Journal: Lecture Notes in Computational Science and Engineering

Abbreviation

Lect. notes comput. sci. eng.

Publisher

Springer

Journal Volumes

ISSN

1439-7358

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Publications 1 - 10 of 35
  • High Order Semi-Lagrangian Particle Methods
    Item type: Conference Paper
    Cottet, Georges-Henri; Koumoutsakos, Petros (2017)
    Lecture Notes in Computational Science and Engineering ~ Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 : Selected Papers from the ICOSAHOM Conference, June 27-July 1, 2016, Rio de Janeiro, Brazil
  • Efficient Resolution of Anisotropic Structures
    Item type: Book Chapter
    Dahmen, Wolfgang; Huang, Chunyan; Kutyniok, Gitta; et al. (2014)
    Lecture Notes in Computational Science and Engineering ~ Extraction of Quantifiable Information from Complex Systems
    We highlight some results obtained in the DFG-SPP project “Adaptive Anisotropic Discretization Concepts”. We focus on new developments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus on the solution of transport equations which exhibit propagation of singularities where, additionally, high-dimensionality enters when the convection field, and hence the solutions, depend on parameters varying over some compact set. Important constituents of our approach are directionally adaptive discretization concepts motivated by compactly supported shearlet systems, and well-conditioned stable variational formulations that support trial spaces with anisotropic refinements with arbitrary directionalities. We prove that they provide tight error-residual relations which are used to contrive rigorously founded adaptive refinement schemes which converge in L 2. Moreover, in the context of parameter dependent problems we discuss two approaches serving different purposes and working under different regularity assumptions. For “frequent query problems”, making essential use of the novel well-conditioned variational formulations, a new Reduced Basis Method is outlined which exhibits a certain rate-optimal performance for indefinite, unsymmetric or singularly perturbed problems. For the radiative transfer problem with scattering a sparse tensor method is presented which mitigates or even overcomes the curse of dimensionality under suitable (so far still isotropic) regularity assumptions. Numerical examples for both methods illustrate the theoretical findings.
  • Flow of aqueous solutions in carbon nanotubes
    Item type: Conference Paper
    Kassinos, S.C.; Walther, Jens Honoré; Kotsalis, E.M.; et al. (2004)
    Lecture Notes in Computational Science and Engineering ~ Multiscale Modelling and Simulation
  • Efficient Pseudorecursive Evaluation Schemes for Non-adaptive Sparse Grids
    Item type: Conference Paper
    Pflüger, Dirk; Jacob, Riko; Buse,Gerrit (2014)
    Lecture Notes in Computational Science and Engineering ~ Sparse Grids and Applications - Munich 2012
  • A Review of Regular Decompositions of Vector Fields: Continuous, Discrete, and Structure-Preserving
    Item type: Conference Paper
    Hiptmair, Ralf; Pechstein, Clemens (2020)
    Lecture Notes in Computational Science and Engineering ~ Spectral and High Order Methods for Partial Differential Euqations, ICOSAHOM 2018
    We elaborate so-called regular decompositions of vector fields on a three-dimensional Lipschitz domain where the field and its rotation/divergence belong to L2 and where the tangential/normal component of the field vanishes on a sufficiently smooth “Dirichlet” part of the boundary. We impose no restrictions on the topology of the domain, its boundary, or the Dirichlet boundary parts. The field is split into a regular vector field, whose Cartesian components lie in H1 and vanish on the Dirichlet boundary, and a remainder contained in the kernel of the rotation/divergence operator. The decomposition is proved to be stable not only in the natural norms, but also with respect to the L2 norm. Besides, for special cases of mixed boundary conditions, we show the existence of H1-regular potentials that characterize the range of the rotation and divergence operator. We conclude with results on discrete counterparts of regular decompositions for spaces of low-order discrete differential forms on simplicial meshes. Essentially, all results for function spaces carry over, though local correction terms may be necessary. These discrete regular decompositions have become an important tool in finite element exterior calculus (FEEC) and for the construction of preconditioners.
  • Transported Probability and Mass Density Function (PDF/MDF) Methods for Uncertainty Assessment and Multi-Scale Problems
    Item type: Book Chapter
    Jenny, Patrick; Meyer, Daniel W. (2012)
    Lecture Notes in Computational Science and Engineering ~ Numerical analysis of multiscale problems
  • Stabilized FEM–BEM Coupling for Maxwell Transmission Problems
    Item type: Book Chapter
    Hiptmair, R.; Meury, P. (2007)
    Lecture Notes in Computational Science and Engineering ~ Modeling and computations in electromagnetics : a volume dedicated to Jean-Claude Nédélec
  • Multiresolution particle methods
    Item type: Conference Paper
    Bergdorf, Michael; Koumoutsakos, Petros (2007)
    Lecture Notes in Computational Science and Engineering ~ Complex Effects in Large Eddy Simulations
  • Automatic performance modeling of HPC applications
    Item type: Conference Paper
    Wolf, Felix; Bischof, Christian; Calotoiu, Alexandru; et al. (2016)
    Lecture Notes in Computational Science and Engineering ~ Software for Exascale Computing - SPPEXA 2013-2015
  • Exponential Convergence of hp-DGFEM for Elliptic Problems in Polyhedral Domains
    Item type: Conference Paper
    Schötzau, Dominik; Schwab, Christoph; Wihler, Thomas; et al. (2014)
    Lecture Notes in Computational Science and Engineering ~ Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 : Selected papers from the ICOSAHOM conference, June 25-29, 2012, Gammarth, Tunisia
Publications 1 - 10 of 35