098
Griebel, M.; Oswald, P.
75
1995
A combination technique for the solution of sparse grid problems. Zbl 0785.65101
Griebel, Michael; Schneider, Michael; Zenger, Christoph
62
1992
A particle-partition of unity method for the solution of elliptic, parabolic, and hyperbolic PDEs. Zbl 0974.65090
Griebel, Michael; Schweitzer, Marc Alexander
52
2000
Tensor product type subspace splittings and multilevel iterative methods for anisotropic problems. Zbl 0826.65099
Griebel, M.; Oswald, P.
51
1995
Optimized general sparse grid approximation spaces for operator equations. Zbl 1198.65053
Griebel, M.; Knapek, S.
39
2009
Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences. Zbl 0918.65078
Griebel, M.
39
1998
A particle-partition of unity method. II: Efficient cover construction and reliable integration. Zbl 1011.65069
Griebel, Michael; Schweitzer, Marc Alexander
39
2002
A particle-partition of unity method. V: Boundary conditions. Zbl 1033.65102
Griebel, M.; Schweitzer, M. A.
38
2003
Optimized tensor-product approximation spaces. Zbl 0969.65107
Griebel, M.; Knapek, S.
37
2000
The problem of selecting the shape functions for a p-type finite element. Zbl 0705.73246
Babuška, I.; Griebel, M.; Pitkäranta, J.
34
1989
Sparse grids and related approximation schemes for higher dimensional problems. Zbl 1106.65332
Griebel, Michael
33
2006
Numerical simulation in fluid dynamics. A practical introduction. Zbl 0945.76001
Griebel, Michael; Dornseifer, Thomas; Neunhoeffer, Tilman
32
1997
Dimension-wise integration of high-dimensional functions with applications to finance. Zbl 1203.65056
Griebel, Michael; Holtz, Markus
31
2010
An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations. Zbl 1269.65076
Bokanowski, Olivier; Garcke, Jochen; Griebel, Michael; Klompmaker, Irene
28
2013
An algebraic multigrid method for linear elasticity. Zbl 1163.65336
Griebel, Michael; Oeltz, Daniel; Schweitzer, Marc Alexander
25
2003
Numerical simulation in molecular dynamics. Numerics, algorithms, parallelization, applications. Zbl 1131.76001
Griebel, Michael; Knapek, Stephan; Zumbusch, Gerhard
25
2007
Multilevel algorithms considered as iterative methods on semidefinite systems. Zbl 0818.65108
Griebel, Michael
23
1994
Sparse grids for the Schrödinger equation. Zbl 1145.65096
Griebel, Michael; Hamaekers, Jan
23
2007
A note on the complexity of solving Poisson’s equation for spaces of bounded mixed derivatives. Zbl 0954.65078
Bungartz, Hans-Joachim; Griebel, Michael
23
1999
On additive Schwarz preconditioners for sparse grid discretizations. Zbl 0791.65019
Griebel, M.; Oswald, P.
22
1994
Sparse grids for boundary integral equations. Zbl 0935.65131
Griebel, M.; Oswald, P.; Schiekofer, T.
22
1999
The smoothing effect of the ANOVA decomposition. Zbl 1205.65017
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.
20
2010
The smoothing effect of integration in \(\mathbb R^d\) and the ANOVA decomposition. Zbl 1264.41030
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.
19
2013
Data mining with sparse grids. Zbl 0987.62045
Garcke, J.; Griebel, M.; Thess, M.
19
2001
A particle-partition of unity method. III: A multilevel solver. Zbl 1027.65168
Griebel, Michael; Schweitzer, Marc Alexander
18
2002
Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions. Zbl 1423.76455
Croce, Roberto; Griebel, Michael; Schweitzer, Marc Alexander
17
2010
Modelling and numerical simulation of martensitic transformation in shape memory alloys. Zbl 1068.74588
Arndt, M.; Griebel, M.; Roubíček, T.
17
2003
Multilevel methods as iteration processes on generating systems. (Multilevelmethoden als Iterationsverfahren über Erzeugendensystemen.) Zbl 0823.65026
Griebel, Michael
16
1994
Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites. Zbl 1079.74665
Griebel, Michael; Hamaekers, Jan
16
2004
A sparse grid space-time discretization scheme for parabolic problems. Zbl 1132.35387
Griebel, M.; Oeltz, D.
15
2007
On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique. Zbl 0979.65101
Garcke, Jochen; Griebel, Michael
15
2000
Greedy and randomized versions of the multiplicative Schwarz method. Zbl 1251.65048
Griebel, Michael; Oswald, Peter
14
2012
Homogenization and numerical simulation of flow in geometries with textile microstructures. Zbl 1383.76445
Griebel, M.; Klitz, M.
14
2010
On the construction of sparse tensor product spaces. Zbl 1267.41012
Griebel, Michael; Harbrecht, Helmut
14
2013
Pointwise convergence of the combination technique for the Laplace equation. Zbl 0807.65105
Bungartz, H.-J.; Griebel, M.; Röschke, D.; Zenger, C.
