Discontinuous Galerkin Finite-element Time-domain Research Articles

Temperature-drift effect analysis of microstrip filters based on parallel high-order DGTD and FETD method with memory reduction technique

The temperature-drift effect of microstrip filters is analyzed by the proposed electromagnetic-thermal co-simulation method based on parallel high-order discontinuous Galerkin time domain (DGTD) and finite-element time-domain (FETD) algorithms with a memory reduction technique. The element matrices of DGTD method are factorized into the product of coefficient matrices and universal matrices. The coefficient matrices are different for each tetrahedral element and need to be stored for all the elements. While the universal matrices are the same for all the tetrahedral elements and only need to be stored for one element. Since the sizes of the coefficient matrices are much smaller than the element matrices of DGTD method, the proposed method avoids storing the large element matrices and greatly reduce the memory requirement of the DGTD method. Thus it reduces the memory requirement of the whole electromagnetic-thermal co-simulation which is dominated by the memory consumption of the DGTD method. Large-scale parallel technique is adopted to accelerate the process of electromagnetic-thermal co-simulation. The proposed method provides a very powerful tool for temperature-drift effect analysis of microstrip filters.

Parallel Higher Order DGTD and FETD for Transient Electromagnetic-Circuital-Thermal Co-Simulation

A hybrid higher order discontinuous Galerkin time-domain (DGTD) method and finite-element time-domain (FETD) method with parallel technique is proposed for electromagnetic (EM)–circuital–thermal co-simulation in this article. For electromagnetic simulation, DGTD method with higher order hierarchical vector basis functions is used to solve Maxwell equation. Circuit simulation is carried out by modified nodal analysis method. For thermal simulation, FETD method with higher order interpolation scalar basis functions is adopted to solve heat conduction equation. To implement electromagnetic–circuital–thermal co-simulation, the electromagnetic and circuital equations are strongly coupled through voltages, currents, and electric fields at the lumped ports first. Then the electromagnetic and thermal equations are weakly coupled with electromagnetic loss and temperature-dependent medium parameters. Finally, large-scale parallel technique is used to accelerate the process of multiphysics simulation. Numerical results are given to validate the correctness and capability of the proposed electromagnetic–circuital–thermal co-simulation method.

A partially staggered discontinuous Galerkin method for transient electromagnetics

Conservation of energy, spurious-free, and optimal convergence are among the most favorite ingredients of a discontinuous Galerkin finite-element time-domain method (DG-FETD) for the analysis of transient electromagnetic problems. Unfortunately, due to the reliance on dissipative upwind flux to suppress spurious modes, most existing DG-FETDs possess only one or two of them. In this paper, we present a novel two-dimensional DG-FETD method, which combines all of the three advantages. The proposed method is based on the electric field E and magnetic field H, whose approximation spaces are composed of Whitney's edge functions. To inhibit the spurious modes while keeping the conservation of numerical energy, the numerical flux with dissipation is not adopted. Instead, a carefully designed interface condition along with the non-dissipative central flux is employed for this purpose. That is, across each face of an element except for those coinciding with boundaries of the computational domain, if E is strongly enforced to be tangential continuous then the continuity of H is weakly imposed, and vice versa. For the convenience of complying with this requirement and without loss of the inherent parallelism of the DG-FETD method, two partially staggered sets of subdomains are built for E and H, respectively. These subdomains are made up of sub-elements generated through a refinement of each cell on the initial mesh into four similar elements. The final discrete system is advanced with a second order leap-frog time-stepping scheme. A series of numerical examples demonstrate that the present method is robust and much more superior to the conventional DG-FETD methods.

A 3-D Continuous–Discontinuous Galerkin Finite-Element Time-Domain Method for Maxwell's Equations

A 3-D continuous-discontinuous Galerkin (CDG) finite-element time-domain method for Maxwell's equations is proposed to analyze transient electromagnetic problems, which is based on the field variables E and B. This method is aimed at exploiting the advantages of reduced number of unknowns for continuous Galerkin (CG) method and block-diagonal property of discontinuous Galerkin (DG) method. The whole domain is divided into several clusters. The CG is used for the elements in the clusters, and they exchange information with adjacent clusters through traditional numerical fluxes in a DG manner. Moreover, compared to the conventional method based on field variables E and H, the proposed method can eliminate spurious modes. Numerical results demonstrate that the proposed CDG method is superior to the DG method in terms of memory and simulation time.

