Journal: Journal of Computational and Applied Mathematics

Abbreviation

J. Comput. Appl. Math.

Publisher

Elsevier

Journal Volumes

ISSN

0377-0427
0771-050X
1879-1778

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Publications 1 - 10 of 23
  • Error-driven dynamical h p-meshes with the Discontinuous Galerkin Method for three-dimensional wave propagation problems
    Item type: Journal Article
    Schnepp, Sascha M. (2014)
    Journal of Computational and Applied Mathematics
  • Eulerian finite element method for the numerical modeling of fluid dynamics of natural and pathological aortic valves
    Item type: Journal Article
    Laadhari, Aymen; Székel, Gábor (2017)
    Journal of Computational and Applied Mathematics
  • The fast reduced QMC matrix–vector product
    Item type: Journal Article
    Dick, Josef; Ebert, Adrian; Herrmann, Lukas; et al. (2024)
    Journal of Computational and Applied Mathematics
    We study the approximation of integrals of the form ∫Df(x⊤A)dμ(x), where the measure μ is of product form and A is a matrix, by quasi-Monte Carlo (QMC) rules N−1∑k=0N−1f(xk⊤A). We are interested in cases where the main computational cost in the approximation arises from calculating the products xk⊤A. We design QMC rules for which the computation of xk⊤A, k=0,1,…,N−1, can be done in a fast way, and for which the approximation error of the QMC rule is similar to the standard QMC error. We do not require that the matrix A has any particular structure. Problems of this form arise in some important applications in statistics and uncertainty quantification. For instance, this approach can be used when approximating the expected value of some function with a multivariate normal random variable with some given covariance matrix, or when approximating the expected value of the solution of a PDE with random coefficients. The speed-up of the computation time of our approach is sometimes better and sometimes worse than the fast QMC matrix–vector product from [Josef Dick, Frances Y. Kuo, Quoc T. Le Gia, and Christoph Schwab, Fast QMC Matrix-Vector Multiplication, SIAM J. Sci. Comput. 37 (2015), no. 3, A1436–A1450]. As in that paper, our approach applies to lattice point sets and polynomial lattice point sets, but also applies to digital nets (we are currently not aware of any approach which allows one to apply the fast QMC matrix–vector paper from the aforementioned paper of Dick, Kuo, Le Gia, and Schwab to digital nets). The method in this paper does not make use of the fast Fourier transform, instead we use repeated values in the quadrature points to derive a significant reduction in the computation time. Such a situation naturally arises from the reduced CBC construction of lattice rules and polynomial lattice rules. The reduced CBC construction has been shown to reduce the computation time for the CBC construction. Here we show that it can additionally be used to also reduce the computation time of the underlying QMC rule. One advantage of the present approach is that it can be combined with random (digital) shifts, whereas this does not apply to the fast QMC matrix–vector product from the earlier paper of Dick, Kuo, Le Gia, and Schwab.
  • Bandlimited shearlet-type frames with nice duals
    Item type: Journal Article
    Grohs, Philipp (2013)
    Journal of Computational and Applied Mathematics
    The present paper constructs a frame/dual frame pair of shearlet type such that both frames possess the distinctive time–frequency localization properties needed in establishing their desirable approximation properties. Our construction is based on a careful pasting together of two bandlimited shearlet Parseval frames associated with two different frequency cones, inspired by domain decomposition methods used primarily for the solution of PDEs.
  • Adaptive anisotropic Petrov–Galerkin methods for first order transport equations
    Item type: Journal Article
    Dahmen, Wolfgang; Kutyniok, Gitta; Lim, Wang-Q; et al. (2018)
    Journal of Computational and Applied Mathematics
  • Almost sure convergence of a Galerkin approximation for SPDEs of Zakai type driven by square integrable martingales
    Item type: Journal Article
    Lang, Annika (2012)
    Journal of Computational and Applied Mathematics
    This work describes a Galerkin type method for stochastic partial differential equations of Zakai type driven by an infinite dimensional càdlàg square integrable martingale. Error estimates in the semidiscrete case, where discretization is only done in space, are derived in $L^P$ and almost sure senses. Simulations confirm the theoretical results.
  • Implicit–explicit schemes for flow equations with stiff source terms
    Item type: Journal Article
    Svärd, Magnus; Mishra, Siddhartha (2011)
    Journal of Computational and Applied Mathematics
  • Optimality of adaptive Galerkin methods for random parabolic partial differential equations
    Item type: Journal Article
    Gittelson, Claude Jeffrey; Andreev, Roman; Schwab, Christoph (2014)
    Journal of Computational and Applied Mathematics
  • Hamiltonian treatment of time dispersive and dissipative media within the linear response theory
    Item type: Other Conference Item
    Figotin, Alexander; Schenker, Jeffrey (2007)
    Journal of Computational and Applied Mathematics
  • Discontinuous Galerkin methods with Trefftz approximations
    Item type: Conference Paper
    Kretzschmar, Fritz; Schnepp, Sascha M.; Tsukermann, Igor; et al. (2014)
    Journal of Computational and Applied Mathematics
Publications 1 - 10 of 23