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Автор: Grafiati
Опубліковано: 6 вересня 2023

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Статті в журналах з теми "Volume Surface Integral Equation"

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Gomez, Luis J., Abdulkadir C. Yucel, and Eric Michielssen. "Volume-Surface Combined Field Integral Equation for Plasma Scatterers." IEEE Antennas and Wireless Propagation Letters 14 (December 2015): 1064–67. http://dx.doi.org/10.1109/lawp.2015.2390533.

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2

Kaplan, Meydan, and Yaniv Brick. "A fast solver framework for acoustic hybrid integral equations." Journal of the Acoustical Society of America 152, no. 4 (October 2022): A119. http://dx.doi.org/10.1121/10.0015743.

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Reliable modeling of the scattering by acoustically large and geometrically complex objects can be achieved by means of subdomain-dependent problem formulation and a numerically rigorous solution. While the objects’ inhomogeneity has driven the development of differential equation formulations and solvers, integral equation formulations, where the object’s background is modeled via a Green’s function, are advantageous for unbounded domains. In the hybrid integral equations approach (Usner et al., 2006), the interaction of separate subdomains with external fields is described by pertinent integral equations. Their Galerkin discretization leads to a dense blocked stiffness matrix. The development of compressed representations of the matrix, which are necessary for the treatment of large systems, becomes non-trivial due to the multitude of integral equation kernels and the different geometrical and physical characteristic of the subdomains. As part of the development of a fast hybrid integral equation solver framework, we consider the case of objects composed of large inhomogeneous volumes, modeled as incompressible fluids, and of simplified solids, modeled via surface integral equations. A hybrid integral equation formulation is derived and solved numerically. The iterative solution is accelerated by employing the butterfly-compressed hierarchical representation of the stiffness matrix, recently used for acoustic volume integral equations (Kaplan, 2022).
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3

Remis, R., and E. Charbon. "An Electric Field Volume Integral Equation Approach to Simulate Surface Plasmon Polaritons." Advanced Electromagnetics 2, no. 1 (February 16, 2013): 15. http://dx.doi.org/10.7716/aem.v2i1.23.

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In this paper we present an electric field volume integral equation approach to simulate surface plasmon propagation along metal/dielectric interfaces. Metallic objects embedded in homogeneous dielectric media are considered. Starting point is a so-called weak-form of the electric field integral equation. This form is discretized on a uniform tensor-product grid resulting in a system matrix whose action on a vector can be computed via the fast Fourier transform. The GMRES iterative solver is used to solve the discretized set of equations and numerical examples, illustrating surface plasmon propagation, are presented. The convergence rate of GMRES is discussed in terms of the spectrum of the system matrix and through numerical experiments we show how the eigenvalues of the discretized volume scattering operator are related to plasmon propagation and the medium parameters of a metallic object.
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Usner, B. C., K. Sertel, and J. L. Volakis. "Doubly periodic volume–surface integral equation formulation for modelling metamaterials." IET Microwaves, Antennas & Propagation 1, no. 1 (2007): 150. http://dx.doi.org/10.1049/iet-map:20050344.

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Ewe, Wei-Bin, Hong-Son Chu, and Er-Ping Li. "Volume integral equation analysis of surface plasmon resonance of nanoparticles." Optics Express 15, no. 26 (2007): 18200. http://dx.doi.org/10.1364/oe.15.018200.

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6

Amundsen, Lasse. "The propagator matrix related to the Kirchhoff‐Helmholtz integral in inverse wavefield extrapolation." GEOPHYSICS 59, no. 12 (December 1994): 1902–10. http://dx.doi.org/10.1190/1.1443577.

