Hans-Joachim Bungartz

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We present a survey of the fundamentals and the applications of sparse grids, with a focus on the solution of partial differential equations (PDEs). The sparse grid approach, introduced in Zenger (1991), is based on a higherdimensional multiscale basis, which is derived from a one-dimensional multiscale basis by a tensor product construction.(More)
The computation of selected eigenvalues and eigenvectors of a symmetric (Hermitian) matrix is an important subtask in many contexts, for example in electronic structure calculations. If a significant portion of the eigensystem is required then typically direct eigensolvers are used. The central three steps are: reduce the matrix to tridiagonal form, compute(More)
This paper presents a new approach to construct more efficient reduced-order models for nonlinear partial differential equations with proper orthogonal decomposition and the discrete empirical interpolation method (DEIM). Whereas DEIM projects the nonlinear term onto one global subspace, our localized discrete empirical interpolation method (LDEIM) computes(More)
In this paper, we study the potential of adaptive sparse grids for multivariate numerical quadrature in the moderate or high dimensional case, i. e. for a number of dimensions beyond three and up to several hundreds. There, conventional methods typically suffer from the curse of dimension or are unsatisfactory with respect to accuracy. Our sparse grid(More)
We introduce a novel method for the transcription of polyphonic piano music by discriminative training of support vector machines (SVMs). As features, we use pitch activations computed by supervised non-negative matrix factorization from low-level spectral features. Different approaches to low-level feature extraction, NMF dictionary learning and activation(More)
The software structure of MarDyn, a molecular dynamics simulation program for nanofluidics in chemical engineering, is presented. Multi-component mixtures in heterogeneous states with huge numbers of particles put great challenges on the simulation of scenarios in this field, which cannot be tackled with the established molecular simulation programs. The(More)
Application of novel analytical and investigative methods such as fluorescence in situ hybridization, confocal laser scanning microscopy (CLSM), microelectrodes and advanced numerical simulation has led to new insights into micro- and macroscopic processes in bioreactors. However, the question is still open whether or not these new findings and the(More)