The Experts below are selected from a list of 9033 Experts worldwide ranked by ideXlab platform
Young Seek Chung - One of the best experts on this subject based on the ideXlab platform.
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a stable solution of time domain electric field integral equation using weighted laguerre polynomials
2007Co-Authors: Young Seek Chung, Yoonju Lee, Joonyeon Kim, Changyul Cheon, Byungje Lee, T K SarkarAbstract:In this article, we propose a new stable solution for the time domain electric field integral equation (TD-EFIE) for arbitrarily shaped conducting structures, which utilizes weighted Laguerre polynomials as temporal basis functions, which means that the unknown surface currents are expanded by these basis functions. The proposed algorithm is based on the Galerkin's scheme that involves separate spatial and temporal testing procedures. By introducing the temporal testing procedure, the conventional marching-on in time procedure can be replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials. In this article, by deriving the integral formulation using the weighted Laguerre polynomials, we solve for the surface current density as the unknown directly. To verify the accuracy of the proposed method, we have compared the results with the inverse discrete Fourier transform of the frequency domain solutions for the electric field integral equation. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2789–2793, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22835
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solution of time domain electric field integral equation using the laguerre polynomials
2004Co-Authors: Young Seek Chung, T K Sarkar, Baek Ho Jung, Magdalena Salazarpalma, Seongman Jang, Kyungjung KimAbstract:In this paper, we propose a numerical method to obtain a solution for the time domain electric field integral equation (TD-EFIE) for arbitrary shaped conducting structures. This method does not utilize the customary marching-on in time (MOT) solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the Galerkin temporal testing procedure, the MOT procedure is replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the current, the spatial and the temporal variables can be separated and the temporal variables can be integrated out. For convenience, we use the Hertz vector as the unknown variable instead of the electric current density. To verify our method, we compare the results of a TD-EFIE and inverse Fourier transform of a frequency domain EFIE.
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an unconditionally stable scheme for the finite difference time domain method
2003Co-Authors: Young Seek Chung, T K Sarkar, Baek Ho Jung, Magdalena SalazarpalmaAbstract:In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TE/sub z/ case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell's equations by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically, which results in an implicit Relation. In this way, the time variable is eliminated from the computations. By introducing the Galerkin temporal testing procedure, the marching-on in time method is replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials if the input waveform is of arbitrary shape. Since the weighted Laguerre polynomials converge to zero as time progresses, the electric and magnetic fields when expanded in a series of weighted Laguerre polynomials also converge to zero. The other novelty of this approach is that, through the use of the entire domain-weighted Laguerre polynomials for the expansion of the temporal variation of the fields, the spatial and the temporal variables can be separated.
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solution of a time domain magnetic field integral equation for arbitrarily closed conducting bodies using an unconditionally stable methodology
2002Co-Authors: Young Seek Chung, T K Sarkar, Baek Ho JungAbstract:In this work, we present a new and efficient numerical method to obtain an unconditionally stable solution for the time-domain magnetic-field integral equation (TD-MFIE) for arbitrarily closed conducting bodies. This novel method does not utilize the customary marching-on-in-time (MOT) solution method often used to solve a hyperbolic partial-differential equation. Instead, we solve the wave equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives in the TD-MFIE formulation can be handled analytically. Since these weighted Laguerre polynomials converge to zero as time progresses, the electric surface currents also converge to zero when expanded in a series of weighted Laguerre polynomials. In order to solve the wave equation, we introduce two separate testing procedures: spatial and temporal testing. By introducing the temporal testing procedure first, the marching-on in time procedure is replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the currents, the spatial and the temporal variables can be separated. To verify our method, we do a comparison with the results of an inverse Fourier transform of a frequency domain MFIE. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 493–499, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10647
Magdalena Salazarpalma - One of the best experts on this subject based on the ideXlab platform.
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solution of time domain electric field integral equation using the laguerre polynomials
2004Co-Authors: Young Seek Chung, T K Sarkar, Baek Ho Jung, Magdalena Salazarpalma, Seongman Jang, Kyungjung KimAbstract:In this paper, we propose a numerical method to obtain a solution for the time domain electric field integral equation (TD-EFIE) for arbitrary shaped conducting structures. This method does not utilize the customary marching-on in time (MOT) solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the Galerkin temporal testing procedure, the MOT procedure is replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the current, the spatial and the temporal variables can be separated and the temporal variables can be integrated out. For convenience, we use the Hertz vector as the unknown variable instead of the electric current density. To verify our method, we compare the results of a TD-EFIE and inverse Fourier transform of a frequency domain EFIE.
