Results 1  10
of
193
On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
Abstract

Cited by 219 (4 self)
 Add to MetaCart
Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
The Finite Volume, Finite Element, and Finite Difference Methods as Numerical Methods for Physical Field Problems
 Journal of Computational Physics
, 2000
"... The present work describes an alternative to the classical partial differential equationsbased approach to the discretization of physical field problems. This alternative is based on a preliminary reformulation of the mathematical model in a partially discrete form, which preserves as much as possi ..."
Abstract

Cited by 66 (2 self)
 Add to MetaCart
The present work describes an alternative to the classical partial differential equationsbased approach to the discretization of physical field problems. This alternative is based on a preliminary reformulation of the mathematical model in a partially discrete form, which preserves as much as possible the physical and geometrical content of the original problem, and is made possible by the existence and properties of a common mathematical structure of physical field theories. The goal is to maintain the focus, both in the modeling and in the discretizati on step, on the physics of the problem, thinking in terms of numerical methods for physical field problems, and not for a particular mathematical form (for example, a partial differential equation) into which the original physical problem happens to be translated.
Fast Solution Methods in Electromagnetics
, 1997
"... Various methods for efficiently solving electromagnetic problems are presented. Electromagnetic scattering problems can be roughly classified into surface and volume problems, while fast methods are either differential or integral equation based. The resultant systems of linear equations are either ..."
Abstract

Cited by 33 (0 self)
 Add to MetaCart
Various methods for efficiently solving electromagnetic problems are presented. Electromagnetic scattering problems can be roughly classified into surface and volume problems, while fast methods are either differential or integral equation based. The resultant systems of linear equations are either solved directly or iteratively. A review of various differential equation solvers, their complexities, and memory requirements is given. The issues of grid dispersion and hybridization with integral equation solvers are discussed. Several fast integral equation solvers for surface and volume scatterers are presented. These solvers have reduced computational complexities and memory requirements. 1. Introduction Computational electromagnetics is a fascinating discipline that has drawn the attention of mathematicians, engineers, physicists, and computer scientists alike. It is a discipline that creates a symbiotic marriage between mathematics, physics, computer science, and various applicatio...
Threedimensional fdtd analysis of a pulsed microwave confocal system for breast cancer detection: Design of an antennaarray element
 IEEE Trans. Antennas Propagat
, 1999
"... Abstract—We are investigating a new ultrawideband (UWB) microwave radar technology to detect and image earlystage malignant breast tumors that are often invisible to X rays. In this paper, we present the methodology and initial results of threedimensional (3D) finitedifference timedomain (FDTD ..."
Abstract

Cited by 31 (3 self)
 Add to MetaCart
(Show Context)
Abstract—We are investigating a new ultrawideband (UWB) microwave radar technology to detect and image earlystage malignant breast tumors that are often invisible to X rays. In this paper, we present the methodology and initial results of threedimensional (3D) finitedifference timedomain (FDTD) simulations. The discussion concentrates on the design of a single resistively loaded bowtie antenna element of a proposed confocal sensor array. We present the reflection, radiation, and scattering properties of the electromagnetic pulse radiated by the antenna element within a homogeneous, layered halfspace model of the human breast and the polarization and frequencyresponse characteristics of generic tumor shapes. We conclude that the dynamic range of a sensor array comprised of such elements in conjunction with existing microwave equipment is adequate to detect small cancerous tumors usually missed by Xray mammography. Index Terms—Antenna array, cancer, FDTD methods. I.
A Capacitively Loaded PIFA for Compact Mobile Telephone Handsets
, 1997
"... A capacitively loaded planar invertedF antenna (PIFA) is proposed and studied. It is found that the capacitive load reduces the resonance length of the PIFA from =4 to less than =8. A design with a bandwidth of 178MHz centered at 1.8GHz is provided to demonstrate that compact antennas for mobile t ..."
Abstract

Cited by 30 (1 self)
 Add to MetaCart
A capacitively loaded planar invertedF antenna (PIFA) is proposed and studied. It is found that the capacitive load reduces the resonance length of the PIFA from =4 to less than =8. A design with a bandwidth of 178MHz centered at 1.8GHz is provided to demonstrate that compact antennas for mobile telephone handsets can be constructed using this approach. The finite difference time domain method is used in the study and experimental verification is also provided. y Supported by the Hong Kong research grant council, Project HKUST788/96E and CRC93/94.EG01. z Corresponding Author. Email: phcrr@ee.ust.hk. Phone: (+852) 2358 7082. Fax: (+852) 2358 1485. 2 I. Introduction In recent years, the demand for compact mobile telephone handsets has grown. Handsets the size of a deck of cards have begun appearing in the market and as the demand for increased electronic mobility grows, the need for smaller handsets will most likely increase. The handset size, however, is limited by the battery and...
Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion
"... We construct reliable finitedifference methods for approximating the solutions to Maxwell's equations and equations of magnetic field diffusion using discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus in discrete form. These method ..."
Abstract