14
1994
Derivation of higher order gradient continuum models from atomistic models for crystalline solids. Zbl 1093.74012
Arndt, M.; Griebel, M.
14
2005
Approximation of bi-variate functions: Singular value decomposition versus sparse grids. Zbl 1287.65009
Griebel, Michael; Harbrecht, Helmut
14
2014
Additive multilevel preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs. Zbl 0879.65085
Grauschopf, T.; Griebel, M.; Regler, H.
14
1997
Fast discrete Fourier transform on generalized sparse grids. Zbl 1316.65119
Griebel, Michael; Hamaekers, Jan
14
2014
A parallelizable and vectorizable multi-level algorithm on sparse grids. Zbl 0741.65090
Griebel, M.
13
1991
Solving incompressible two-phase flows on multi-GPU clusters. Zbl 1284.76012
Zaspel, Peter; Griebel, Michael
12
2013
Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves. Zbl 0945.65138
Griebel, M.; Zumbusch, G.
12
1999
Martensitic transformation in NiMnGa single crystals: numerical simulation and experiments. Zbl 1099.74049
Arndt, M.; Griebel, M.; Novák, V.; Roubíček, T.; Šittner, P.
11
2006
Extrapolation, combination, and sparse grid techniques for elliptic boundary value problems. Zbl 0824.65104
Bungartz, H.; Griebel, M.; Rüde, U.
10
1994
Adaptive wavelet solvers for the unsteady incompressible Navier-Stokes equations. Zbl 0985.35062
Griebel, Michael; Koster, Frank
10
2000
Hyperbolic cross approximation in infinite dimensions. Zbl 1349.41053
Dũng, Dinh; Griebel, Michael
10
2016
A general asset-liability management model for the efficient simulation of portfolios of life insurance policies. Zbl 1152.91581
Gerstner, Thomas; Griebel, Michael; Holtz, Markus; Goschnick, Ralf; Haep, Marcus
9
2008
Multiscale approximation and reproducing kernel Hilbert space methods. Zbl 1312.41025
Griebel, Michael; Rieger, Christian; Zwicknagl, Barbara
9
2015
On the convergence of the combination technique. Zbl 1316.65054
Griebel, Michael; Harbrecht, Helmut
9
2014
Space-time approximation with sparse grids. Zbl 1114.35082
Griebel, Michael; Oeltz, Daniel; Vassilevski, Panayot
9
2006
Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems. Zbl 1320.76079
Engel, Martin; Griebel, Michael
8
2006
A note on the construction of \(L\)-fold sparse tensor product spaces. Zbl 1283.41015
Griebel, Michael; Harbrecht, Helmut
8
2013
Multilevel Gauss-Seidel-algorithms for full and sparse grid problems. Zbl 0771.65084
Griebel, M.; Zenger, C.; Zimmer, S.
8
1993
On tensor product approximation of analytic functions. Zbl 1342.41036
Griebel, Michael; Oettershagen, Jens
8
2016
A particle-partition of unity method. VII: Adaptivity. Zbl 1119.65419
Griebel, Michael; Schweitzer, Marc Alexander
8
2007
A multigrid-homogenization method. Zbl 0884.76063
Griebel, M.; Knapek, S.
7
1997
A finite element method for density estimation with Gaussian process priors. Zbl 1211.65007
Griebel, Michael; Hegland, Markus
6
2010
Hash-storage techniques for adaptive multilevel solvers and their domain decomposition parallelization. Zbl 0910.65084
Griebel, Michael; Zumbusch, Gerhard
6
1998
Coarse grid classification: a parallel coarsening scheme for algebraic multigrid methods. Zbl 1174.65544
Griebel, Michael; Metsch, Bram; Oeltz, Daniel; Schweitzer, Marc Alexander
6
2006
The efficient solution of fluid dynamics problems by the combination technique. Zbl 0824.76064
Griebel, Michael; Thurner, Veronika
6
1995
Algebraic multigrid methods for the solution of the Navier-Stokes equations in complicated geometries. Zbl 0906.76046
Griebel, Michael; Neunhoeffer, Tilman; Regler, Hans
6
1998
Principal manifold learning by sparse grids. Zbl 1171.65054
Feuersänger, Christian; Griebel, Michael
5
2009
Optimal scaling parameters for sparse grid discretizations. Zbl 1349.65557
Griebel, Michael; Hullmann, Alexander; Oswald, Peter
5
2015
Adaptive sparse grids for hyperbolic conservation laws. Zbl 0929.65075
Griebel, Michael; Zumbusch, Gerhard
5
1999
Robust norm equivalencies for diffusion problems. Zbl 1117.65155
Griebel, Michael; Scherer, Karl; Schweitzer, Marc Alexander
5
2007
Note on “The smoothing effect of integration in \(\mathbb {R}^d\) and the ANOVA decomposition”. Zbl 1365.41020
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.
5
2017
A multigrid method for constrained optimal control problems. Zbl 1222.49034
Engel, M.; Griebel, M.