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an unconditionally stable scheme for the finite difference time domain method
2003Co-Authors: Young Seek Chung, T K Sarkar, Baek Ho Jung, Magdalena SalazarpalmaAbstract:In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TE/sub z/ case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell's equations by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically, which results in an implicit Relation. In this way, the time variable is eliminated from the computations. By introducing the Galerkin temporal testing procedure, the marching-on in time method is replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials if the input waveform is of arbitrary shape. Since the weighted Laguerre polynomials converge to zero as time progresses, the electric and magnetic fields when expanded in a series of weighted Laguerre polynomials also converge to zero. The other novelty of this approach is that, through the use of the entire domain-weighted Laguerre polynomials for the expansion of the temporal variation of the fields, the spatial and the temporal variables can be separated.
T K Sarkar - One of the best experts on this subject based on the ideXlab platform.
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a stable solution of time domain electric field integral equation using weighted laguerre polynomials
2007Co-Authors: Young Seek Chung, Yoonju Lee, Joonyeon Kim, Changyul Cheon, Byungje Lee, T K SarkarAbstract:In this article, we propose a new stable solution for the time domain electric field integral equation (TD-EFIE) for arbitrarily shaped conducting structures, which utilizes weighted Laguerre polynomials as temporal basis functions, which means that the unknown surface currents are expanded by these basis functions. The proposed algorithm is based on the Galerkin's scheme that involves separate spatial and temporal testing procedures. By introducing the temporal testing procedure, the conventional marching-on in time procedure can be replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials. In this article, by deriving the integral formulation using the weighted Laguerre polynomials, we solve for the surface current density as the unknown directly. To verify the accuracy of the proposed method, we have compared the results with the inverse discrete Fourier transform of the frequency domain solutions for the electric field integral equation. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2789–2793, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22835
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solution of time domain electric field integral equation using the laguerre polynomials
2004Co-Authors: Young Seek Chung, T K Sarkar, Baek Ho Jung, Magdalena Salazarpalma, Seongman Jang, Kyungjung KimAbstract:In this paper, we propose a numerical method to obtain a solution for the time domain electric field integral equation (TD-EFIE) for arbitrary shaped conducting structures. This method does not utilize the customary marching-on in time (MOT) solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the Galerkin temporal testing procedure, the MOT procedure is replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the current, the spatial and the temporal variables can be separated and the temporal variables can be integrated out. For convenience, we use the Hertz vector as the unknown variable instead of the electric current density. To verify our method, we compare the results of a TD-EFIE and inverse Fourier transform of a frequency domain EFIE.
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an unconditionally stable scheme for the finite difference time domain method
2003Co-Authors: Young Seek Chung, T K Sarkar, Baek Ho Jung, Magdalena SalazarpalmaAbstract:In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TE/sub z/ case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell's equations by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically, which results in an implicit Relation. In this way, the time variable is eliminated from the computations. By introducing the Galerkin temporal testing procedure, the marching-on in time method is replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials if the input waveform is of arbitrary shape. Since the weighted Laguerre polynomials converge to zero as time progresses, the electric and magnetic fields when expanded in a series of weighted Laguerre polynomials also converge to zero. The other novelty of this approach is that, through the use of the entire domain-weighted Laguerre polynomials for the expansion of the temporal variation of the fields, the spatial and the temporal variables can be separated.
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solution of a time domain magnetic field integral equation for arbitrarily closed conducting bodies using an unconditionally stable methodology
2002Co-Authors: Young Seek Chung, T K Sarkar, Baek Ho JungAbstract:In this work, we present a new and efficient numerical method to obtain an unconditionally stable solution for the time-domain magnetic-field integral equation (TD-MFIE) for arbitrarily closed conducting bodies. This novel method does not utilize the customary marching-on-in-time (MOT) solution method often used to solve a hyperbolic partial-differential equation. Instead, we solve the wave equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives in the TD-MFIE formulation can be handled analytically. Since these weighted Laguerre polynomials converge to zero as time progresses, the electric surface currents also converge to zero when expanded in a series of weighted Laguerre polynomials. In order to solve the wave equation, we introduce two separate testing procedures: spatial and temporal testing. By introducing the temporal testing procedure first, the marching-on in time procedure is replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the currents, the spatial and the temporal variables can be separated. To verify our method, we do a comparison with the results of an inverse Fourier transform of a frequency domain MFIE. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 493–499, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10647
Alexander Russell - One of the best experts on this subject based on the ideXlab platform.