Efficient Noniterative Implicit Time-Stepping Scheme Based on E and B Fields for Sequential DG-FETD Systems

The discontinuous Galerkin finite-element time-domain (DG-FETD) method with implicit time integration has an advantage in modeling electrically fine-scale electromagnetic problems. Based on domain decomposition methods, it avoids the direct inversion of a large system matrix as in the conventional FETD method; by employing implicit time integration, it obviates an extremely small time-step interval to maintain stability as in explicit schemes. Based on curl-conforming basis functions for the electric field intensity E field and divergence-conforming basis functions for the magnetic flux density B field, a new noniterative implicit time-stepping scheme is proposed to efficiently solve sequentially ordered systems for electrically fine-scale problems. Compared with the previous EH-based scheme, the new scheme introduces fewer unknowns and, thereby, results in a smaller matrix system. Based on the Crank–Nicholson algorithm for time integration, the matrix system is in a block tridiagonal form. Then, through separating the surface unknowns from the volume unknowns, a block lower-diagonal-upper (LDU) decomposition is implemented, reducing the computational complexity of the original system. The adaptivity of parallel computing in subdomain level during preprocessing further helps shorten the computation time. Numerical results confirm that the proposed LDU scheme presents improved efficiency in terms of memory and CPU time while retaining the same accuracy, compared with the previous implicit block-Thomas method. With respect to the explicit Runge–Kutta method and the standard FDTD, it also shows an advantage in CPU time. The proposed scheme will help improve the performance of DG-FETD in modeling electrically fine-scale problems.

Numerical Dispersion in DG-FETD Method Using Brick and Tetrahedral Edge Elements

A numerical dispersion analysis (NDA) of the discontinuous Galerkin finite-element time-domain (DG-FETD) method is presented. Vector basis functions under the NDA are with brick and tetrahedral elements. This NDA shows that there exist both normal and spurious modes in the DG-FETD method. A DG-FETD modeling of transverse electromagnetic (TEM) wave propagation in a parallel waveguide is applied to verify the NDA for zeroth-order vector bases. The effect of wave propagation direction and electrical size of elements on numerical dispersion is investigated. It is shown from the NDA for higher-order interpolatory vector bases that the phase error of normal modes can be significantly reduced by using higher-order bases.

A DGFETD Port Formulation for Photoconductive Antenna Analysis

A discontinuous Galerkin finite-element time-domain (DGFETD) port formulation of the coupled Maxwell’s equations and Drift-Diffusion equations for a photoconductive antenna is derived. The formulation is cast in a form such that static quantities are extracted. The resulting system is used to analyze terahertz-band photoconductive antennas with well-defined gap regions excited by pulsed lasers. Several antenna types are investigated, and results are compared to measured results from the literature .

A memory efficient discontinuous galerkin finite-element time-domain scheme for simulations of finite periodic structures

A discontinuous Galerkin finite-element time-domain (DG-FETD) scheme with nonconforming interface meshes is proposed for transient simulations of finite periodic structures. A finite periodic structure is divided into an array of identical building blocks. Each building block is decomposed into a volume part and six surface parts, and they are computed and stored separately. By doing this one building block can represent the whole discretized structure, and the repeat of meshes and system matrices can be exploited to the maximum extent. This DG-FETD scheme costs much less memory compared to conventional methods in simulating finite periodic structures. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1929–1933, 2014

A Hybrid Electromagnetics-Circuit Simulation Method Exploiting Discontinuous Galerkin Finite Element Time Domain Method

A hybrid electromagnetics (EM)-circuit simulation method employing the discontinuous Galerkin finite element time domain (DGFETD) method is developed to model single lumped port networks comprised of both linear and non-linear elements. The whole computational domain is split into two subsystems: one is the EM subsystem that is analyzed by DGFETD, while another is the circuit subsystem that is modeled by the Modified Nodal Analysis method to generate a circuit subsystem. The coupling between the EM and circuit subsystems is achieved through a lumped port. Due to the local properties of DGFETD operations, only small coupling matrix equation systems are involved. To handle non-linear devices, the standard Newton-Raphson method is applied to the established non-linear matrix equations. Numerical examples are presented to validate the proposed algorithm.

A NEW 2D NON-SPURIOUS DISCONTINUOUS GALERKIN FINITE ELEMENT TIME DOMAIN (DG-FETD) METHOD FOR MAXWELL'S EQUATIONS

A new discontinuous Galerkin Finite Element Time Domain (DG-FETD) method for Maxwell's equations is developed. It can suppress spurious modes using basis functions based on polynomials with the same order of interpolation for electric fleld intensity E and magnetic ∞ux density B. Compared to FETD based on EH scheme, which requires difierent orders of interpolation polynomials for electric and magnetic fleld intensities, this method uses fewer unknowns and reduces the computation load. The discontinuous Galerkin method is employed to implement domain decomposition for the EB scheme based FETD. In addition, a well-posed time-domain perfectly matched layer (PML) is extended to the EB scheme to simulate the unbounded problem. Leap frog method is utilized for explicit time stepping. Numerical results demonstrate that the above proposed methods are efiective and e-cient for 2D time domain TMz multi-domain problems.