4
2011
A sparse grid based method for generative dimensionality reduction of high-dimensional data. Zbl 1351.62120
Bohn, Bastian; Garcke, Jochen; Griebel, Michael
4
2016
A particle-partition of unity method. VI: A \(p\)-robust multilevel solver. Zbl 1065.65138
Griebel, Michael; Oswald, Peter; Schweitzer, Marc Alexander
4
2005
Simulation of droplet impact with dynamic contact angle boundary conditions. Zbl 1321.76051
Griebel, Michael; Klitz, Margrit
4
2014
Dimension-adaptive sparse grid quadrature for integrals with boundary singularities. Zbl 1316.65032
Griebel, Michael; Oettershagen, Jens
4
2014
Classification with sparse grids using simplicial basis functions. Zbl 1088.68550
Garcke, Jochen; Griebel, Michael
4
2002
Parallel adaptive subspace correction schemes with applications to elasticity. Zbl 0980.74079
Griebel, Michael; Zumbusch, Gerhard
4
2000
Numerical simulation in the fluid dynamics. A practice-oriented introduction. (Numerische Simulation in der Strömungslehre. Eine praxisorientierte Einführung.) Zbl 0873.76001
Griebel, Michael; Dornseifer, Thomas; Neunhoeffer, Tilman
4
1995
Meshfree methods for partial differential equations. International workshop, Univ. Bonn, Germany, September 11–14, 2001. Zbl 0996.00042
Griebel, Michael (ed.); Schweitzer, Marc Alexander (ed.)
4
2002
A proof of convergence for the combination technique for the Laplace equation using tools of symbolic computation. Zbl 1037.65508
Bungartz, H.; Griebel, M.; Röschke, D.; Zenger, C.
4
1996
Fast approximation of the discrete Gauss transform in higher dimensions. Zbl 1273.65192
Griebel, Michael; Wissel, Daniel
4
2013
On the decay rate of the singular values of bivariate functions. Zbl 1391.41007
Griebel, Michael; Li, Guanglian
4
2018
Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance. Zbl 1162.91412
Gerstner, Thomas; Griebel, Michael; Holtz, Markus
3
2009
Parallel domain-oriented multilevel methods. Zbl 0834.65019
Griebel, Michael
3
1995
Parallel point- and domain-oriented multilevel methods for elliptic PDE’s on workstation networks. Zbl 0858.65122
Griebel, Michael; Neunhoeffer, Tilman
3
1996
Adaptive wavelet methods for the Navier-Stokes equations. Zbl 1019.76034
Schneider, Kai; Farge, Marie; Koster, F.; Griebel, M.
3
2001
The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth. Zbl 1365.41021
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.
3
2017
\(\varepsilon\)-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs. Zbl 1391.41018
Dũng, Dinh; Griebel, Michael; Huy, Vu Nhat; Rieger, Christian
3
2018
Multiscale methods for the simulation of turbulent flows. Zbl 1088.76017
Griebel, Michael; Koster, Frank
2
2003
On the optimal convergence rate of universal and nonuniversal algorithms for multivariate integration and approximation. Zbl 1096.65028
Griebel, Michael; Wozniakowski, Henryk
2
2006
On a constructive proof of Kolmogorov’s superposition theorem. Zbl 1194.26020
Braun, Jürgen; Griebel, Michael
2
2009
On a multilevel preconditioner and its condition numbers for the discretized Laplacian on full and sparse grids in higher dimensions. Zbl 1330.65051
Griebel, Michael; Hullmann, Alexander
2
2014
Introduction to computer graphics. (Einführung in die Computergraphik.) Zbl 0869.68102
Bungartz, Hans-Joachim; Griebel, Michael; Zenger, Christoph
2
1996
Parallel multigrid in an adaptive PDE solver based on hashing. Zbl 0923.68066
Griebel, Michael; Zumbusch, Gerhard
2
1998
A particle-parition of unity method. IV: Parallelization. (With color plate 5, p. 463). Zbl 1016.65100
Griebel, Michael; Schweitzer, Marc Alexander
2
2002
Numerical simulation in the dynamics of molecules. Numerics, algorithms, parallelization, applications. (Numerische Simulation in der Moleküldynamik. Numerik, Algorithmen, Parallelisierung, Anwendungen.) Zbl 1038.81004
Griebel, Michael; Knapek, Stephan; Zumbusch, Gerhard; Caglar, Attila
2
2004
A wavelet based sparse grid method for the electronic Schrödinger equation. Zbl 1130.65134
Griebel, Michael; Hamaekers, Jan
2
2006
Meshfree methods for partial differential equations III. Selected papers based on the presentations at the 3rd international workshop, Bonn, Germany, September 12–15, 2005. Zbl 1104.65003
Griebel, Michael (ed.); Schweitzer, Marc A. (ed.)
2
2007
Photorealistic visualization and fluid animation: coupling of Maya with a two-phase Navier-Stokes fluid solver. Zbl 1358.76026
Zaspel, Peter; Griebel, Michael
2
2011
Stable splittings of Hilbert spaces of functions of infinitely many variables. Zbl 1378.46019
Griebel, Michael; Oswald, Peter
2
2017
Error estimates for multivariate regression on discretized function spaces. Zbl 1403.62058
Bohn, Bastian; Griebel, Michael
2
2017
Multilevel quadrature for elliptic parametric partial differential equations in case of polygonal approximations of curved domains. Zbl 1434.65256
Griebel, Michael; Harbrecht, Helmut; Multerer, Michael D.