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The Kirchhoff‐Helmholtz formula for the wavefield inside a closed surface surrounding a volume is most commonly given as a surface integral over the field and its normal derivative, given the Green’s function of the problem. In this case the source point of the Green’s function, or the observation point, is located inside the volume enclosed by the surface. However, when locating the observation point outside the closed surface, the Kirchhoff‐Helmholtz formula constitutes a functional relationship between the field and its normal derivative on the surface, and thereby defines an integral equation for the fields. By dividing the closed surface into two parts, one being identical to the (infinite) data measurement surface and the other identical to the (infinite) surface onto which we want to extrapolate the data, the solution of the Kirchhoff‐Helmholtz integral equation mathematically gives exact inverse extrapolation of the field when constructing a Green’s function that generates either a null pressure field or a null normal gradient of the pressure field on the latter surface. In the case when the surfaces are plane and horizontal and the medium parameters are constant between the surfaces, analysis in the wavenumber domain shows that the Kirchhoff‐Helmholtz integral equation is equivalent to the Thomson‐Haskell acoustic propagator matrix method. When the medium parameters have smooth vertical gradients, the Kirchhoff‐Helmholtz integral equation in the high‐frequency approximation is equivalent to the WKBJ propagator matrix method, which also is equivalent to the extrapolation method denoted by extrapolation by analytic continuation.
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Roco, M. C., and S. Mahadevan. "Scale-up Technique of Slurry Pipelines—Part 2: Numerical Integration." Journal of Energy Resources Technology 108, no. 4 (December 1, 1986): 278–85. http://dx.doi.org/10.1115/1.3231277.

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A kinetic energy turbulence model has been proposed for the computer flow simulation and scale-up of slurry pipelines (in Part 1 [1]). The numerical integration is performed by using a modified finite volume technique, with application to high-convective two-phase flows in two and three dimensions (in Part 2). The mixture kinetic energy and eddy viscosity turbulence models are compared. The one-equation eddy-viscosity turbulence model (εt - model) is formulated in Part 2 and applied for the multi-species particle slurry flow in cylindrical pipes. A modified finite volume technique is proposed for high convective transport equations, for one and two-phase flows. The integral formulation per volume yields surface and volume integrals, that are stored and counted only by interfaces using a multidimensional approach. The nonlinear distributions in volumes and on interfaces are approximated employing the derivatives in the normal and tangent directions to the bounding surfaces. Linear, analytical (upwind) and logarithmic laws of interpolations are considered for internal flows. The numerical approach was tested with good results for transport equations of momentum and various contaminants (solid particles, temperature, eddy-viscosity) in pipes. Experimental data for one and two-phase flows are compared to the integral finite volume predictions. The proposed finite volume technique can economically simulate complex flow situations encountered in the slurry pipeline scale-up applications.
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NWOGU, OKEY G. "Interaction of finite-amplitude waves with vertically sheared current fields." Journal of Fluid Mechanics 627 (May 25, 2009): 179–213. http://dx.doi.org/10.1017/s0022112009005850.

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A computationally efficient numerical method is developed to investigate nonlinear interactions between steep surface gravity waves and depth-varying ocean currents. The free-surface boundary conditions are used to derive a coupled set of equations that are integrated in time for the evolution of the free-surface elevation and tangential component of the fluid velocity at the free surface. The vector form of Green's second identity is used to close the system of equations. The closure relationship is consistent with Helmholtz's decomposition of the velocity field into rotational and irrotational components. The rotational component of the flow field is given by the Biot–Savart integral, while the irrotational component is obtained from an integral of a mixed distribution of sources and vortices over the free surface. Wave-induced changes to the vorticity field are modelled using the vorticity transport equation. For weak currents, an explicit expression is derived for the wave-induced vorticity field in Fourier space that negates the need to numerically solve the vorticity transport equation. The computational efficiency of the numerical scheme is further improved by expanding the kernels of the boundary and volume integrals in the closure relationship as a power series in a wave steepness parameter and using the fast Fourier transform method to evaluate the leading-order contribution to the convolution integrals. This reduces the number of operations at each time step from O(N2) to O(NlogN) for the boundary integrals and O[(NM)2] to O(NlogN) for the volume integrals, where N is the number of horizontal grid points and M is the number of vertical layers, making the model an order of magnitude faster than traditional boundary/volume integral methods. The numerical model is used to investigate nonlinear wave–current interaction in depth-uniform current fields and the modulational instability of gravity waves in an exponentially sheared current in deep water. The numerical results demonstrate that the mean flow vorticity can significantly affect the growth rate of extreme waves in narrowband sea states.
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NATSIOPOULOS, GEORGIOS. "ALTERNATIVE TIME DOMAIN BOUNDARY INTEGRAL EQUATIONS FOR THE SCALAR WAVE EQUATION USING DIVERGENCE-FREE REGULARIZATION TERMS." Journal of Computational Acoustics 17, no. 02 (June 2009): 211–18. http://dx.doi.org/10.1142/s0218396x09003938.

