Learn More
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 higher-dimensional multiscale basis, which is derived from a one-dimensional multi-scale basis by a tensor product construction.(More)
Article history: Available online xxxx Keywords: Electronic structure calculations Eigenvalue and eigenvector computation Blocked Householder transformations Divide-and-conquer tridiagonal eigensolver Parallelization a b s t r a c t The computation of selected eigenvalues and eigenvectors of a symmetric (Hermitian) matrix is an important subtask in many(More)
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. This paper presents a new approach to construct more efficient(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)
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)
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)