The Experts below are selected from a list of 12081 Experts worldwide ranked by ideXlab platform
Thomas F. Eibert - One of the best experts on this subject based on the ideXlab platform.
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an accurate low order discretization scheme for the Identity Operator in the magnetic field and combined field integral equations
arXiv: Numerical Analysis, 2020Co-Authors: Jonas Kornprobst, Thomas F. EibertAbstract:A new low-order discretization scheme for the Identity Operator in the magnetic field integral equation (MFIE) is discussed. Its concept is derived from the weak-form representation of combined sources which are discretized with Rao-Wilton-Glisson (RWG) functions. The resulting MFIE overcomes the accuracy problem of the classical MFIE while it maintains fast iterative solver convergence. The improvement in accuracy is verified with a mesh refinement analysis and with near- and far-field scattering results. Furthermore, simulation results for a combined field integral equation (CFIE) involving the new MFIE show that this CFIE is interior-resonance free and well-conditioned like the classical CFIE, but also accurate as the EFIE.
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Accurate Identity Operator Discretization for the Combined Field Integral Equation
2018 IEEE International Symposium on Antennas and Propagation & USNC URSI National Radio Science Meeting, 2018Co-Authors: Jonas Kornprobst, Thomas F. EibertAbstract:The accuracy problem of the classically Rao-Wilton-Glisson (RWG) discretized magnetic field and combined field integral equations originates from the strong singularity of the Identity Operator. With a novel basis transformation scheme, i.e. two subsequent weak-form rotations of the RWG basis functions, the accuracy of the Identity Operator discretization is improved. The presented discretization scheme is immediately compatible with fast algorithms and is combined with the multilevel fast multipole algorithm. The good accuracy and the good conditioning behavior of the formulation are verified in several numerical simulations, also including electrically large problems.
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An Accurate Low-Order Discretization Scheme for the Identity Operator in the Magnetic Field and Combined Field Integral Equations
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Jonas Kornprobst, Thomas F. EibertAbstract:A new low-order discretization scheme for the Identity Operator in the magnetic field integral equation (MFIE) is discussed. Its concept is derived from the weak-form representation of combined sources that are discretized with Rao-Wilton-Glisson functions. The resulting MFIE overcomes the accuracy problem of the classical MFIE while it maintains fast iterative-solver convergence. The improvement in accuracy is verified with a mesh refinement analysis and with near- and far-field scattering results. Furthermore, simulation results for a combined field integral equation (CFIE) involving the new MFIE show that this CFIE is interior resonance free and well-conditioned like the classical CFIE but also accurate as the electric field integral equation.
Jonas Kornprobst - One of the best experts on this subject based on the ideXlab platform.
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an accurate low order discretization scheme for the Identity Operator in the magnetic field and combined field integral equations
arXiv: Numerical Analysis, 2020Co-Authors: Jonas Kornprobst, Thomas F. EibertAbstract:A new low-order discretization scheme for the Identity Operator in the magnetic field integral equation (MFIE) is discussed. Its concept is derived from the weak-form representation of combined sources which are discretized with Rao-Wilton-Glisson (RWG) functions. The resulting MFIE overcomes the accuracy problem of the classical MFIE while it maintains fast iterative solver convergence. The improvement in accuracy is verified with a mesh refinement analysis and with near- and far-field scattering results. Furthermore, simulation results for a combined field integral equation (CFIE) involving the new MFIE show that this CFIE is interior-resonance free and well-conditioned like the classical CFIE, but also accurate as the EFIE.
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Accurate Identity Operator Discretization for the Combined Field Integral Equation
2018 IEEE International Symposium on Antennas and Propagation & USNC URSI National Radio Science Meeting, 2018Co-Authors: Jonas Kornprobst, Thomas F. EibertAbstract:The accuracy problem of the classically Rao-Wilton-Glisson (RWG) discretized magnetic field and combined field integral equations originates from the strong singularity of the Identity Operator. With a novel basis transformation scheme, i.e. two subsequent weak-form rotations of the RWG basis functions, the accuracy of the Identity Operator discretization is improved. The presented discretization scheme is immediately compatible with fast algorithms and is combined with the multilevel fast multipole algorithm. The good accuracy and the good conditioning behavior of the formulation are verified in several numerical simulations, also including electrically large problems.
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An Accurate Low-Order Discretization Scheme for the Identity Operator in the Magnetic Field and Combined Field Integral Equations
IEEE Transactions on Antennas and Propagation, 2018Co-Authors: Jonas Kornprobst, Thomas F. EibertAbstract:A new low-order discretization scheme for the Identity Operator in the magnetic field integral equation (MFIE) is discussed. Its concept is derived from the weak-form representation of combined sources that are discretized with Rao-Wilton-Glisson functions. The resulting MFIE overcomes the accuracy problem of the classical MFIE while it maintains fast iterative-solver convergence. The improvement in accuracy is verified with a mesh refinement analysis and with near- and far-field scattering results. Furthermore, simulation results for a combined field integral equation (CFIE) involving the new MFIE show that this CFIE is interior resonance free and well-conditioned like the classical CFIE but also accurate as the electric field integral equation.
L Gurel - One of the best experts on this subject based on the ideXlab platform.
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discretization error due to the Identity Operator in surface integral equations
Computer Physics Communications, 2009Co-Authors: Ozgur Ergul, L GurelAbstract:We consider the accuracy of surface integral equations for the solution of scattering and radiation problems in electromagnetics. In numerical solutions, second-kind integral equations involving welltested Identity Operators are preferable for efficiency, because they produce diagonally-dominant matrix equations that can be solved easily with iterative methods. However, the existence of the well-tested Identity Operators leads to inaccurate results, especially when the equations are discretized with low-order basis functions, such as the Rao–Wilton–Glisson functions. By performing a computational experiment based on the nonradiating property of the tangential incident fields on arbitrary surfaces, we show that the discretization error of the Identity Operator is a major error source that contaminates the accuracy of the second-kind integral equations significantly.