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In this short note alternative time domain boundary integral equations (TDBIE) for the scalar wave equation are formulated on a surface enclosing a volume. The technique used follows the traditional approach of subtracting and adding back relevant Taylor expansion terms of the field variable, but does not restrict this to the surface patches that contain the singularity only. From the divergence-free property of the added-back integrands, together with an application of Stokes' theorem, it follows that the added-back terms can be evaluated using line integrals defined on a cut between the surface and a sphere whose radius increases with time. Moreover, after a certain time, the line integrals may be evaluated directly. The results provide additional insight into the theoretical formulations, and might be used to improve numerical implementations in terms of stability and accuracy.
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Jin, J. M., V. V. Liepa, and C. T. Tai. "A Volume-Surface Integral Equation for Electromagnetic Scattering by Inhomogeneous Cylinders." Journal of Electromagnetic Waves and Applications 2, no. 5-6 (January 1988): 573–88. http://dx.doi.org/10.1163/156939388x00170.

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Дисертації з теми "Volume Surface Integral Equation"

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Cao, Xiande. "Volume and Surface Integral Equations for Solving Forward and Inverse Scattering Problems." UKnowledge, 2014. http://uknowledge.uky.edu/ece_etds/65.

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In this dissertation, a hybrid volume and surface integral equation is used to solve scattering problems. It is implemented with RWG basis on the surface and the edge basis in the volume. Numerical results shows the correctness of the hybrid VSIE in inhomogeneous medium. The MLFMM method is also implemented for the new VSIEs. Further more, a synthetic apature radar imaging method is used in a 2D microwave imaging for complex objects. With the mono-static and bi-static interpolation scheme, a 2D FFT is applied for the imaging with the data simulated with VSIE method. Then we apply a background cancelling scheme to improve the imaging quality for the targets in interest. Numerical results shows the feasibility of applying the background canceling into wider applications.
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Pillain, Axelle. "Line, Surface, and Volume Integral Equations for the Electromagnetic Modelling of the Electroencephalography Forward Problem." Thesis, Télécom Bretagne, 2016. http://www.theses.fr/2016TELB0412/document.

