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- Thomas Gerstner, Michael Griebel
- Computing
- 2003

We consider the numerical integration of multivariate functions defined over the unit hypercube. Here, we especially address the highâ€“dimensional case, where in general the curse of dimension isâ€¦ (More)

- Thomas Gerstner, Michael Griebel
- Numerical Algorithms
- 1998

We present new and review existing algorithms for the numerical integration of multivariate functions defined over d-dimensional cubes using several variants of the sparse grid method firstâ€¦ (More)

- Michael Griebel
- 2009

The efficient numerical treatment of high-dimensional problems is hampered by the curse of dimensionality. We review approximation techniques which overcome this problem to some extent. Here, weâ€¦ (More)

- Michael Griebel
- Computing
- 1997

We present a multilevel approach for the solution of partial differential equations. It is based on a multiscale basis which is constructed from a one-dimensional multiscale basis by the tensorâ€¦ (More)

This paper is concerned with the construction of optimized grids and approximation spaces for elliptic diierential and integral equations. The main result is the analysis of the approximation of theâ€¦ (More)

We propose a modiied approach to the abstract convergence theory of the additive and multiplicative Schwarz iterative methods associated with a subspace splitting for solving symmetric positiveâ€¦ (More)

- Michael Griebel
- SIAM J. Scientific Computing
- 1994

For the representation of piecewise d-linear functions, instead of the usual nite element basis, we introduce a generating system that contains the nodal basis functions of the nest level and of allâ€¦ (More)

- Michael Griebel, Peter Oswald
- Adv. Comput. Math.
- 1995

We describe tensor product type techniques to derive robust solvers for anisotropic elliptic model problems on rectangular domains in ~d. Our analysis is based on the theory of additive subspaceâ€¦ (More)

- Michael Griebel, Stephan Knapek
- Math. Comput.
- 2009

This paper is concerned with the construction of optimized sparse grid approximation spaces for elliptic pseudodifferential operators of arbitrary order. Based on the framework of tensor-productâ€¦ (More)

- Jochen Garcke, Michael Griebel, M. Thess
- Computing
- 2001

(h n âˆ’1 n d âˆ’1) instead of O(h n âˆ’d ) grid points and unknowns are involved. Here d denotes the dimension of the feature space and h n = 2 âˆ’n gives the mesh size. To be precise, we suggest to use theâ€¦ (More)