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the combinatorics of the longest chain rule linear consistency for proof of stake blockchains
2020Co-Authors: Erica Blum, Aggelos Kiayias, Cristopher Moore, Saad Quader, Alexander RussellAbstract:The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth from the end of the chain. While the analysis of Bitcoin guarantees consistency with error 2−k for blocks of depth O(k), the state-of-the-art of proof-of-stake (PoS) blockchains suffers from a quadratic dependence on k: these protocols, exemplified by Ouroboros (Crypto 2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017), can only establish that depth Θ(k2) is sufficient. Whether this quadratic gap is an intrinsic limitation of PoS---due to issues such as the nothing-at-stake problem---has been an urgent open question, as deployed PoS blockchains further rely on consistency for protocol correctnes. We give an axiomatic theory of blockchain dynamics that permits rigorous reasoning about the longest-chain rule and achieve, in broad generality, Θ(k) dependence on depth in order to achieve consistency error 2−k. In particular, for the first time we show that PoS protocols can match proof-of-work protocols for linear consistency. We analyze the associated stochastic process, give a Recursive Relation for the critical functionals of this process, and derive tail bounds in both i.i.d. and martingale settings via associated generating functions.
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linear consistency for proof of stake blockchains
2019Co-Authors: Erica Blum, Aggelos Kiayias, Cristopher Moore, Saad Quader, Alexander RussellAbstract:The blockchain data structure maintained via the longest-chain rule---popularized by Bitcoin---is a powerful algorithmic tool for consensus algorithms. Such algorithms achieve consistency for blocks in the chain as a function of their depth from the end of the chain. While the analysis of Bitcoin guarantees consistency with error $2^{-k}$ for blocks of depth $O(k)$, the state-of-the-art of proof-of-stake (PoS) blockchains suffers from a quadratic dependence on $k$: these protocols, exemplified by Ouroboros (Crypto 2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017), can only establish that depth $\Theta(k^2)$ is sufficient. Whether this quadratic gap is an intrinsic limitation of PoS---due to issues such as the nothing-at-stake problem---has been an urgent open question, as deployed PoS blockchains further rely on consistency for protocol correctness. We give an axiomatic theory of blockchain dynamics that permits rigorous reasoning about the longest-chain rule and achieve, in broad generality, $\Theta(k)$ dependence on depth in order to achieve consistency error $2^{-k}$. In particular, for the first time, we show that PoS protocols can match proof-of-work protocols for linear consistency. We analyze the associated stochastic process, give a Recursive Relation for the critical functionals of this process, and derive tail bounds in both i.i.d. and martingale settings via associated generating functions.
Kyungjung Kim - One of the best experts on this subject based on the ideXlab platform.
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solution of time domain electric field integral equation using the laguerre polynomials
2004Co-Authors: Young Seek Chung, T K Sarkar, Baek Ho Jung, Magdalena Salazarpalma, Seongman Jang, Kyungjung KimAbstract:In this paper, we propose a numerical method to obtain a solution for the time domain electric field integral equation (TD-EFIE) for arbitrary shaped conducting structures. This method does not utilize the customary marching-on in time (MOT) solution method often used to solve a hyperbolic partial differential equation. Instead we solve the wave equation by expressing the transient behaviors in terms of Laguerre polynomials. By using these causal orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically. In order to solve the wave equation, we introduce two separate testing procedures, a spatial and temporal testing. By introducing first the Galerkin temporal testing procedure, the MOT procedure is replaced by a Recursive Relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the current, the spatial and the temporal variables can be separated and the temporal variables can be integrated out. For convenience, we use the Hertz vector as the unknown variable instead of the electric current density. To verify our method, we compare the results of a TD-EFIE and inverse Fourier transform of a frequency domain EFIE.