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La reconstruction des sources de l'activité cérébrale à partir des mesures de potentiel fournies par un électroencéphalographie (EEG) nécessite de résoudre le problème connu sous le nom de « problème inverse de l'EEG ». La solution de ce problème dépend de la solution du « problème direct de l'EEG », qui fournit à partir de sources de courant connues, le potentiel mesuré au niveau des électrodes. Pour des modèles de tête réels, ce problème ne peut être résolut que de manière numérique. En particulier, les équations intégrales de surfaces requièrent uniquement la discrétisation des interfaces entre les différents compartiments constituant le milieu cérébral. Cependant, les formulations intégrales existant actuellement ne prennent pas en comptent l'anisotropie du milieu. Le travail présenté dans cette thèse introduit deux nouvelles formulations intégrales permettant de palier à cette faiblesse. Une formulation indirecte capable de prendre en compte l'anisotropie du cerveau est proposée. Elle est discrétisée à l'aide de fonctions conformes aux propriétés spectrales des opérateurs impliqués. L'effet de cette discrétisation de type mixe lors de la reconstruction des sources cérébrales est aussi étudié. La seconde formulation se concentre sur l'anisotropie due à la matière blanche. Calculer rapidement la solution du système numérique obtenu est aussi très désirable. Le travail est ainsi complémenté d'une preuve de l'applicabilité des stratégies de préconditionnement de type Calderon pour les milieux multicouches. Le théorème proposé est appliqué dans le contexte de la résolution du problème direct de l'EEG. Un préconditionneur de type Calderon est aussi introduit pour l'équation intégrale du champ électrique (EFIE) dans le cas de structures unidimensionnelles. Finalement, des résultats préliminaires sur l'impact d'un solveur rapide direct lors de la résolution rapide du problème direct de l'EEG sont présentés
Electroencephalography (EEG) is a very useful tool for characterizing epileptic sources. Brain source imaging with EEG necessitates to solve the so-called EEG inverse problem. Its solution depends on the solution of the EEG forward problem that provides from known current sources the potential measured at the electrodes positions. For realistic head shapes, this problem can be solved with different numerical techniques. In particular surface integral equations necessitates to discretize only the interfaces between the brain compartments. However, the existing formulations do not take into account the anisotropy of the media. The work presented in this thesis introduces two new integral formulations to tackle this weakness. An indirect formulation that can handle brain anisotropies is proposed. It is discretized with basis functions conform to the mapping properties of the involved operators. The effect of this mixed discretization on brain source reconstruction is also studied. The second formulation focuses on the white matter fiber anisotropy. Obtaining the solution to the obtained numerical system rapidly is also highly desirable. The work is hence complemented with a proof of the preconditioning effect of Calderon strategies for multilayered media. The proposed theorem is applied in the context of solving the EEG forward problem. A Calderon preconditioner is also introduced for the wire electric field integral equation. Finally, preliminary results on the impact of a fast direct solver in solving the EEG forward problem are presented
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Aas, Rune Øistein. "Electromagnetic Scattering : A Surface Integral Equation Formulation." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19240.

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A numerical approach to solving the problem of electromagnetic (EM) scattering on a single scatterer is studied. The problem involves calculating the total EM field in arbitrary observation points when a planar EM wave is scattered.The method considered is a surface integral equation (SIE) formulation involving the use of a dyadic Green's function. A theoretical derivation of the magnetic field integral equation (MFIE) and the electric field integral equation (EFIE) from Maxwell's equations are shown. The Method of Weighted Residuals (MWR) and Kirchoff's Approximation (KA) with their respective domains of application are studied as ways of estimating the surface current densities. A parallelized implementation of the SIE method including both the KA and the MWRis written using the FORTRAN language. The implementation is applied in three concrete versions of the scattering problem, all involving a spherical perfectly conducting scatterer, namely the cases of incoming wavelength much larger, much smaller and comparable with the radius of the scatterer. The problems are divided into two separate solution categories, separated by whether or not the KA is assumed valid. A recursive discretization algorithm was found to be superior to a Delaunay triangulationalgorithm due to less spread in element shape and area. The produced resultsfitted well considering the interference pattern and symmetry requirements with relative errors in the order of magnitude $10^{-5}$ and less. The case of having large wavelength compared to the radius was also compared with Rayleigh scattering theory considering the far field dependence on wavelenth, scattering angle and distance from the scatterer. This resulted in relative errors of 2.1 percent and less. The main advantage of the SIE method is only requiring the surface of the scatterer to be discretized thus saving computational time and memory compared to methods requiring discretization of volume. The method is also capable of producing accurate results for observation points arbitrary close to the scatterer surface. A brief discussion on how the program may be modified in order to extend its capabilities is also included.
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HENRY, CLEMENT BERNARD PIERRE. "Volume Integral Equation Methods for Forward and Inverse Bioelectromagnetic Approaches." Doctoral thesis, Politecnico di Torino, 2021. http://hdl.handle.net/11583/2914544.

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Wei, Jiangong. "Surface Integral Equation Methods for Multi-Scale and Wideband Problems." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1408653442.

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Rockway, John Dexter. "Integral equation formulation for object scattering above a rough surface /." Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/5832.

