James B. Cole - Academia.edu (original) (raw)

Papers by James B. Cole

Research paper thumbnail of Application of Nonstandard Finite Differences to Solve the Wave Equation and Maxwell's Equations

Applications of Nonstandard Finite Difference Schemes

Research paper thumbnail of Nonstandard Finite Difference Models for the Discrete Green's Function of the Scattered Field

Research paper thumbnail of A Low Cost Absorbing Boundary Condition for FDTD Calculations Based on a Nonstandard Finite Difference Model

Research paper thumbnail of Discrete Green’s Function Methodology to Solve Nanophotonics Design Problems

Advanced Photonics 2015, 2015

We introduce a discrete Green’s function (DGF) methodology to solve a nonstandard finite differen... more We introduce a discrete Green’s function (DGF) methodology to solve a nonstandard finite difference model of Maxwell’s equations. The DGF is found using FDTD (finite time domain), can solve design problems faster than FDTD alone.

Research paper thumbnail of Extraterrestrials

Research paper thumbnail of High-Accuracy FDTD Solution of the Absorbing Wave Equation, and Conducting Maxwell's Equations Based on a Nonstandard Finite-Difference Model

IEEE Transactions on Antennas and Propagation, 2004

Research paper thumbnail of The statistical mechanics of image recovery and pattern recognition

American Journal of Physics, 1991

Many kinds of problems in physics and engineering can be cast as optimization problems in which a... more Many kinds of problems in physics and engineering can be cast as optimization problems in which a solution must be picked out of a very large and ‘‘complicated’’ solution candidate space. The simulated annealing algorithm, which derives from statistical mechanical theory, and Bayes’ theorem are introduced and it is shown how they can be combined to solve such problems. As an example, the problem of image recovery from noisy data is considered.

Research paper thumbnail of Nonstandard finite difference models for the discrete Green's function of the scattered field

International Symposium on Antennas and Propagation, Dec 31, 2012

Research paper thumbnail of Fast and high accuracy FDTD using numerical Green's functions based on a nonstandard finite difference model for photonics design

Proceedings of SPIE, Sep 26, 2013

ABSTRACT The use of Green's functions to solve inhomogeneous differential equations, such... more ABSTRACT The use of Green's functions to solve inhomogeneous differential equations, such as the Maxwell's equations with source currents is well known. Unfortunately, it is usually difficult - if not impossible - to find a Green's function which satisfies the boundary conditions. The finite difference time domain (FDTD) algorithm is derived from a finite difference equation (FDE) of Maxwell's equations. FDTD, which automatically takes boundary conditions into account, is often used to solve the FDE, but its computational cost increases much faster than the accuracy as the grid spacing (h) decreases; moreover small h must be used to capture fine features of structures such as subwavelength gratings. A discrete Green's function (DGF), computed using FDTD, can be used to overcome some of the shortcomings of FDTD alone. A DGF computed using FDTD automatically includes the boundary conditions of the problem. In this paper we use a DGF based on what is called a nonstandard finite difference model of Maxwell's equations to compute scattering off subwavelength structures. We verify the accuracy of our method by comparing our calculations with analytic solutions given by Mie theory.

Research paper thumbnail of Fast and high accuracy FDTD using numerical Green's functions based on a nonstandard finite difference model for photonics design

Nanoengineering: Fabrication, Properties, Optics, and Devices X, 2013

ABSTRACT The use of Green's functions to solve inhomogeneous differential equations, such... more ABSTRACT The use of Green's functions to solve inhomogeneous differential equations, such as the Maxwell's equations with source currents is well known. Unfortunately, it is usually difficult - if not impossible - to find a Green's function which satisfies the boundary conditions. The finite difference time domain (FDTD) algorithm is derived from a finite difference equation (FDE) of Maxwell's equations. FDTD, which automatically takes boundary conditions into account, is often used to solve the FDE, but its computational cost increases much faster than the accuracy as the grid spacing (h) decreases; moreover small h must be used to capture fine features of structures such as subwavelength gratings. A discrete Green's function (DGF), computed using FDTD, can be used to overcome some of the shortcomings of FDTD alone. A DGF computed using FDTD automatically includes the boundary conditions of the problem. In this paper we use a DGF based on what is called a nonstandard finite difference model of Maxwell's equations to compute scattering off subwavelength structures. We verify the accuracy of our method by comparing our calculations with analytic solutions given by Mie theory.

Research paper thumbnail of A cellular automation methodology for solving the wave equation

Proceedings of the 7th international conference on Supercomputing, 1993

We describe a parallel finite difference algorithm in the form of a cellular automaton fbr solvin... more We describe a parallel finite difference algorithm in the form of a cellular automaton fbr solving the full form of the wave equation. Since we do not use the far field approximation, this algorithm is particularly effective for solving near-and intermediate field problems. Problems are solved in the time domain and real time animakd displays show the field evolution. The algorithm is perfectly matched to the architecture of "single instruction multiple data" (SIMD) parallel processors. On the CM-200, for example, it typically takes several minutes to compute wave fields and display themona512x512 grid. A good personal computer, however, is sufficient to develop many interesting classroom demonstrations of wave propagation phenomena.

