Journal: Mathematics of Computation

Abbreviation

Math. Comp.

Publisher

American Mathematical Society

Journal Volumes

ISSN

0025-5718
1088-6842

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Publications 1 - 10 of 25
  • Floquet–Bloch analysis of wave propagation with time-periodic coefficients
    Item type: Journal Article
    Nick, Jörg; Hiptmair, Ralf; Ammari, Habib (2025)
    Mathematics of Computation
    This paper presents a numerical investigation of acoustic wave propagation in an obstacle with periodically time-modulated material parameters. We focus on the numerical construction of Floquet–Bloch solutions, which are quasi-periodic kernel elements of the hyperbolic operator appearing on the left-hand side of the acoustic wave equation. Using the temporal Fourier expansion yields a system of coupled harmonics, which can be truncated. Rewriting this system then provides different (generally nonlinear) eigenvalue formulations for discretized Floquet–Bloch solutions. Deriving energy estimates and the necessary conditions for Riesz–Schauder theory show basic properties of the occurring Floquet exponents. To derive fully discrete schemes, we employ a general Galerkin space discretization. Under assumptions on the relation of the temporal Fourier truncation and the Galerkin space discretization, we prove that the approximated Floquet exponents exhibit the same limitations as their continuous counterparts. Moreover, the approximated modes are shown to satisfy the defining properties of Floquet–Bloch solutions, with a defect that tends to zero as the number of harmonics approaches infinity. Numerical experiments demonstrate the effectiveness of the proposed approach and illustrate the theoretical findings.
  • Computing genus 1 Jacobi forms
    Item type: Journal Article
    Raum, Martin (2016)
    Mathematics of Computation
  • Convergence of an Engquist-Osher scheme for a multi-dimensional triangular systems of conservation laws
    Item type: Journal Article
    Coclite, Giuseppe M.; Mishra, Siddhartha; Risebro, Nils H. (2010)
    Mathematics of Computation
  • Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems
    Item type: Journal Article
    Herrmann, Lukas; Keller, Magdalena; Schwab, Christoph (2021)
    Mathematics of Computation
    We analyze rates of convergence for quasi-Monte Carlo (QMC) integration for Bayesian inversion of linear, elliptic partial differential equations with uncertain input from function spaces. Adopting a Riesz or Schauder basis representation of the uncertain inputs, function space priors are constructed as product measures on spaces of (sequences of) coefficients in the basis representations. The numerical approximation of the posterior expectation, given data, then amounts to a high- or infinite-dimensional numerical integration problem. We consider in particular so-called Besov priors on the admissible uncertain inputs. We extend the QMC convergence theory from the Gaussian case, and establish sufficient conditions on the uncertain inputs for achieving dimension-independent convergence rates greater than 1/2 of QMC integration with randomly shifted lattice rules. We apply the theory to a concrete class of linear, second order elliptic boundary value problems with log-Besov uncertain diffusion coefficient.
  • Computing Gröbner fans
    Item type: Journal Article
    Fukuda, Komei; Jensen, Anders N.; Thomas, Rekha R. (2007)
    Mathematics of Computation
  • First order k-th moment finite element analysis of nonlinear operator equations with stochastic data
    Item type: Journal Article
    Chernov, Alexey; Schwab, Christoph (2013)
    Mathematics of Computation
  • Extension by zero in discrete trace spaces: Inverse estimates
    Item type: Journal Article
    Hiptmair, Ralf; Jerez-Hanckes, Carlos; Mao, Shipeng (2015)
    Mathematics of Computation
  • The best ways to slice a Polytope
    Item type: Journal Article
    Brandenburg, Marie-Charlotte; De Loera, Jesús A.; Meroni, Chiara (2025)
    Mathematics of Computation
    We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of possible combinatorial types of sections and craft algorithms that compute optimal sections of the polytope according to various combinatorial and metric criteria, including sections that maximize the number of k-dimensional faces, maximize the volume, and maximize the integral of a polynomial. Our optimization algorithms run in polynomial time in fixed dimension, but the same problems show computational complexity hardness otherwise. Our tools can be extended to intersection with halfspaces and projections onto hyperplanes. Finally, we present several experiments illustrating our theorems and algorithms on famous polytopes.
  • Evaluating modular forms on Shimura curves
    Item type: Journal Article
    Nelson, Paul D. (2015)
    Mathematics of Computation
  • An adaptive stochastic Galerkin method for random elliptic operators
    Item type: Journal Article
    Gittelson,Claude J. (2013)
    Mathematics of Computation
Publications 1 - 10 of 25