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Caudron, Boris. "Couplages FEM-BEM faibles et optimisés pour des problèmes de diffraction harmoniques en acoustique et en électromagnétisme." Thesis, Université de Lorraine, 2018. http://www.theses.fr/2018LORR0062/document.

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Dans cette thèse, nous proposons de nouvelles méthodes permettant de résoudre numériquement des problèmes de diffraction harmoniques et tridimensionnels, aussi bien acoustiques qu'électromagnétiques, pour lesquels l'objet diffractant est pénétrable et inhomogène. La résolution de tels problèmes est centrale pour des calculs de surfaces équivalentes sonar et radar (SES et SER). Elle est toutefois connue pour être difficile car elle requiert de discrétiser des équations aux dérivées partielles posées dans un domaine extérieur. Étant infini, ce domaine ne peut pas être maillé en vue d'une résolution par la méthode des éléments finis volumiques. Deux approches classiques permettent de contourner cette difficulté. La première consiste à tronquer le domaine extérieur et rend alors possible une résolution par la méthode des éléments finis volumiques. Étant donné qu'elles approximent les problèmes de diffraction au niveau continu, les méthodes de troncature de domaine peuvent toutefois manquer de précision pour des calculs de SES et de SER. Les problèmes de diffraction harmoniques, pénétrables et inhomogènes peuvent également être résolus en couplant une formulation variationnelle volumique associée à l'objet diffractant et des équations intégrales surfaciques rattachées au domaine extérieur. Nous parlons de couplages FEM-BEM (Finite Element Method-Boundary Element Method). L'intérêt de cette approche réside dans le fait qu'elle est exacte au niveau continu. Les couplages FEM-BEM classiques sont dits forts car ils couplent la formulation variationnelle volumique et les équations intégrales surfaciques au sein d'une même formulation. Ils ne sont toutefois pas adaptés à la résolution de problèmes à haute fréquence. Pour pallier cette limitation, d'autres couplages FEM-BEM, dits faibles, ont été proposés. Ils correspondent concrètement à des algorithmes de décomposition de domaine itérant entre l'objet diffractant et le domaine extérieur. Dans cette thèse, nous introduisons de nouveaux couplages faibles FEM-BEM acoustiques et électromagnétiques basés sur des approximations de Padé récemment développées pour les opérateurs Dirichlet-to-Neumann et Magnetic-to-Electric. Le nombre d'itérations nécessaires à la résolution de ces couplages ne dépend que faiblement de la fréquence et du raffinement du maillage. Les couplages faibles FEM-BEM que nous proposons sont donc adaptés pour des calculs précis de SES et de SER à haute fréquence
In this doctoral dissertation, we propose new methods for solving acoustic and electromagnetic three-dimensional harmonic scattering problems for which the scatterer is penetrable and inhomogeneous. The resolution of such problems is key in the computation of sonar and radar cross sections (SCS and RCS). However, this task is known to be difficult because it requires discretizing partial differential equations set in an exterior domain. Being unbounded, this domain cannot be meshed thus hindering a volume finite element resolution. There are two standard approaches to overcome this difficulty. The first one consists in truncating the exterior domain and renders possible a volume finite element resolution. Given that they approximate the scattering problems at the continuous level, truncation methods may however not be accurate enough for SCS and RCS computations. Inhomogeneous penetrable harmonic scattering problems can also be solved by coupling a volume variational formulation associated with the scatterer and surface integral equations related to the exterior domain. This approach is known as FEM-BEM coupling (Finite Element Method-Boundary Element Method). It is of great interest because it is exact at the continuous level. Classical FEM-BEM couplings are qualified as strong because they couple the volume variational formulation and the surface integral equations within one unique formulation. They are however not suited for solving high-frequency problems. To remedy this drawback, other FEM-BEM couplings, said to be weak, have been proposed. These couplings are actually domain decomposition algorithms iterating between the scatterer and the exterior domain. In this thesis, we introduce new acoustic and electromagnetic weak FEM-BEM couplings based on recently developed Padé approximations of Dirichlet-to-Neumann and Magnetic-to-Electric operators. The number of iterations required to solve these couplings is only slightly dependent on the frequency and the mesh refinement. The weak FEM-BEM couplings that we propose are therefore suited to accurate SCS and RCS computations at high frequencies
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Chen, Yongpin, and 陈涌频. "Surface integral equation method for analyzing electromagnetic scattering in layered medium." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B4775283X.

