Multidomain Pseudospectral Time-domain Research Articles

Dispersive multidomain pseudospectral time‐domain method for full‐wave analysis of radio‐frequency invisible cloaks

To implement full-wave simulation of electromagnetic wave impinging invisible cloaks, an efficient multidomain pseudospectral time-domain algorithm is developed in this study. The proposed method solves the same forms of Maxwell's equations in both the regular and cloaking areas, and then applies different methods to update the electric and magnetic field components, respectively. The new method requires less grid points per wavelength, meanwhile, the multidomain strategy relieves the complicated treatment of electric and magnetic field components based on Yee grids within finite-difference time-domain methods, and shows advantage of dealing with internal inhomogeneities within the cloaking materials. The results validated feasibility and efficiency of the proposed method in left-hand materials.

Scattering of Object Buried below Random Rough Surface—A Monte Carlo Pseudospectral Time-Domain Approach

Absract This article presents a numerical technique combining the multi-domain pseudospectral time-domain method and the Monte Carlo method for determining the scattering of an object buried below a random rough surface separating two half-spaces. The numerical technique is employed to determine the scattering of a cylinder buried below a random rough surface of finite length under various conditions. Sample numerical results are presented, validated, and analyzed. The results illustrate the significant impact of the roughness of the surface and the electromagnetic properties of the lower half-space on the scattered signature of the buried cylinder.

Applications of the multidomain pseudospectral time-domain algorithm for waveguide structures

The authors have analysed the complex waveguide structures by the multidomain pseudospectral time-domain (MPSTD) algorithm, and discussed the design of a filtering procedure through improving the stability of the MPSTD method for the corner singularities. These numerical results of the MPSTD method have shown an excellent agreement with those results of the analytical solution and the traditional finite-difference time-domain method for the resonant frequencies of the waveguide structures. It is evident that the MPSTD method can achieve high efficiency and accuracy when we use to analyse inhomogeneous media and curved objects.

Multidomain Pseudospectral Time Domain Algorithm Using a Symplectic Integrator

The novel multidomain pseudospectral time domain method based on a symplectic integrator scheme is presented in this paper. A symplectic integrator scheme is a decomposition of the exponential operator or a general propagation technique. The scheme is nondissipative and does not require additional memory for temporary storage of data for the internal stages. The good performance of the scheme is demonstrated by numerical examples

Characteristic Variables Patching Conditions in Multidomain Pseudospectral Time Domain

In this letter, a uniform representation for patching conditions using characteristic variables (CVs) is proposed to treat distinct types of interfaces in multidomain pseudospectral time domain (MPSTD) algorithm. Patching conditions using CVs implicitly consider wave propagation property and physical boundary conditions. Instead of direct use of physical boundary conditions, it is more accurate and stable to match boundary conditions at the interfaces separating two subdomains of different materials. The good performance of the scheme is demonstrated by numerical examples.

Two Dimensional Multidomain Pseudospectral Time-Domain Algorithm Based on Alternating-Direction Implicit Method

In order to deal with the stability problem restricted by the finite-difference time-domain (FDTD) and conventional pseudospectral time domain (PSTD), the multidomain PSTD algorithm based on alternating-direction implicit (ADI) technique is proposed in this paper. This algorithm improves the stability and efficiency of conventional PSTD, while it maintains the accuracy and flexibility of conventional PSTD for an accurate treatment of arbitrarily curved objects. A compact matrix form is derived to effectively describe two-dimensional ADI multidomain pseudospectral time domain (ADI-MPSTD) algorithm. Numerical results show an excellent agreement with analytical solutions as well as results obtained by the FDTD algorithm, and fully demonstrate a remarkable improvement in stability and efficiency.

Multidomain pseudospectral time-domain algorithm based on super-time-stepping method

A new time-domain algorithm which combines the super-time-stepping (STS) method and the multidomain pseudospectral time-domain (PSTD) algorithm is presented. This algorithm not only maintains accuracy and flexibility of PSTD for an accurate treatment of arbitrarily curved objects but also relaxes the stability restriction for the explicit time integration scheme, establishing it for possible use in any implicit time integration scheme. Some numerical examples are given to illustrate the accuracy and efficiency of this proposed approach.

Multidomain pseudospectral time‐domain method for computation of electromagnetic scattering by bodies of revolution

AbstractWe present a multidomain pseudospectral method using cylindrical and spherical coordinates for the accurate and efficient time‐domain computation of scattering by bodies of revolution (BOR). In the BOR formulation of Maxwell's equations, the Fourier collocation method is utilized in the azimuthal direction and the Chebyshev collocation method in the other directions. Using the complex‐coordinate‐stretching approach, the strongly well‐posed perfectly matched layer (PML) formulations are derived in cylindrical and spherical coordinates. A comparison of the results obtained using the multidomain pseudospectral method and those using the finite‐difference time‐domain (FDTD) method clearly illustrates the superiority of the algorithm developed in this paper. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 47: 92–96, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21091

The ADI Multi-Domain Pseudospectral Time-Domain Algorithm For 2-D Arbitrary Inhomogeneous Media

A new time domain algorithm which combines alternating-direction implicit (ADI) technique and the multi-domain pseudospectral time domain (PSTD) algorithm is presented in the paper. This algorithm not only maintains accuracy and flexibility of PSTD for an accurate treatment of arbitrarily curved objects but also effectively improves the stability problem. Some numerical examples of two dimensional scattering are given to illustrate the accuracy and stability of the proposed approach in this paper.

