1,721,000 research outputs found
Moment equations for the mixed formulation of the Hodge Laplacian with stochastic data
No full textWe study the mixed formulation of the stochastic Hodge-Laplace problem defined on a n-dimensional domain D (n ≥ 1), with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three dimensional case. We derive and analyze the moment equations, that is the deterministic equations solved by the m-th moment (m ≥ 1) of the unique stochastic solution of the stochastic problem. We find stable tensor product finite element discretizations, both full and sparse, and provide optimal order of convergence estimates. In particular,
we prove the inf-sup condition for sparse tensor product finite element spaces
Distributed sampling for rational approximation of the acoustic scattering of an airfoil
No full textIn this paper we compute a reduced order model for a time‐harmonic external acoustic scattering problem with parametric frequency. The employed technique is minimal rational interpolation, an explicit moment‐matching method for Hilbert space‐valued meromorphic maps. We study the approximation and stability properties of this technique for different choices of the sample point set, namely fully distributed in the parameter range, and partially and fully confluent. The proposed technique is also compared with an implicit multi moment‐matching method based on Galerkin projection.CSQISpecial Issue: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM
Tensor-Product Vertex Patch Smoothers for Biharmonic Problems
No full textWe discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very efficient and yield high convergence rates. Furthermore, we discuss low rank tensor approximations for their efficient implementation. Our experiments demonstrate that the inexact local solver yields a method which converges fast and uniformly with respect to mesh refinement and polynomial degree. The multiplicative smoother shows superior performance in terms of solution efficiency, requiring fewer iterations in both two- and three-dimensional cases. Additionally, the solver infrastructure supports a mixed-precision approach, executing the multigrid preconditioner in single precision while performing the outer iteration in double precision, thereby increasing throughput by up to 70 %
Discrete tensor product BGG sequences: Splines and finite elements
Full text linkIn this paper, we provide a systematic discretization of the Bernstein-Gelfand-Gelfand diagrams and complexes over cubical meshes in arbitrary dimension via the use of tensor product structures of one-dimensional piecewise-polynomial spaces, such as spline and finite element spaces. We demonstrate the construction of the Hessian, the elasticity, and div div complexes as examples for our construction
Convergence analysis of Padé approximations for Helmholtz frequency response problems
Full text linkThe present work concerns the approximation of the solution map S associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution of the Helmholtz equation. We introduce a least squares rational Padé-type approximation technique applicable to any meromorphic Hilbert space-valued univariate map, and we prove the uniform convergence of the Padé approximation error on any compact subset of the interval of interest that excludes any pole. This general result is then applied to the Helmholtz solution map S, which is proven to be meromorphic in ℂ, with a pole of order one in every (single or multiple) eigenvalue of the Laplace operator with the considered boundary conditions. Numerical tests are provided that confirm the theoretical upper bound on the Padé approximation error for the Helmholtz solution map.</jats:p
Structure Preserving Polytopal Discontinuous Galerkin Methods for the Numerical Modeling of Neurodegenerative Diseases
Full text linkMany neurodegenerative diseases are connected to the spreading of misfolded prionic proteins. In this paper, we analyse the process of misfolding and spreading of both -synuclein and Amyloid-, related to Parkinson\u27s and Alzheimer\u27s diseases, respectively. We introduce and analyze a positivity-preserving numerical method for the discretization of the Fisher-Kolmogorov equation, modelling accumulation and spreading of prionic proteins. The proposed approximation method is based on the discontinuous Galerkin method on polygonal and polyhedral grids for space discretization and on method time integration scheme. We prove the existence of the discrete solution and a convergence result where the Implicit Euler scheme is employed for time integration. We show that the proposed approach is structure-preserving, in the sense that it guaranteed that the discrete solution is non-negative, a feature that is of paramount importance in practical application. The numerical verification of our numerical model is performed both using a manufactured solution and considering wavefront propagation in two-dimensional polygonal grids. Next, we present a simulation of -synuclein spreading in a two-dimensional brain slice in the sagittal plane. The polygonal mesh for this simulation is agglomerated maintaining the distinction of white and grey matter, taking advantage of the flexibility of PolyDG methods in the mesh construction. Finally, we simulate the spreading of Amyloid- in a patient-specific setting by using a three-dimensional geometry reconstructed from magnetic resonance images and an initial condition reconstructed from positron emission tomography. Our numerical simulations confirm that the proposed method is able to capture the evolution of Parkinson\u27s and Alzheimer\u27s diseases
Discontinuous Galerkin approximations of the heterodimer model for protein-protein interaction
Full text linkMathematical models of protein-protein dynamics, such as the heterodimer model, play a crucial role in understanding many physical phenomena. This model is a system of two semilinear parabolic partial differential equations describing the evolution and mutual interaction of biological species. An example is the neurodegenerative disease progression in some significant pathologies, such as Alzheimer\u27s and Parkinson\u27s diseases, characterized by the accumulation and propagation of toxic prionic proteins. This article presents and analyzes a flexible high-order discretization method for the numerical approximation of the heterodimer model. We propose a space discretization based on a Discontinuous Galerkin method on polygonal/polyhedral grids, which provides flexibility in handling complex geometries. Concerning the semi-discrete formulation, we prove stability and a-priori error estimates for the first time. Next, we adopt a -method scheme as a time integration scheme. Convergence tests are carried out to demonstrate the theoretical bounds and the ability of the method to approximate traveling wave solutions, considering also complex geometries such as brain sections reconstructed from medical images. Finally, the proposed scheme is tested in a practical test case stemming from neuroscience applications, namely the simulation of the spread of -synuclein in a realistic test case of Parkinson\u27s disease in a two-dimensional sagittal brain section geometry reconstructed from medical images
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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