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Surface integral equation (SIE) method with the kernel of layered medium Green's function (LMGF) is investigated in details from several fundamental aspects. A novel implementation of discrete complex image method (DCIM) is developed to accelerate the evaluation of Sommerfeld integrals and especially improve the far field accuracy of the conventional one. To achieve a broadband simulation of thin layered structure such as microstrip antennas, the mixed-form thin-stratified medium fast-multipole algorithm (MF-TSM-FMA) is developed by applying contour deformation and combining the multipole expansion and plane wave expansion into a single multilevel tree. The low frequency breakdown of the integral operator is further studied and remedied by using the loop-tree decomposition and the augmented electric field integral equation (A-EFIE), both in the context of layered medium integration kernel. All these methods are based on the EFIE for the perfect electric conductor (PEC) and hence can be applied in antenna and circuit applications. To model general dielectric or magnetic objects, the layered medium Green's function based on pilot vector potential approach is generalized for both electric and magnetic current sources. The matrix representation is further derived and the corresponding general SIE is setup. Finally, this SIE is accelerated with the DCIM and applied in quantum optics, such as the calculation of spontaneous emission enhancement of a quantum emitter embedded in a layered structure and in the presence of nano scatterers.
published_or_final_version
Electrical and Electronic Engineering
Doctoral
Doctor of Philosophy
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9

Grandison, Scott. "Boundary integral equation techniques in protein electrostatics and free surface flow problems." Thesis, University of East Anglia, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.410096.

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10

Hidle, Frederick B. "Application of the integral equation asymptotic phase method to penetrable scatterers." Thesis, Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/15797.

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Книги з теми "Volume Surface Integral Equation"

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Słobodzian, Piotr M. Electromagnetic analysis of shielded microwave structures: The surface integral equation approach. Wrocław: Oficyna Wydawnicza Politechniki Wrocławskiej, 2007.

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2

Dunn, Mark H. The solution of a singular integral equation arising from a lifting surface theory for rotating blades. [S.l.]: Old Dominion University, 1991.

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3

P, Lock A., and United States. National Aeronautics and Space Administration., eds. The flux-integral method for multidimensional convection and diffusion. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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4

P, Lock A., and United States. National Aeronautics and Space Administration., eds. The flux-integral method for multidimensional convection and diffusion. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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5

P, Lock A., and United States. National Aeronautics and Space Administration., eds. The flux-integral method for multidimensional convection and diffusion. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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6

Institute for Computer Applications in Science and Engineering., ed. Illustrating surface shape in volume data via principal direction-driven 3D line integral convolution. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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7

Dual Surface Electric Field Integral Equation. Storming Media, 2001.

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8

The flux-integral method for multidimensional convection and diffusion. [Washington, DC]: National Aeronautics and Space Administration, 1994.

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9

Mathematical Tables Part-Volume B : the Airy Integral : Volume 2: Giving Tables of Solutions of the Differential Equation. Cambridge University Press, 2016.

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10

Horing, Norman J. Morgenstern. Retarded Green’s Functions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0005.