Higher-Order DG-FETD Modeling of Wideband Antennas With Resistive Loading

A discontinuous Galerkin finite-element time-domain (DG-FETD) method with higher-order tetrahedral elements is developed to model wideband antennas with resistive loading. To fully characterize the wideband fundamental parameters of the antennas with multiscaled structures, several schemes are adopted to effectively model resistive loading and accurately calculate return loss, directivity, and radiation pattern. Successful simulation of interesting antennas using the proposed DG-FETD method demonstrates its capability of modeling wideband antennas without or with resistive loading.

Simulation of Electromagnetic Waves in the Magnetized Cold Plasma by a DGFETD Method

The properties of electromagnetic waves propagating in magnetized plasma slabs and scattering from plasma coated spheres are investigated using the discontinuous Galerkin finite-element time-domain (DGFETD) method. The magnetized plasma is a kind of gyroelectric anisotropic dispersive medium. This anisotropy must be described by an electric permittivity tensor with both nonzero diagonal and off-diagonal elements. Instead of doing the convolution directly in the time domain, an auxiliary differential equations (ADE) method is employed to represent the constitutive relation. The algorithm is validated by studying the transmission characteristics via electron-composed plasma slabs and radar cross section (RCS) of plasma-coated spheres. All numerical results demonstrate very good agreements with exact solutions and comply with the plasma physics.

SPICE Lumped Circuit Subcell Model for the Discontinuous Galerkin Finite-Element Time-Domain Method

A SPICE lumped circuit subcell model is formulated within the discontinuous Galerkin finite-element time-domain (DGFETD) discretization of Maxwell's equations. A fourth-order exponential time difference (ETD) algorithm is used for circuits that lead to stiff systems. The ETD method reduces to a standard fourth-order Runge-Kutta (RK4) time-integration for nonstiff regions. A number of test cases, including a microstrip transmission line terminated with general RLC networks, load arrays, and a diode detector are presented for the validation of the proposed hybrid DGFETD/SPICE solution method.

Modeling of Waveguide Structures Using DG-FETD Method With Higher Order Tetrahedral Elements

In this paper, the discontinuous Galerkin (DG) finite-element time-domain (FETD) method is developed to model electromagnetic (EM) structures with waveguide excitations. Several specific issues about the DG-FETD modeling are addressed. First, the higher order tetrahedral elements are employed to accurately model the geometry of EM structures and effectively reduce the dispersion error so that the efficiency of the FETD method is increased. To further increase the efficiency of the DG-FETD method, the local time-stepping scheme is applied. Secondly, the conformal perfect matching layer (PML) is applied to terminate the waveguide. The formulation of the conformal PML is presented in this paper. Thirdly, a novel approach is proposed to extract the S-parameters of waveguide structures. This approach applies the surface magnetic current to excite the EM fields in the waveguide structures. Taking advantage of the relationship between the excitation current and excited fields in the uniform waveguide, one can readily obtain the incident electric fields that are required for calculating the S-parameters. This approach avoids the pre-simulation of the uniform waveguide. Finally, the numerical results are given to validate the DG-FETD modeling.

A Discontinuous Galerkin Finite Element Time-Domain Method Modeling of Dispersive Media

A method is proposed for solving the time-dependent Maxwell's equations via the discontinuous Galerkin finite-element time-domain (DGFETD) method with dispersive media. An auxiliary differential equation (ADE) method is used to represent the constitutive relations. The method is applied to Drude materials, as well as to multiple pole Debye and Lorentz materials. An efficient implementation for high-order Runge-Kutta time integration schemes is presented. The method is validated and is shown to exhibit high-order convergence.

An Auxiliary Differential Equation Formulation for the Complex-Frequency Shifted PML

An efficient auxiliary-differential equation (ADE) form of the complex frequency shifted perfectly matched layer (CPML) absorbing media derived from a stretched coordinate PML formulation is presented. It is shown that a unit step response of the ADE-CPML equations leads to a discrete form that is identical to Roden's convolutional PML method for FDTD implementations. The derivation of discrete difference operators for the ADE-CPML equations for FDTD is also presented. The ADE-CPML method is also extended in a compact form to a multiple-pole PML formulation. The advantage of the ADE-CPML method is that it provides a more flexible representation that can be extended to higher-order methods. In this paper, it is applied to the discontinuous Galerkin finite element time-domain (DGFETD) method. It is demonstrated that the ADE-CPML maintains the exponential convergence of the DGFETD method.

A Nonspurious 3-D Vector Discontinuous Galerkin Finite-Element Time-Domain Method

We propose a nonspurious vector discontinuous Galerkin finite-element time-domain (DG-FETD) method for 3-D electromagnetic simulation. To facilitate the implementation of numerical fluxes for domain decomposition, we construct the DG-FETD scheme based on the first-order Maxwell's equations with variables E and H. The LT/QN and the CT/LN edge elements are employed to represent E and H, respectively (or vice versa), to suppress spurious modes, and the Riemann solver is utilized as the numerical flux to correct fields on the interfaces between adjacent subdomains. Numerical experiments show the nonspurious property of the proposed method.