1
2020
On the decay rate of the singular values of bivariate functions. Zbl 1391.41007
Griebel, Michael; Li, Guanglian
4
2018
\(\varepsilon\)-dimension in infinite dimensional hyperbolic cross approximation and application to parametric elliptic PDEs. Zbl 1391.41018
Dũng, Dinh; Griebel, Michael; Huy, Vu Nhat; Rieger, Christian
3
2018
Stochastic subspace correction in Hilbert space. Zbl 1416.65084
Griebel, Michael; Oswald, Peter
2
2018
Multiscale simulation of polymeric fluids using the sparse grid combination technique. Zbl 1426.76418
Rüttgers, A.; Griebel, M.
1
2018
Note on “The smoothing effect of integration in \(\mathbb {R}^d\) and the ANOVA decomposition”. Zbl 1365.41020
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.
5
2017
The ANOVA decomposition of a non-smooth function of infinitely many variables can have every term smooth. Zbl 1365.41021
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.
3
2017
Stable splittings of Hilbert spaces of functions of infinitely many variables. Zbl 1378.46019
Griebel, Michael; Oswald, Peter
2
2017
Error estimates for multivariate regression on discretized function spaces. Zbl 1403.62058
Bohn, Bastian; Griebel, Michael
2
2017
Upwind schemes for scalar advection-dominated problems in the discrete exterior calculus. Zbl 1391.76545
Griebel, Michael; Rieger, Christian; Schier, Alexander
2
2017
Meshfree methods for partial differential equations VIII. Selected contributions based on the presentations at the 8th international workshop, Bonn, Germany, September 7–9, 2015. Zbl 1369.65003
Griebel, Michael; Schweitzer, Marc Alexander
1
2017
Reproducing kernel Hilbert spaces for parametric partial differential equations. Zbl 1371.35345
Griebel, Michael; Rieger, Christian
1
2017
Hyperbolic cross approximation in infinite dimensions. Zbl 1349.41053
Dũng, Dinh; Griebel, Michael
10
2016
On tensor product approximation of analytic functions. Zbl 1342.41036
Griebel, Michael; Oettershagen, Jens
8
2016
A sparse grid based method for generative dimensionality reduction of high-dimensional data. Zbl 1351.62120
Bohn, Bastian; Garcke, Jochen; Griebel, Michael
4
2016
Schwarz iterative methods: infinite space splittings. Zbl 1356.65145
Griebel, Michael; Oswald, Peter
1
2016
A full three dimensional numerical simulation of the sediment transport and the scouring at a rectangular obstacle. Zbl 1390.76049
Burkow, M.; Griebel, M.
1
2016
Multiscale approximation and reproducing kernel Hilbert space methods. Zbl 1312.41025
Griebel, Michael; Rieger, Christian; Zwicknagl, Barbara
9
2015
Optimal scaling parameters for sparse grid discretizations. Zbl 1349.65557
Griebel, Michael; Hullmann, Alexander; Oswald, Peter
5
2015
Simulation of the oil storage process in the scopa of specialized bees. Zbl 1390.76942
Rüttgers, A.; Griebel, M.; Pastrik, L.; Schmied, H.; Wittmann, D.; Scherrieble, A.; Dinkelmann, A.; Stegmaier, T.
1
2015
Approximation of bi-variate functions: Singular value decomposition versus sparse grids. Zbl 1287.65009
Griebel, Michael; Harbrecht, Helmut
14
2014
Fast discrete Fourier transform on generalized sparse grids. Zbl 1316.65119
Griebel, Michael; Hamaekers, Jan
14
2014
On the convergence of the combination technique. Zbl 1316.65054
Griebel, Michael; Harbrecht, Helmut
9
2014
Simulation of droplet impact with dynamic contact angle boundary conditions. Zbl 1321.76051
Griebel, Michael; Klitz, Margrit
4
2014
Dimension-adaptive sparse grid quadrature for integrals with boundary singularities. Zbl 1316.65032
Griebel, Michael; Oettershagen, Jens
4
2014
On a multilevel preconditioner and its condition numbers for the discretized Laplacian on full and sparse grids in higher dimensions. Zbl 1330.65051
Griebel, Michael; Hullmann, Alexander
2
2014
Singular phenomena and scaling in mathematical models. Zbl 1278.00016
Griebel, Michael
1
2014
A bond order dissection ANOVA approach for efficient electronic structure calculations. Zbl 1316.81094
Griebel, Michael; Hamaekers, Jan; Heber, Frederik
1
2014
Dimensionality reduction of high-dimensional data with a nonlinear principal component aligned generative topographic mapping. Zbl 1418.62135
Griebel, M.; Hullmann, A.
1
2014
An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations. Zbl 1269.65076
Bokanowski, Olivier; Garcke, Jochen; Griebel, Michael; Klompmaker, Irene
28
2013
The smoothing effect of integration in \(\mathbb R^d\) and the ANOVA decomposition. Zbl 1264.41030
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.