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Chapter 5 introduces single-particle retarded Green’s functions, which provide the probability amplitude that a particle created at (x, t) is later annihilated at (x′,t′). Partial Green’s functions, which represent the time development of one (or a few) state(s) that may be understood as localized but are in interaction with a continuum of states, are discussed and applied to chemisorption. Introductions are also made to the Dyson integral equation, T-matrix and the Dirac delta-function potential, with the latter applied to random impurity scattering. The retarded Green’s function in the presence of random impurity scattering is exhibited in the Born and self-consistent Born approximations, with application to Ando’s semi-elliptic density of states for the 2D Landau-quantized electron-impurity system. Important retarded Green’s functions and their methods of derivation are discussed. These include Green’s functions for electrons in magnetic fields in both three dimensions and two dimensions, also a Hamilton equation-of-motion method for the determination of Green’s functions with application to a 2D saddle potential in a time-dependent electric field. Moreover, separable Hamiltonians and their product Green’s functions are discussed with application to a one-dimensional superlattice in axial electric and magnetic fields. Green’s function matching/joining techniques are introduced and applied to spatially varying mass (heterostructures) and non-local electrostatics (surface plasmons).
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Частини книг з теми "Volume Surface Integral Equation"

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Setukha, A. V. "Shifting the Boundary Conditions to the Middle Surface in the Numerical Solution of Neumann Boundary Value Problems Using Integral Equations." In Integral Methods in Science and Engineering, Volume 2, 233–43. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59387-6_23.

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Søndergaard, Thomas M. "Surface integral equation method for 2D scattering problems." In Green’s Function Integral Equation Methods in Nano-Optics, 49–204. First edition. | Boca Raton, FL : CRC Press/Taylor & Francis Group, 2019.: CRC Press, 2019. http://dx.doi.org/10.1201/9781351260206-4.

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Søndergaard, Thomas M. "Surface integral equation method for the quasistatic limit." In Green’s Function Integral Equation Methods in Nano-Optics, 341–58. First edition. | Boca Raton, FL : CRC Press/Taylor & Francis Group, 2019.: CRC Press, 2019. http://dx.doi.org/10.1201/9781351260206-8.

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Søndergaard, Thomas M. "Surface integral equation method for 3D scattering problems." In Green’s Function Integral Equation Methods in Nano-Optics, 359–80. First edition. | Boca Raton, FL : CRC Press/Taylor & Francis Group, 2019.: CRC Press, 2019. http://dx.doi.org/10.1201/9781351260206-9.

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Ferreira, M., and N. Vieira. "Multidimensional Time Fractional Diffusion Equation." In Integral Methods in Science and Engineering, Volume 1, 107–17. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59384-5_10.

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Liggett, James A. "Boundary Integral Equation Method for Free Surface Flow Analysis." In Computer Modeling of Free-Surface and Pressurized Flows, 83–113. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0964-2_4.

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Søndergaard, Thomas M. "Volume integral equation method for 3D scattering problems." In Green’s Function Integral Equation Methods in Nano-Optics, 265–304. First edition. | Boca Raton, FL : CRC Press/Taylor & Francis Group, 2019.: CRC Press, 2019. http://dx.doi.org/10.1201/9781351260206-6.

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Søndergaard, Thomas M. "Volume integral equation method for cylindrically symmetric structures." In Green’s Function Integral Equation Methods in Nano-Optics, 305–40. First edition. | Boca Raton, FL : CRC Press/Taylor & Francis Group, 2019.: CRC Press, 2019. http://dx.doi.org/10.1201/9781351260206-7.

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Amosov, A., and G. Panasenko. "Homogenization of the Integro-Differential Burgers Equation." In Integral Methods in Science and Engineering, Volume 1, 1–8. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4899-2_1.

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Mennouni, A. "Kulkarni Method for the Generalized Airfoil Equation." In Integral Methods in Science and Engineering, Volume 2, 179–85. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-59387-6_18.

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Тези доповідей конференцій з теми "Volume Surface Integral Equation"

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Yan-Nan, Liu, and Xiao-Min Pan. "A Skeletonization accelerated MLFMA for Volume-Surface Integral Equation." In 2020 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO). IEEE, 2020. http://dx.doi.org/10.1109/nemo49486.2020.9343568.

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Wei, F., and A. E. Yilmaz. "Surface-preconditioned AIM-accelerated surface-volume integral equation solution for bioelectromagnetics." In 2012 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2012. http://dx.doi.org/10.1109/iceaa.2012.6328757.