Research paper thumbnail of Application of Nonstandard Finite Differences to Solve the Wave Equation and Maxwell's Equations

Applications of Nonstandard Finite Difference Schemes

Research paper thumbnail of Nonstandard Finite Difference Models for the Discrete Green's Function of the Scattered Field

Research paper thumbnail of A Low Cost Absorbing Boundary Condition for FDTD Calculations Based on a Nonstandard Finite Difference Model

Research paper thumbnail of Discrete Green’s Function Methodology to Solve Nanophotonics Design Problems

Advanced Photonics 2015, 2015

We introduce a discrete Green’s function (DGF) methodology to solve a nonstandard finite differen... more We introduce a discrete Green’s function (DGF) methodology to solve a nonstandard finite difference model of Maxwell’s equations. The DGF is found using FDTD (finite time domain), can solve design problems faster than FDTD alone.

Research paper thumbnail of Extraterrestrials

Research paper thumbnail of High-Accuracy FDTD Solution of the Absorbing Wave Equation, and Conducting Maxwell's Equations Based on a Nonstandard Finite-Difference Model

IEEE Transactions on Antennas and Propagation, 2004

Research paper thumbnail of The statistical mechanics of image recovery and pattern recognition

American Journal of Physics, 1991

Many kinds of problems in physics and engineering can be cast as optimization problems in which a... more Many kinds of problems in physics and engineering can be cast as optimization problems in which a solution must be picked out of a very large and ‘‘complicated’’ solution candidate space. The simulated annealing algorithm, which derives from statistical mechanical theory, and Bayes’ theorem are introduced and it is shown how they can be combined to solve such problems. As an example, the problem of image recovery from noisy data is considered.

Research paper thumbnail of Nonstandard finite difference models for the discrete Green's function of the scattered field

International Symposium on Antennas and Propagation, Dec 31, 2012

Research paper thumbnail of Fast and high accuracy FDTD using numerical Green's functions based on a nonstandard finite difference model for photonics design

Proceedings of SPIE, Sep 26, 2013

ABSTRACT The use of Green's functions to solve inhomogeneous differential equations, such... more ABSTRACT The use of Green's functions to solve inhomogeneous differential equations, such as the Maxwell's equations with source currents is well known. Unfortunately, it is usually difficult - if not impossible - to find a Green's function which satisfies the boundary conditions. The finite difference time domain (FDTD) algorithm is derived from a finite difference equation (FDE) of Maxwell's equations. FDTD, which automatically takes boundary conditions into account, is often used to solve the FDE, but its computational cost increases much faster than the accuracy as the grid spacing (h) decreases; moreover small h must be used to capture fine features of structures such as subwavelength gratings. A discrete Green's function (DGF), computed using FDTD, can be used to overcome some of the shortcomings of FDTD alone. A DGF computed using FDTD automatically includes the boundary conditions of the problem. In this paper we use a DGF based on what is called a nonstandard finite difference model of Maxwell's equations to compute scattering off subwavelength structures. We verify the accuracy of our method by comparing our calculations with analytic solutions given by Mie theory.

Research paper thumbnail of Fast and high accuracy FDTD using numerical Green's functions based on a nonstandard finite difference model for photonics design

Nanoengineering: Fabrication, Properties, Optics, and Devices X, 2013

ABSTRACT The use of Green's functions to solve inhomogeneous differential equations, such... more ABSTRACT The use of Green's functions to solve inhomogeneous differential equations, such as the Maxwell's equations with source currents is well known. Unfortunately, it is usually difficult - if not impossible - to find a Green's function which satisfies the boundary conditions. The finite difference time domain (FDTD) algorithm is derived from a finite difference equation (FDE) of Maxwell's equations. FDTD, which automatically takes boundary conditions into account, is often used to solve the FDE, but its computational cost increases much faster than the accuracy as the grid spacing (h) decreases; moreover small h must be used to capture fine features of structures such as subwavelength gratings. A discrete Green's function (DGF), computed using FDTD, can be used to overcome some of the shortcomings of FDTD alone. A DGF computed using FDTD automatically includes the boundary conditions of the problem. In this paper we use a DGF based on what is called a nonstandard finite difference model of Maxwell's equations to compute scattering off subwavelength structures. We verify the accuracy of our method by comparing our calculations with analytic solutions given by Mie theory.

Research paper thumbnail of A cellular automation methodology for solving the wave equation

Proceedings of the 7th international conference on Supercomputing, 1993

We describe a parallel finite difference algorithm in the form of a cellular automaton fbr solvin... more We describe a parallel finite difference algorithm in the form of a cellular automaton fbr solving the full form of the wave equation. Since we do not use the far field approximation, this algorithm is particularly effective for solving near-and intermediate field problems. Problems are solved in the time domain and real time animakd displays show the field evolution. The algorithm is perfectly matched to the architecture of "single instruction multiple data" (SIMD) parallel processors. On the CM-200, for example, it typically takes several minutes to compute wave fields and display themona512x512 grid. A good personal computer, however, is sufficient to develop many interesting classroom demonstrations of wave propagation phenomena.