Mathematisch-Naturwissenschaftliche Fakultät: Suche
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An adaptive sparse grid semi-Lagrangian scheme for first order Hamilton-Jacobi Bellman equations
(2012-09)
We propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions ......
Dimensionality reduction of high-dimensional data with a non-linear principal component aligned generative topographic mapping
(2013-07)
Most high-dimensional real-life data exhibit some dependencies such that data points do not populate the whole data space but lie approximately on a lower-dimensional manifold. A major problem in many data mining applications ...
3D incompressible two-phase flow benchmark computations for rising droplets
(2014-03)
We perform 3D incompressible two-phase flow simulations of rising droplets. Based on a similar 2D benchmark, a 3D benchmark configuration with two test cases is formulated in which we compare the flow solvers DROPS, NaSt3DGPF ...
An adaptive multiscale approach for electronic structure methods
(2016)
In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr¨odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the bond ...
A wavelet based sparse grid method for the electronic Schrödinger equation
(2006-05)
We present a direct discretization of the electronic Schrödinger equation. It is based on one-dimensional Meyer wavelets from which we build an anisotropic multiresolution analysis for general particle spaces by a tensor ...
Numerical simulation of the temporal evolution of a three dimensional barchanoid dune and the corresponding sediment dynamics
(2016-09)
In this paper we present the results of the numerical simulation of a three-dimensional current-driven sediment transport process. In detail, the temporal evolution of a barchanoid dune is studied. Two phenomena are treated ...
On a multilevel preconditioner and its condition numbers for the discretized Laplacian on full and sparse grids in higher dimensions
(2013-01)
We first discretize the d-dimensional Laplacian in (0, 1)d for varying d on a full uniform grid and build a new preconditioner that is based on a multilevel generating system. We show that the resulting condition ......
A dimension-adaptive combination technique for uncertainty quantification
(2022-04)
We present an adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic PDE where the diffusion coefficient is parametrized by means of a Karhunen-Loève expansion. The ...
Fast approximation of the discrete Gauss transform in higher dimensions
(2011-10)
We present a novel approach for the fast approximation of the discrete Gauss transform in higher dimensions. The algorithm is based on the dual-tree technique and introduces a new Taylor series expansion. It compares ...
An adaptive sparse grid approach for time series predictions
(2012-01)
A real valued, deterministic and stationary time series can be embedded in a — sometimes high-dimensional — real vector space. This leads to a one-to-one relationship between the embedded, time dependent vectors in ......