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Xie, Hui, Jiming Song, Ming Yang, Norio Nakagawa, Donald O. Thompson, and Dale E. Chimenti. "A NOVEL BOUNDARY INTEGRAL EQUATION FOR SURFACE CRACK MODEL." In REVIEW OF PROGRESS IN QUANTITATIVE NONDESTRUCTIVE EVALUATION VOLUME 29. AIP, 2010. http://dx.doi.org/10.1063/1.3362412.

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Rebenaque, D. C., F. D. Q. Pereira, J. P. Garcia, J. L. G. Tornero, and A. A. Melcon. "Volume/surface integral equation analysis of circular patch finite antennas." In IEEE Antennas and Propagation Society Symposium, 2004. IEEE, 2004. http://dx.doi.org/10.1109/aps.2004.1330201.

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Li, Xianjin, Jun Hu, Yongpin Chen, Lin Lei, Ming Jiang, and Zhi Rong. "Efficient Matrix Filling for a Volume-Surface Integral Equation Method." In 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2019. http://dx.doi.org/10.1109/iceaa.2019.8879054.

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Chobanyan, Elene, Branislav M. Notaros, and Milan M. Ilic. "Scattering analysis using generalized volume-surface integral equation method of moments." In 2014 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting. IEEE, 2014. http://dx.doi.org/10.1109/aps.2014.6905394.

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Yucel, Abdulkadir C., Luis J. Gomez, and Eric Michielssen. "An internally combined volume-surface integral equation for 3D plasma scatterers." In 2015 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium). IEEE, 2015. http://dx.doi.org/10.1109/usnc-ursi.2015.7303406.

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Ewe, Wei-Bin, Hong-Son Chu, Er-Ping Li, and Le-Wei Li. "Investigation of Surface Plasmon Resonance of Nanoparticles using Volume Integral Equation." In 2007 Asia-Pacific Microwave Conference - (APMC 2007). IEEE, 2007. http://dx.doi.org/10.1109/apmc.2007.4554525.

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Li, Xianjin, Jun Hu, Yongpin Chen, Ming Jiang, and Zaiping Nie. "A Domain Decomposition Method Based on Simplified Volume-Surface Integral Equation." In 2018 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting. IEEE, 2018. http://dx.doi.org/10.1109/apusncursinrsm.2018.8608301.

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Moselhy, Tarek, and Luca Daniel. "Stochastic High Order Basis Functions for Volume Integral Equation with Surface Roughness." In 2007 IEEE Electrical Performance of Electronic Packaging. IEEE, 2007. http://dx.doi.org/10.1109/epep.2007.4387127.

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Звіти організацій з теми "Volume Surface Integral Equation"

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Samn, Sherwood. On a Volume Integral Equation Used in Solving 3-D Electromagnetic Interior Scattering Problems. Fort Belvoir, VA: Defense Technical Information Center, September 1997. http://dx.doi.org/10.21236/ada329439.

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Luc, Brunet. Systematic Equations Handbook : Book 1-Energy. R&D Médiation, May 2015. http://dx.doi.org/10.17601/rd_mediation2015:1.

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The energy equation handbook is the complete collection of physically coherent expression of energy computed using from 2 to 7 physical units among: density(ML-3) energy (ML2T-2) time (T) force (MLT-2) power (ML2T-3) current (I) temperature (Th) quantity (N) mass (M) length (L) candela (J) surface (L2) volume (L3) concentration (ML-3) frequency (T-1) acceleration (LT- 2) speed (LT-1) pressure (ML-1T-2) viscosity (ML-1T-1) luminance (L- 2J) MolarMass (MN-1) MassicEnergy (L2T-2) resistance (ML2T-3I-2) voltage (ML2T-3I-1) Farad (M-1L-2T4I2) Thermal- Conductivity (MLT-3Th-1) SpecificHeat (L2T-2Th-1) MassFlux (MT-1) SurfaceTension (MT-2) Charge (TI) Resistivity (ML3T-3I-2) The complete list of 4196 equations is sorted by number of variable required to obtain an energy in Joules. All the units are in MKSA.
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