19
2013
On the construction of sparse tensor product spaces. Zbl 1267.41012
Griebel, Michael; Harbrecht, Helmut
14
2013
Solving incompressible two-phase flows on multi-GPU clusters. Zbl 1284.76012
Zaspel, Peter; Griebel, Michael
12
2013
A note on the construction of \(L\)-fold sparse tensor product spaces. Zbl 1283.41015
Griebel, Michael; Harbrecht, Helmut
8
2013
Fast approximation of the discrete Gauss transform in higher dimensions. Zbl 1273.65192
Griebel, Michael; Wissel, Daniel
4
2013
Sparse grids and applications. Selected contributions based on the presentations at the workshop, Bonn, Germany, May 16–20, 2011. Zbl 1330.65005
Garcke, Jochen; Griebel, Michael
1
2013
Greedy and randomized versions of the multiplicative Schwarz method. Zbl 1251.65048
Griebel, Michael; Oswald, Peter
14
2012
A multigrid method for constrained optimal control problems. Zbl 1222.49034
Engel, M.; Griebel, M.
4
2011
Photorealistic visualization and fluid animation: coupling of Maya with a two-phase Navier-Stokes fluid solver. Zbl 1358.76026
Zaspel, Peter; Griebel, Michael
2
2011
Dimension-wise integration of high-dimensional functions with applications to finance. Zbl 1203.65056
Griebel, Michael; Holtz, Markus
31
2010
The smoothing effect of the ANOVA decomposition. Zbl 1205.65017
Griebel, Michael; Kuo, Frances Y.; Sloan, Ian H.
20
2010
Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions. Zbl 1423.76455
Croce, Roberto; Griebel, Michael; Schweitzer, Marc Alexander
17
2010
Homogenization and numerical simulation of flow in geometries with textile microstructures. Zbl 1383.76445
Griebel, M.; Klitz, M.
14
2010
A finite element method for density estimation with Gaussian process priors. Zbl 1211.65007
Griebel, Michael; Hegland, Markus
6
2010
Data mining for the category management in the retail market. Zbl 1202.00016
Garcke, Jochen; Griebel, Michael; Thess, Michael
1
2010
Optimized general sparse grid approximation spaces for operator equations. Zbl 1198.65053
Griebel, M.; Knapek, S.
39
2009
Principal manifold learning by sparse grids. Zbl 1171.65054
Feuersänger, Christian; Griebel, Michael
5
2009
Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance. Zbl 1162.91412
Gerstner, Thomas; Griebel, Michael; Holtz, Markus
3
2009
On a constructive proof of Kolmogorov’s superposition theorem. Zbl 1194.26020
Braun, Jürgen; Griebel, Michael
2
2009
A general asset-liability management model for the efficient simulation of portfolios of life insurance policies. Zbl 1152.91581
Gerstner, Thomas; Griebel, Michael; Holtz, Markus; Goschnick, Ralf; Haep, Marcus
9
2008
Meshfree methods for partial differential equations IV. Papers based on the presentations at the 4th international workshop, Bonn, Germany, September 17–20, 2007. Zbl 1149.65002
Griebel, Michael; Schweitzer, Marc Alexander
1
2008
Numerical simulation in molecular dynamics. Numerics, algorithms, parallelization, applications. Zbl 1131.76001
Griebel, Michael; Knapek, Stephan; Zumbusch, Gerhard
25
2007
Sparse grids for the Schrödinger equation. Zbl 1145.65096
Griebel, Michael; Hamaekers, Jan
23
2007
A sparse grid space-time discretization scheme for parabolic problems. Zbl 1132.35387
Griebel, M.; Oeltz, D.
15
2007
A particle-partition of unity method. VII: Adaptivity. Zbl 1119.65419
Griebel, Michael; Schweitzer, Marc Alexander
8
2007
Robust norm equivalencies for diffusion problems. Zbl 1117.65155
Griebel, Michael; Scherer, Karl; Schweitzer, Marc Alexander
5
2007
Meshfree methods for partial differential equations III. Selected papers based on the presentations at the 3rd international workshop, Bonn, Germany, September 12–15, 2005. Zbl 1104.65003
Griebel, Michael; Schweitzer, Marc A.
2
2007
Sparse grids and related approximation schemes for higher dimensional problems. Zbl 1106.65332
Griebel, Michael
33
2006
Martensitic transformation in NiMnGa single crystals: numerical simulation and experiments. Zbl 1099.74049
Arndt, M.; Griebel, M.; Novák, V.; Roubíček, T.; Šittner, P.
11
2006
Space-time approximation with sparse grids. Zbl 1114.35082
Griebel, Michael; Oeltz, Daniel; Vassilevski, Panayot
9
2006
Flow simulation on moving boundary-fitted grids and application to fluid-structure interaction problems. Zbl 1320.76079
Engel, Martin; Griebel, Michael
8
2006
Coarse grid classification: a parallel coarsening scheme for algebraic multigrid methods. Zbl 1174.65544
Griebel, Michael; Metsch, Bram; Oeltz, Daniel; Schweitzer, Marc Alexander
6
2006
On the optimal convergence rate of universal and nonuniversal algorithms for multivariate integration and approximation. Zbl 1096.65028
Griebel, Michael; Wozniakowski, Henryk
2
2006
A wavelet based sparse grid method for the electronic Schrödinger equation. Zbl 1130.65134
Griebel, Michael; Hamaekers, Jan
2
2006
Derivation of higher order gradient continuum models from atomistic models for crystalline solids. Zbl 1093.74012
Arndt, M.; Griebel, M.
