1,721,026 research outputs found
The Full-Wave Alternative to Eddy-Current Solvers: on a Low-Frequency and Dense-Discretization Stable PMCHWT Equation for Dielectric and Conductive Media
Full text linkPreconditioning Strategies and Conformal Discretizations Empowered by High-Order Projectors
Full text linkWe present novel discretization schemes for surface inte-
gral equations within the framework of high-order bound-
ary element methods. To overcome major limitations in
existing high-order techniques, this paper introduces three
key contributions: (i) a new conformal testing based on
high-order quasi-Helmholtz projectors ensures the adequate
high-order convergence of the magnetic field integral equa-
tion; (ii) this strategy allows to properly discretize the com-
bined field integral equation, resulting for the first time in
a resonance-free high-order formulation; and (iii) an origi-
nal Calderón-like preconditioner also based on high-order
conformal testing stabilizes these formulations for low-
frequency and dense-refinement scenarios. This guarantees
the rapid convergence of iterative solvers while enabling the
efficient use of high-order methods across a wide frequency
range and dense-mesh scenarios. Numerical experiments
are provided to showcase the effectiveness of our approac
Resonance-free single-current inverse source formulations based on Steklov-Poincaré mappings
Full text linkOn a High-Frequency Analysis of Some Relevant Integral Equations in Electromagnetics
Full text linkIn this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular, a comparison with the eigenvalues of the continuous operators will be presented that highlights deviations in the high frequency regime and impacts, in a peculiar way, the accuracy of the numerical solutions of each formulation.
A study and a proactive analysis of numerical results from standard boundary element solvers and the predictions from the theoretical analysis will corroborate the analytical framework employed and the validity of our observations
Quasi-Helmholtz Projectors for High-Order Basis Functions: Definitions, Computational Strategies, Applications
Full text link
High-Fidelity Imaging of the Brain’s Electrophysiological Activity Based on a Fast Direct Solver
Full text linkImaging of the electrophysiologic activity of the brain is important for diagnosing or treating several neurological diseases. Electroencephalography source imaging (ESI) is a modality that reconstructs the electrophysiologic activity from external potential measurement at the scalp. Despite being non-invasive and being capable of offering high temporal and spatial resolutions, its adoption is hampered by its complexity and high computational cost caused by its need to solve a complex forward problem from hundreds to thousands of times per subject. In this contribution, we tackle this issue by presenting a fast direct solver for ESI that yields a low-rank skeleton form of the inverse of the forward problem, allowing for a drastic reduction in the computational load of the imaging modality
On a time domain Calderón preconditioned CFIE discretized with convolution quadratures
Full text linkSeveral standard integral equations in the time domain suffer from at least one of the following limitations: 1) conditioning breakdowns, 2) internal resonances, or 3) DC-instabilities. The standard time domain combined field integral equation (CFIE) being no exception, is plagued by the large time step and dense discretization breakdowns. Calderón preconditioning strategies are commonly proposed to address these issues in the frequency domain but, to this day, they were not available for convolution quadrature CFIEs. This work will fill this gap proposing a new Calderón approach leading to a well-conditioned and resonant-free convolution quadrature discretized equation
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
- …