MULTIDOMAIN PSEUDOSPECTRAL TIME-DOMAIN (PSTD) METHOD FOR ACOUSTIC WAVES IN LOSSY MEDIA

A multidomain pseudospectral time-domain (PSTD) method is developed for acoustic wave equations in lossy media. The method is based on the spectral derivative operator approximated by Chebyshev Lagrange polynomials. In this multidomain scheme, the computational domain is decomposed into a set of subdomains conformal to the problem geometry. Each curved subdomain is then mapped onto a cube in the curvilinear coordinates so that a tensor-product Chebyshev grid can be utilized without the staircasing error. An unsplit-field, well-posed PML is developed as the absorbing boundary condition. The algorithm is validated by analytical solutions. The numerical solutions show that this algorithm is efficient for simulating acoustic wave phenomena in the presence of complex objects in inhomogeneous media. To our knowledge, the multidomain PSTD method for acoustics is a new development in three dimensions, although in two dimensions the method can be made equivalent to the two-dimensional method in electromagnetics.

A Multidomain PSTD Method for 3D Elastic Wave Equations

A 3D multidomain pseudospectral time-domain method is developed for elastic wave equations. The method is based on the spectral derivative operator approximated by Chebyshev or Lagrange polynomials. Unlike the Fourier method that assumes periodic boundary conditions, the Chebyshev pseudospectral method allows for the incorporation of various boundary conditions (such as the free surface boundary condition) into the numerical scheme. In this multidomain scheme, the computational domain is decomposed into a set of subdomains conformal to the problem geometry. Each curved subdomain is then mapped onto a cube in the curvilinear coordinates so that a tensor-product Chebyshev grid can be utilized without the staircasing error. An unsplit-field perfectly matched layer is developed as the absorbing boundary condition. Numerical examples show that this scheme is efficient for simulating elastic waves phenomena in the presence of complex objects. The method is found to be significantly more efficient than the finite-difference time-domain method in terms of memory and run-time requirements.

The 3-D Multidomain Pseudospectral Time-Domain Algorithm for Inhomogeneous Conductive Media

A three-dimensional (3-D) multidomain pseudospectral time-domain (PSTD) method with a strongly well-posed perfectly matched layer (PML) is developed as an accurate and flexible tool for the simulation of electromagnetic wave propagation and scattering in inhomogeneous and conductive media. This approach allows for an accurate treatment of curved geometries by multidomain decomposition and curvilinear coordinate transformation. Numerical experiments show the results agree excellently with analytical solutions and results of other well-known algorithms, and demonstrate a remarkable improvement in accuracy and efficiency over the FDTD method. The 3-D multidomain PSTD algorithm is then applied to calculate radar cross sections (RCS).

The 3-D multidomain pseudospectral time-domain method for wideband simulation

A three-dimensional (3-D) multidomain pseudospectral time-domain (PSTD) method with a well-posed PML is developed as an accurate and efficient solver for Maxwell's equations in conductive and inhomogeneous media. The curved object is accurately treated by curvilinear coordinate transformation. Spatial derivatives are obtained by the Chebyshev collocation method to achieve a high-order accuracy. Numerical results show an excellent agreement with solutions obtained by the FDTD method under fine sampling.

The 2.5-D multidomain pseudospectral time-domain algorithm

A 2.5-D multidomain pseudospectral time-domain (PSTD) method with a suitable well-posed perfectly matched layer is developed as an accurate and flexible tool for the simulation of electromagnetic wave propagation and scattering in conductive and inhomogeneous media. This approach allows for an accurate treatment of curved geometries with a high efficiency. Numerical results show an excellent agreement with analytical solutions for lossy dielectric cylinders. The 2.5-D multidomain PSTD algorithm is applied to several scattering and waveguiding problems.

Multidomain pseudospectral time-domain simulations of scattering by objects buried in lossy media

A multidomain pseudospectral time-domain (PSTD) method with a newly developed well-posed PML is introduced as an accurate and flexible tool for the modeling of electromagnetic scattering by 2-D objects buried in an inhomogeneous lossy medium. Compared with the previous single-domain Fourier PSTD method, this approach allows for an accurate treatment of curved geometries with subdomains, curvilinear mapping, and high-order Chebyshev polynomials. The effectiveness of the algorithm is confirmed by an excellent agreement between the numerical results and analytical solutions for perfectly conducting as well as permeable dielectric cylinders. The algorithm has been applied to model various ground-penetrating radar (GPR) applications involving curved objects in a lossy half space with an undulating surface. This multidomain PSTD algorithm is potentially a very useful tool for simulating antennas near complex objects and inhomogeneous media.

3-D multidomain PSTD for elasticity

A 3-D numerical modeling scheme is developed in general curvilinear coordinates by using a multidomain pseudospectral time-domain (PSTD) method. The computational domain is naturally divided into subdomains of piecewise homogeneous, curvilinear quadrilaterals conforming to the problem geometry. These curvilinear quadrilaterals are then mapped onto a unit square, where the spatial derivatives are approximated by the Chebyshev PSTD method. Characteristic conditions and physical boundary conditions are used to patch the solution between adjacent subdomains. A newly developed unsplit perfectly matched layer (PML) is used to absorb outgoing waves at the computational edge. This multidomain PSTD algorithm allows natural incorporation of curved boundaries into the numerical scheme, thus providing more increased flexibility and accuracy than the conventional finite-difference method. The numerical scheme is validated by analytical solutions and by other numerical methods. Applications of this multidomain PSTD method will be shown for acoustic landmine detection.