14
2005
A particle-partition of unity method. VI: A \(p\)-robust multilevel solver. Zbl 1065.65138
Griebel, Michael; Oswald, Peter; Schweitzer, Marc Alexander
4
2005
Meshfree methods for partial differential equations II. Selected contributions of the second international workshop, Bonn, Germany, September 15–17, 2003. Zbl 1055.65003
Griebel, Michael; Schweitzer, Marc A.
1
2005
Sparse grids. Zbl 1118.65388
Bungartz, Hans-Joachim; Griebel, Michael
300
2004
Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites. Zbl 1079.74665
Griebel, Michael; Hamaekers, Jan
16
2004
Numerical simulation in the dynamics of molecules. Numerics, algorithms, parallelization, applications. (Numerische Simulation in der Moleküldynamik. Numerik, Algorithmen, Parallelisierung, Anwendungen.) Zbl 1038.81004
Griebel, Michael; Knapek, Stephan; Zumbusch, Gerhard; Caglar, Attila
2
2004
Dimension-adaptive tensor-product quadrature. Zbl 1030.65015
Gerstner, T.; Griebel, M.
111
2003
A particle-partition of unity method. V: Boundary conditions. Zbl 1033.65102
Griebel, M.; Schweitzer, M. A.
38
2003
An algebraic multigrid method for linear elasticity. Zbl 1163.65336
Griebel, Michael; Oeltz, Daniel; Schweitzer, Marc Alexander
25
2003
Modelling and numerical simulation of martensitic transformation in shape memory alloys. Zbl 1068.74588
Arndt, M.; Griebel, M.; Roubíček, T.
17
2003
Multiscale methods for the simulation of turbulent flows. Zbl 1088.76017
Griebel, Michael; Koster, Frank
2
2003
A particle-partition of unity method. II: Efficient cover construction and reliable integration. Zbl 1011.65069
Griebel, Michael; Schweitzer, Marc Alexander
39
2002
A particle-partition of unity method. III: A multilevel solver. Zbl 1027.65168
Griebel, Michael; Schweitzer, Marc Alexander
18
2002
Classification with sparse grids using simplicial basis functions. Zbl 1088.68550
Garcke, Jochen; Griebel, Michael
4
2002
Meshfree methods for partial differential equations. International workshop, Univ. Bonn, Germany, September 11–14, 2001. Zbl 0996.00042
Griebel, Michael; Schweitzer, Marc Alexander
4
2002
A particle-parition of unity method. IV: Parallelization. (With color plate 5, p. 463). Zbl 1016.65100
Griebel, Michael; Schweitzer, Marc Alexander
2
2002
Data mining with sparse grids. Zbl 0987.62045
Garcke, J.; Griebel, M.; Thess, M.
19
2001
Adaptive wavelet methods for the Navier-Stokes equations. Zbl 1019.76034
Schneider, Kai; Farge, Marie; Koster, F.; Griebel, M.
3
2001
A particle-partition of unity method for the solution of elliptic, parabolic, and hyperbolic PDEs. Zbl 0974.65090
Griebel, Michael; Schweitzer, Marc Alexander
52
2000
Optimized tensor-product approximation spaces. Zbl 0969.65107
Griebel, M.; Knapek, S.
37
2000
On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique. Zbl 0979.65101
Garcke, Jochen; Griebel, Michael
15
2000
Adaptive wavelet solvers for the unsteady incompressible Navier-Stokes equations. Zbl 0985.35062
Griebel, Michael; Koster, Frank
10
2000
Parallel adaptive subspace correction schemes with applications to elasticity. Zbl 0980.74079
Griebel, Michael; Zumbusch, Gerhard
4
2000
A note on the complexity of solving Poisson’s equation for spaces of bounded mixed derivatives. Zbl 0954.65078
Bungartz, Hans-Joachim; Griebel, Michael
23
1999
Sparse grids for boundary integral equations. Zbl 0935.65131
Griebel, M.; Oswald, P.; Schiekofer, T.
22
1999
Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves. Zbl 0945.65138
Griebel, M.; Zumbusch, G.
12
1999
Adaptive sparse grids for hyperbolic conservation laws. Zbl 0929.65075
Griebel, Michael; Zumbusch, Gerhard
5
1999
Mathematical modeling and numerical simulation of freezing processes of a supercooled melt under consideration of density changes. Zbl 1015.76088
Griebel, M.; Merz, W.; Neunhoeffer, T.
1
1999
Numerical integration using sparse grids. Zbl 0921.65022
Gerstner, Thomas; Griebel, Michael
170
1998
Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences. Zbl 0918.65078
Griebel, M.
