Stable FFT-JVIE solvers for fast analysis of highly inhomogeneous dielectric objects

Polimeridis, Athanasios G.; Villena, Jorge Fernández; Daniel, Luca; White, Jacob K.

doi:10.1016/j.jcp.2014.03.026

Cited by 88 publications

(132 citation statements)

References 18 publications

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“…III, we describe a fast procedure for the computation of the proposed matrix-trace, which relies on a straightforward and easily implemented FFT-based fast algorithm presented in Ref. 25 that scales as O(N log N ) for each matrix-vector product and requires O(N ) memory.…”

Section: 162mentioning

confidence: 99%

“…There are however fast FFT-based procedures for evaluating matrix-vector products of the JM-VIE system matrix and the Green matrix. 25 Here we describe a framework based on iterative methods for the fast computation of the associated trace formulas above.…”

Section: Fast Trace Computationsmentioning

confidence: 99%

“…Additional numerical experiments (not shown) confirm that the effect of mesh density on the ranks is negligible, yet another manifestation of the favourable convergence prop-erties of the JM-VIE formulation. 25 This also suggests a strategy for obtaining the finite rank of sym G pp with prescribed accuracy: we begin by computing the rank of the operator for a prescribed accuracy by using a coarse mesh and then run a fixed-rank rSVD algorithm with finer mesh. Finally, Fig.…”

Section: A Low-rank Approximationsmentioning

confidence: 99%

“…The absorbed power χinc(x) inside the sphere, obtained by solving a single scattering problem as described in Ref. 25, is shown in the top contour plots along three sphere cross-sections. Φ is computed exactly (blue line) or via a homogeneous approximation Φ eff in which the absorbed power is taken to be uniformly distributed inside the sphere and given by χ eff =´V d 3 xχinc(x) (red line).…”

Section: B Thermal Radiation and Heat Transfermentioning

confidence: 99%

“…In particular, we derive a fluctuating volume-current (FVC) formulation of EM fluctuations that exploits techniques from the volume-integral equation (VIE) formulation of EM scattering 24,25 and which expands the range and validity of current methods to situations involving inhomogeneous media. Although FVC is similar in spirit to our previous fluctuating surface-current (FSC) methods, 26,27 unlike FSC our new approach is not limited to piecewisehomogeneous objects.…”

Section: Introductionmentioning

confidence: 99%

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Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries

et al. 2015

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We describe a fluctuating volume-current formulation of electromagnetic fluctuations that extends our recent work on heat exchange and Casimir interactions between arbitrarily shaped homogeneous bodies [Phys. Rev. B. 88, 054305] to situations involving incandescence and luminescence problems, including thermal radiation, heat transfer, Casimir forces, spontaneous emission, fluorescence, and Raman scattering, in inhomogeneous media. Unlike previous scattering formulations based on field and/or surface unknowns, our work exploits powerful techniques from the volume-integral equation (VIE) method, in which electromagnetic scattering is described in terms of volumetric, current unknowns throughout the bodies. The resulting trace formulas (boxed equations) involve products of well-studied VIE matrices and describe power and momentum transfer between objects with spatially varying material properties and fluctuation characteristics. We demonstrate that thanks to the low-rank properties of the associated matrices, these formulas are susceptible to fast-trace computations based on iterative methods, making practical calculations tractable. We apply our techniques to study thermal radiation, heat transfer, and fluorescence in complicated geometries, checking our method against established techniques best suited for homogeneous bodies as well as applying it to obtain predictions of radiation from complex bodies with spatially varying permittivities and/or temperature profiles.

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Section: 162mentioning

confidence: 99%

Section: Fast Trace Computationsmentioning

confidence: 99%

Section: A Low-rank Approximationsmentioning

confidence: 99%

Section: B Thermal Radiation and Heat Transfermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries

et al. 2015

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Equivalent source of reflector in finite‐different time‐domain for rapid analysis of corner scattering in terahertz computed tomography imaging

Feng,

Cha,

Shi

et al. 2024

Micro & Optical Tech Letters

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We propose the equivalent source of reflector in finite‐different time‐domain (ESR‐FDTD) for rapid analysis of corner scattering in terahertz computed tomography (THz‐CT) imaging. The ESR‐FDTD is used instead of the reflector in the THz‐CT imaging system, which can significantly reduce the computational domain of the THz‐CT imaging system and effectively reduce the computational time and memory usage. The electric field distribution of the beam reflected by the reflector and that of the beam radiated from the ESR of the reflector are compared, and the results show that the electric field distributions of the reflector and its ESR are almost the same. The results of the corner scattering show that the phenomenon of corner scattering does not fully satisfy the behaviors of reflection and refraction. Therefore, the corner scattering cannot be accurately analyzed by the ray‐tracing method.

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The ultimate signal‐to‐noise ratio in realistic body models

2017

Magnetic Resonance in Med

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Purpose-We compute the ultimate signal-to-noise ratio (uSNR) and G-factor (uGF) in a realistic head model from 0.5 to 21 Tesla.Methods-We excite the head model and a uniform sphere with a large number of electric and magnetic dipoles placed at 3 cm from the object. The resulting electromagnetic fields are computed using an ultrafast volume integral solver, which are used as basis functions for the uSNR and uGF computations.Results-Our generalized uSNR calculation shows good convergence in the sphere and the head and is in close agreement with the dyadic Green's function approach in the uniform sphere. In both models, the uSNR versus B 0 trend was linear at shallow depths and supralinear at deeper locations. At equivalent positions, the rate of increase of the uSNR with B 0 was greater in the sphere than in the head model. The uGFs were lower in the realistic head than in the sphere for acceleration in the anterior-posterior direction, but similar for the left-right direction.Conclusion-The uSNR and uGFs are computable in nonuniform body models and provide fundamental performance limits for human imaging with close-fitting MRI array coils.

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Stable FFT-JVIE solvers for fast analysis of highly inhomogeneous dielectric objects

Cited by 88 publications

References 18 publications

Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries

Fluctuating volume-current formulation of electromagnetic fluctuations in inhomogeneous media: Incandescence and luminescence in arbitrary geometries

Equivalent source of reflector in finite‐different time‐domain for rapid analysis of corner scattering in terahertz computed tomography imaging

The ultimate signal‐to‐noise ratio in realistic body models

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