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on the errors arising in surface integral equations due to the discretization of the Identity Operator
IEEE Antennas and Propagation Society International Symposium, 2009Co-Authors: Ozgur Ergul, L GurelAbstract:Surface integral equations (SIEs) are commonly used to formulate scattering and radiation problems involving three-dimensional metallic and homogeneous dielectric objects with arbitrary shapes [1]–[3]. For numerical solutions, equivalent electric and/or magnetic currents defined on surfaces are discretized and expanded in a series of basis functions, such as the Rao-Wilton-Glisson (RWG) functions on planar triangles. Then, the boundary conditions are tested on surfaces via a set of testing functions. Solutions of the resulting dense matrix equations provide the expansion coefficients of the equivalent currents, which can be used to compute the scattered or radiated electromagnetic fields. In general, SIEs involve three basic Operators, i.e., integro-differential K and T Operators, and the Identity Operator I{X}(r) = X(r). Depending on the testing scheme and the boundary conditions used, there are four basic SIEs [2],[3], namely, the tangential electric-field integral equation (T-EFIE), the normal electric-field integral equation (N-EFIE), the tangential magnetic-field integral equation (T-MFIE), and the normal magnetic-field integral equation (N-MFIE). In the tangential equations, boundary conditions are tested directly by sampling the tangential components of the electric and magnetic fields on the surface. In the normal equations, however, electromagnetic fields are tested after they are projected onto the surface via a cross-product operation with the outward normal vector.
Haifeng Lang - One of the best experts on this subject based on the ideXlab platform.
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generalized discrete truncated wigner approximation for nonadiabatic quantum classical dynamics
Journal of Chemical Physics, 2021Co-Authors: Haifeng Lang, Oriol Vendrell, Philipp HaukeAbstract:Nonadiabatic molecular dynamics occur in a wide range of chemical reactions and femtochemistry experiments involving electronically excited states. These dynamics are hard to treat numerically as the system’s complexity increases, and it is thus desirable to have accurate yet affordable methods for their simulation. Here, we introduce a linearized semiclassical method, the generalized discrete truncated Wigner approximation (GDTWA), which is well-established in the context of quantum spin lattice systems, into the arena of chemical nonadiabatic systems. In contrast to traditional continuous mapping approaches, e.g., the Meyer–Miller–Stock–Thoss and the spin mappings, GDTWA samples the electron degrees of freedom in a discrete phase space and thus forbids an unphysical unbounded growth of electronic state populations. The discrete sampling also accounts for an effective reduced but non-vanishing zero-point energy without an explicit parameter, which makes it possible to treat the Identity Operator and other Operators on an equal footing. As numerical benchmarks on two linear vibronic coupling models and Tully’s models show, GDTWA has a satisfactory accuracy in a wide parameter regime, independent of whether the dynamics is dominated by relaxation or by coherent interactions. Our results suggest that the method can be very adequate to treat challenging nonadiabatic dynamics problems in chemistry and related fields.
Ozgur Ergul - One of the best experts on this subject based on the ideXlab platform.
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discretization error due to the Identity Operator in surface integral equations
Computer Physics Communications, 2009Co-Authors: Ozgur Ergul, L GurelAbstract:We consider the accuracy of surface integral equations for the solution of scattering and radiation problems in electromagnetics. In numerical solutions, second-kind integral equations involving welltested Identity Operators are preferable for efficiency, because they produce diagonally-dominant matrix equations that can be solved easily with iterative methods. However, the existence of the well-tested Identity Operators leads to inaccurate results, especially when the equations are discretized with low-order basis functions, such as the Rao–Wilton–Glisson functions. By performing a computational experiment based on the nonradiating property of the tangential incident fields on arbitrary surfaces, we show that the discretization error of the Identity Operator is a major error source that contaminates the accuracy of the second-kind integral equations significantly.
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on the errors arising in surface integral equations due to the discretization of the Identity Operator
IEEE Antennas and Propagation Society International Symposium, 2009Co-Authors: Ozgur Ergul, L GurelAbstract:Surface integral equations (SIEs) are commonly used to formulate scattering and radiation problems involving three-dimensional metallic and homogeneous dielectric objects with arbitrary shapes [1]–[3]. For numerical solutions, equivalent electric and/or magnetic currents defined on surfaces are discretized and expanded in a series of basis functions, such as the Rao-Wilton-Glisson (RWG) functions on planar triangles. Then, the boundary conditions are tested on surfaces via a set of testing functions. Solutions of the resulting dense matrix equations provide the expansion coefficients of the equivalent currents, which can be used to compute the scattered or radiated electromagnetic fields. In general, SIEs involve three basic Operators, i.e., integro-differential K and T Operators, and the Identity Operator I{X}(r) = X(r). Depending on the testing scheme and the boundary conditions used, there are four basic SIEs [2],[3], namely, the tangential electric-field integral equation (T-EFIE), the normal electric-field integral equation (N-EFIE), the tangential magnetic-field integral equation (T-MFIE), and the normal magnetic-field integral equation (N-MFIE). In the tangential equations, boundary conditions are tested directly by sampling the tangential components of the electric and magnetic fields on the surface. In the normal equations, however, electromagnetic fields are tested after they are projected onto the surface via a cross-product operation with the outward normal vector.