39
1998
Hash-storage techniques for adaptive multilevel solvers and their domain decomposition parallelization. Zbl 0910.65084
Griebel, Michael; Zumbusch, Gerhard
6
1998
Algebraic multigrid methods for the solution of the Navier-Stokes equations in complicated geometries. Zbl 0906.76046
Griebel, Michael; Neunhoeffer, Tilman; Regler, Hans
6
1998
Parallel multigrid in an adaptive PDE solver based on hashing. Zbl 0923.68066
Griebel, Michael; Zumbusch, Gerhard
2
1998
Numerical simulation in fluid dynamics. A practical introduction. Zbl 0945.76001
Griebel, Michael; Dornseifer, Thomas; Neunhoeffer, Tilman
32
1997
Additive multilevel preconditioners based on bilinear interpolation, matrix-dependent geometric coarsening and algebraic multigrid coarsening for second-order elliptic PDEs. Zbl 0879.65085
Grauschopf, T.; Griebel, M.; Regler, H.
14
1997
A multigrid-homogenization method. Zbl 0884.76063
Griebel, M.; Knapek, S.
7
1997
...and 25 more Documents
all top 5

Cited by 1,926 Authors

58 Griebel, Michael
29 Schwab, Christoph
26 Harbrecht, Helmut
15 Brenner, Susanne Cecelia
15 Bungartz, Hans-Joachim
15 Tempone, Raúl F.
14 Nobile, Fabio
12 Dinh Dũng
12 Ullrich, Tino
11 Stevenson, Rob P.
10 Oswald, Peter
10 Peters, Michael D.
10 Schweitzer, Marc Alexander
10 Tamellini, Lorenzo
10 Xu, Yuesheng
9 Chen, Peng
9 Kuo, Frances Y.
9 Rahman, Sharif
9 Schillinger, Dominik
9 Schneider, Reinhold
9 Zikatanov, Ludmil T.
8 Cheng, Yingda
8 Chernov, Alexey
8 Dick, Josef
8 Gunzburger, Max D.
8 Hegland, Markus
8 Jiang, Ying
8 Le Maître, Olivier P.
8 Rieger, Christian
8 Xu, Jinchao
7 Babuška, Ivo
7 Carey, Graham Francis
7 Davis, Christopher B.
7 Garcke, Jochen
7 Kämmerer, Lutz
7 Karniadakis, George Em
7 Khoromskij, Boris N.
7 Knio, Omar M.
7 Narayan, Akil C.
7 Peherstorfer, Benjamin
7 Roubíček, Tomáš
7 Sickel, Winfried
7 Stefanelli, Ulisse
6 Chinesta, Francisco
6 Coutinho, Alvaro L. G. A.
6 Dölz, Jürgen
6 Hackbusch, Wolfgang
6 Jakeman, John Davis
6 Neckel, Tobias
6 Pflüger, Dirk
6 Potts, Daniel
6 Shu, Shi
6 Siebenmorgen, Markus
6 Sloan, Ian Hugh
6 Venturi, Daniele
6 Volkmer, Toni
6 Wasilkowski, Grzegorz W.
6 Webster, Clayton G.
6 Xiao, Yingxiong
6 Zabaras, Nicholas J.
5 Abdulle, Assyr
5 Dolgov, Sergey V.
5 Gnewuch, Michael
5 Haji-Ali, Abdul-Lateef
5 Hoang, Viet Ha
5 Kalise, Dante
5 Kunisch, Karl
5 Leovey, Hernan
5 Matthies, Hermann Georg
5 Nouy, Anthony
5 Novak, Erich
5 Nuyens, Dirk
5 Ruess, Martin
5 Zhang, Guannan
5 Zhang, Qinghui
4 Ammar, Amine
4 Cohen, Albert
4 Fackeldey, Konstantin
4 Fernández-Méndez, Sonia
4 Ganapathysubramanian, Baskar
4 Gorobets, Andrey V.
4 Guo, Wei
4 Heuer, Norbert
4 Hinrichs, Aicke
4 Holtz, Markus
4 Kestler, Sebastian
4 Kühn, Thomas
4 Li, Guanglian
4 Lötstedt, Per
4 Luo, Xiaopeng
4 Mandel, Jan
4 Oh, Hae-Soo
4 Pflaum, Christoph
4 Quarteroni, Alfio M.
4 Reisinger, Christoph
4 Rozza, Gianluigi
4 Rüde, Ulrich
4 Schillings, Claudia
4 Sukumar, Natarajan
4 Tan, Yongji
...and 1,826 more Authors
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Cited in 207 Serials

103 Computer Methods in Applied Mechanics and Engineering
96 Journal of Computational Physics
56 SIAM Journal on Scientific Computing
50 Numerische Mathematik
43 Journal of Computational and Applied Mathematics
35 Computers & Mathematics with Applications
35 Mathematics of Computation
33 Journal of Scientific Computing
28 Applied Numerical Mathematics
25 Journal of Complexity
24 Computational Mechanics
23 International Journal for Numerical Methods in Engineering
23 SIAM/ASA Journal on Uncertainty Quantification
21 Applied Mathematics and Computation
20 Computers and Fluids
18 SIAM Journal on Numerical Analysis
18 Numerical Linear Algebra with Applications
16 Computing
15 Advances in Computational Mathematics
13 International Journal for Numerical Methods in Fluids
13 Constructive Approximation
13 Engineering Analysis with Boundary Elements
12 Journal of Approximation Theory
12 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
10 Numerical Algorithms
10 Linear Algebra and its Applications
10 Foundations of Computational Mathematics
9 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
9 Applied Mathematical Modelling
9 Archives of Computational Methods in Engineering
9 Multiscale Modeling & Simulation
8 BIT
8 Mathematics and Computers in Simulation
8 International Journal of Computer Mathematics
8 Continuum Mechanics and Thermodynamics
