1,721,121 research outputs found
Large Time Step and DC Stable TD-EFIE Discretized with Implicit Runge-Kutta Methods
Full text linkThe time domain-electric field integral equation (TD-EFIE) and its differentiated version are widely used to simulate the transient scattering of a time dependent electromagnetic field by a perfect electric conductor (PEC). The time discretization of the TD-EFIE can be achieved by a space-time Galerkin approach or, as it is considered in this contribution, by a convolution quadrature using implicit Runge-Kutta methods. The solution is then computed using the marching-on-in-time (MOT) algorithm. The differentiated TD-EFIE has two problems: 1) the system matrix suffers from ill-conditioning when the time step increases (low frequency breakdown) and 2) it suffers from the DC instability, i.e., the formulation allows for the existence of spurious solenoidal currents that grow slowly in the solution. In this article, we show that 1) and 2) can be alleviated by leveraging quasi-Helmholtz projectors to separate the Helmholtz components of the induced current and rescale them independently. The efficacy of the approach is demonstrated by numerical examples including benchmarks and real-life applications.Numerical Analysi
An operator preconditioned combined field integral equation for electromagnetic scattering
Full text linkThis paper aims to address two issues of integral equations for the scattering of time- harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: ill-conditioned boundary element Galerkin discretization matrices on fine meshes and instability at spurious resonant frequencies. The remedy to ill-conditioned matrices is operator preconditioning, and resonant instability is eliminated by means of a combined field integral equation. Exterior traces of single and double layer potentials are complemented by their interior counterparts for a purely imaginary wave number. We derive the corresponding variational formulation in the natural trace space for electromagnetic fields and establish its well-posedness for all wave numbers. A Galerkin discretization scheme is employed using conforming edge boundary elements on dual meshes, which produces well-conditioned discrete linear systems of the variational formulation. Some numerical results are also provided to support the numerical analysis
A stabilized time-domain combined field integral equation using the quasi-Helmholtz projectors
Full text linkThis article introduces a time-domain combined field integral equation (TD-CFIE) for electromagnetic scattering by a perfect electric conductor (PEC). The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown and the source fields into solenoidal and irrotational components. These two components are then appropriately rescaled to cure the solution from a loss of accuracy occurring when the time step is large. Yukawa-type integral operators of a purely imaginary wavenumber are also used as a Calderon preconditioner to eliminate the ill-conditioning of matrix systems. The stabilized time-domain electric and magnetic field integral equations are linearly combined in a Calderon-like fashion, then temporally discretized using an appropriate pair of trial functions, resulting in a marching-on-in-time (MOT) linear system. The novel formulation is immune to spurious resonances, dense discretization breakdown, large-time step breakdown, and dc instabilities stemming from non-trivial kernels. Numerical results for both simply-connected and multiply-connected scatterers corroborate the theoretical analysis
A Yukawa-Calderón time-domain combined field integral equation for electromagnetic scattering
Full text linkThis paper introduces a Yukawa-Calderón time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The time-domain electric and magnetic field integral operators are composed with Yukawa-type integral operators. The linearly combined formulation is well-conditioned when the spatial discretization is dense, and it is also free from interior resonant frequencies. Several numerical results corroborate the properties of the proposed formulation
A DC stable, well-conditioned and low-frequency regularized time-domain PMCHWT equation
No full textThis paper introduces a low-frequency regularized time-domain PMCHWT equation, which is obtained by lever-aging a multiplicative preconditioning and the quasi-Helmholtz projectors. The new formulation is free from all numerical issues of the standard time-domain PMCHWT equation at low frequencies, including dense grid breakdown, large-time step breakdown, DC instabilities, and the loss of solution accuracy. Those properties are corroborated by numerical experiments
Discrétisations conformes des solutions aux éléments de frontière du problème direct en électroencéphalographie
Full text linkOn the Late-Time Instability of MOT Solution to the Time-Domain PMCHWT Equation
Full text linkThis letter investigates the late-time instability of marching-on-in-time solution to the time-domain Poggio–Miller– Chang–Harrington–Wu–Tsai (PMCHWT) equation. The stability analysis identifies the static solenoidal nullspace of the time-domain electric field integral operator as the primary cause of instability. Furthermore, it reveals that the instability mechanisms of the time-domain PMCHWT equation are fundamentally different from those of the time-domain electric field integral equation. In particular, the PMCHWT’s instability is much more sensitive to numerical quadrature errors, and its spectral characteristics are strongly influenced by the topology and smoothness of the scatterer surface
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
Accurate and efficient integral equations for the modeling of composite and non-uniform systems
No full textDe digitale revolutie heeft ons dagelijks leven getransformeerd, en ging gepaard met de integratie van elektromagnetische systemen in verschillende toepassingsdomeinen, waaronder communicatie en medische beeldvorming. De vooruitgang van elektronische technologie wordt voor een belangrijk deel mogelijk gemaakt door het vakgebied computationeel elektromagnetisme, waarin men de vergelijkingen van Maxwell numeriek oplost. Deze discipline combineert kennis uit de natuurkunde, wiskunde en computerwetenschappen om modelleringsuitdagingen aan te pakken.
Deze dissertatie behandelt uitdagingen in het modelleren van elektromagnetische interacties met integraalvergelijkingen, met name voor samengestelde objecten die heterogene materialen kunnen bevatten. Het introduceert een nieuwe numerieke kwadratuurregel voor volume-integraalvergelijkingen om de efficiëntie en nauwkeurigheid bij het berekenen van singuliere interactie-integralen te verbeteren. Bovendien presenteert het een globale multi-trace, single source integraalformulering om de terugkaatsing en transmissie van tijdsharmonische golven door complexe structuren te modelleren.
Daarnaast verkent het werk snelle algoritmen voor tijdsdomein integraalvergelijkingen. Het voorgestelde 'lazy plan-wave' tijdsdomeinalgoritme minimaliseert het geheugengebruik en zorgt voor een nauwkeurige reconstructie van het veld. Met zo een efficient algoritme kunnen veel grotere problemen worden aangepakt door middel van numerieke methoden
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