Cited by 27 (12 self)
 Add to MetaCart
We construct reliable finitedifference methods for approximating the solutions to Maxwell's equations and equations of magnetic field diffusion using discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus in discrete form. These methods mimic many fundamental properties of the underlying physical problem, including the conservation laws, the symmetries in the solution, the nondivergence of particular vector fields and they do not allow spurious modes. The constructed method can be applied when there are strongly discontinuous properties of the media and nonorthogonal, nonsmooth computational grids. In this paper we apply discrete vector analysis techniques [1][4] to construct mimetic finitedifference methods to Maxwell's firstorder curl equations (hyperbolic type) and to the equations of magnetic diffusion (parabolic type). The system of firstorder Maxwell's curl equations can be written as follows: @ ~ B=@t = \Gammacur...
Nonreflecting Boundary Conditions For Maxwell's Equations
 J. Comput. Phys
, 1997
"... Exact nonreflecting boundary conditions are derived for the time dependent Maxwell equations in three space dimensions. These conditions hold on a spherical surface B, outside of which the medium is assumed to be homogeneous, isotropic, and sourcefree. They are local in time and nonlocal on B, and ..."
Abstract

Cited by 27 (0 self)
 Add to MetaCart
(Show Context)
Exact nonreflecting boundary conditions are derived for the time dependent Maxwell equations in three space dimensions. These conditions hold on a spherical surface B, outside of which the medium is assumed to be homogeneous, isotropic, and sourcefree. They are local in time and nonlocal on B, and they do not involve highorder derivatives. Thus they are easy to incorporate into finite difference or finite element methods. These boundary conditions are similar to the exact nonreflecting boundary conditions for the scalar wave equation [1], which yield high numerical accuracy [2]. 1 Introduction We consider electromagnetic scattering in unbounded threedimensional space. The scattering region may contain obstacles, inhomogeneities, and nonlinearities. To treat it numerically we surround the region of interest by an artificial boundary B, and we denote by\Omega the computational domain inside B. At B we impose an exact nonreflecting boundary condition upon the scattered field. This co...
HighOrder RKDG methods for computational electromagnetics
 J. Sci. Comput
"... Abstract. In this paper we introduce a new RKDG method for problems of wave propagation that achieves full highorder convergence in time and space. The novelty of the method resides in the way in which it marches in time. It uses an mthorder, mstage, low storage SSPRK scheme which is an extensio ..."
Abstract

Cited by 19 (1 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we introduce a new RKDG method for problems of wave propagation that achieves full highorder convergence in time and space. The novelty of the method resides in the way in which it marches in time. It uses an mthorder, mstage, low storage SSPRK scheme which is an extension to a class of nonautonomous linear systems of a recently designed method for autonomous linear systems. This extension allows for a highorder accurate treatment of the inhomogeneous, timedependent terms that enter the semidiscrete problem on account of the physical boundary conditions. Thus, if polynomials of degree k are used in the space discretization, the RKDG method is of overall order m = k + 1, for any k> 0. Moreover, we also show that the attainment of highorder spacetime accuracy allows for an efficient implementation of postprocessing techniques that can double the convergence order. We explore this issue in a onedimensional setting and show that the superconvergence of fluxes previously observed in full spacetime DG formulations is also attained in our new RKDG scheme. This allows for the construction of higherorder solutions via local interpolating polynomials. Indeed, if polynomials of degree k are used in the space discretization together with a timemarching method of order 2 k +1, a postprocessed approximation of order 2 k +1 is obtained. Numerical results in one and two space dimensions are presented that confirm the predicted convergence properties.
An FPGA Implementation of the Two Dimensional Finite Difference Time
 Domain (FDTD) Algorithm, 12th ACM/SIGDA International Symposium on FieldProgrammable Gate Arrays (FPGA), 2004
"... Understanding and predicting electromagnetic behavior is needed more and more in modern technology. The FiniteDifference TimeDomain (FDTD) method is a powerful computational electromagnetic technique for modelling the electromagnetic space. The 3D FDTD buried object detection forward model is e ..."
Abstract

Cited by 16 (0 self)
 Add to MetaCart
(Show Context)
Understanding and predicting electromagnetic behavior is needed more and more in modern technology. The FiniteDifference TimeDomain (FDTD) method is a powerful computational electromagnetic technique for modelling the electromagnetic space. The 3D FDTD buried object detection forward model is emerging as a useful application in mine detection and other subsurface sensing areas. However, the computation of this model is complex and time consuming. Implementing this algorithm in hardware will greatly increase its computational speed and widen its use in many other areas. We present an FPGA implementation to speedup the pseudo2D FDTD algorithm which is a simplified version of the 3D FDTD model. The pseudo2D model can be upgraded to 3D with limited modification of structure. We implement the pseudo2D FDTD model for layered media and complete boundary conditions on an FPGA. The computational speed on the reconfigurable hardware design is about 24 times faster than a software implementation on a 3.0GHz PC. The speedup is due to pipelining, parallelism, use of fixed point arithmetic, and careful memory architecture design.