8 Computing and Visualization in Science
7 Insurance Mathematics & Economics
7 Applied and Computational Harmonic Analysis
6 Computer Physics Communications
6 Numerical Methods for Partial Differential Equations
6 Mathematical Problems in Engineering
6 Computational Geosciences
5 Journal of the Mechanics and Physics of Solids
5 SIAM Review
5 Computational Optimization and Applications
5 The Journal of Fourier Analysis and Applications
5 Quantitative Finance
5 Computational Methods in Applied Mathematics
5 Structural and Multidisciplinary Optimization
5 Science China. Mathematics
4 Journal of Mathematical Analysis and Applications
4 SIAM Journal on Matrix Analysis and Applications
4 Journal of Mathematical Chemistry
4 Stochastic and Partial Differential Equations. Analysis and Computations
3 Archive for Rational Mechanics and Analysis
3 Journal of Fluid Mechanics
3 Calcolo
3 Journal of Integral Equations and Applications
3 Journal of Global Optimization
3 Journal of Mathematical Imaging and Vision
3 Communications in Numerical Methods in Engineering
3 Mathematics and Mechanics of Solids
3 SIAM Journal on Applied Dynamical Systems
3 Acta Numerica
3 International Journal for Numerical Methods in Biomedical Engineering
2 Acta Mechanica
2 International Journal of Plasticity
2 Journal of the Franklin Institute
2 Mathematical Methods in the Applied Sciences
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Physica D
2 Parallel Computing
2 Journal of Economic Dynamics & Control
2 Applications of Mathematics
2 Computational Statistics
2 Physics of Fluids
2 Monte Carlo Methods and Applications
2 Applied Mathematical Finance
2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
2 European Journal of Mechanics. A. Solids
2 Acta Mathematica Sinica. English Series
2 Communications in Nonlinear Science and Numerical Simulation
2 Engineering Computations
2 Journal of Machine Learning Research (JMLR)
2 Analysis and Applications (Singapore)
2 International Journal of Computational Methods
2 GAMM-Mitteilungen
2 SIAM Journal on Financial Mathematics
2 European Actuarial Journal
2 The Journal of Mathematical Neuroscience
2 Statistics and Computing
2 Research in the Mathematical Sciences
2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys
2 SMAI Journal of Computational Mathematics
1 Applicable Analysis
1 Artificial Intelligence
1 Biological Cybernetics
1 The Canadian Journal of Statistics
1 International Journal of Engineering Science
1 International Journal of Systems Science
...and 107 more Serials
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Cited in 42 Fields

861 Numerical analysis (65-XX)
315 Partial differential equations (35-XX)
189 Mechanics of deformable solids (74-XX)
158 Fluid mechanics (76-XX)
129 Probability theory and stochastic processes (60-XX)
117 Approximations and expansions (41-XX)
74 Statistics (62-XX)
53 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
50 Computer science (68-XX)
48 Calculus of variations and optimal control; optimization (49-XX)
43 Harmonic analysis on Euclidean spaces (42-XX)
40 Operations research, mathematical programming (90-XX)
35 Functional analysis (46-XX)
33 Systems theory; control (93-XX)
28 Linear and multilinear algebra; matrix theory (15-XX)
23 Operator theory (47-XX)
23 Optics, electromagnetic theory (78-XX)
23 Statistical mechanics, structure of matter (82-XX)
21 Biology and other natural sciences (92-XX)
20 Classical thermodynamics, heat transfer (80-XX)
19 Quantum theory (81-XX)
13 Dynamical systems and ergodic theory (37-XX)
13 Geophysics (86-XX)
13 Information and communication theory, circuits (94-XX)
11 Ordinary differential equations (34-XX)
10 Integral equations (45-XX)
8 Special functions (33-XX)
8 Mechanics of particles and systems (70-XX)
6 Number theory (11-XX)
6 Real functions (26-XX)
4 Difference and functional equations (39-XX)
4 Global analysis, analysis on manifolds (58-XX)
3 Potential theory (31-XX)
2 Differential geometry (53-XX)
2 Astronomy and astrophysics (85-XX)
1 General and overarching topics; collections (00-XX)
1 Mathematical logic and foundations (03-XX)
1 Commutative algebra (13-XX)
1 Topological groups, Lie groups (22-XX)
1 Measure and integration (28-XX)
1 General topology (54-XX)
1 Relativity and gravitational theory (83-XX)

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