A Spurious-Free Discontinuous Galerkin Time-Domain Method for the Accurate Modeling of Microwave Filters

Alvarez, Jesus; Angulo, Luis D.; Bretones, A. Rubio; Garcia, S.G.

doi:10.1109/tmtt.2012.2202683

Cited by 50 publications

(40 citation statements)

References 26 publications

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“…However, for DGTD, they can be easily mitigated, with a slight increase in computational cost, by using upwind or penalized fluxes instead of centered fluxes, at the cost of introducing some dissipation. This dissipation especially affects spurious modes which are much further attenuated than physical ones [54], thus resulting in a cleaner spectrum and better convergence properties [12], [16], [55]. Centered flux can also be proven to be spurious-free in highly regular meshes [41], though this is not a realistic situation found in a general problem.…”

Section: Cgtd Versus Dgtd: the Cdgtd Methodsmentioning

confidence: 99%

A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations

Angulo

Alvarez

Teixeira

et al. 2015

IEEE Trans. Microwave Theory Techn.

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A new nodal hybrid continuous-discontinuous Galerkin time-domain (CDGTD) method for the solution of Maxwell's curl equations is proposed and analyzed. This hybridization is made by clustering small collections of elements with a continuous Galerkin (CG) formalism. These clusters exchange information with their exterior through a discontinuous Galerkin (DG) numerical flux. This scheme shows reduced numerical dispersion error with respect to classical DG formulations for certain orders and numbers of clustered elements. The spectral radius of the clustered semi-discretized operator is smaller than its DG counterpart allowing for larger time steps in explicit time integrators. Additionally, the continuity across the element boundaries allows us a reduction of the number of degrees of freedom of up to about 80% for a low-order three-dimensional implementation. Index Terms-Continuous-discontinuous Galerkin time-domain (CDGTD), continuous Galerkin (CG) method, discontinuous Galerkin (DG) method, discontinuous Galerkin time-domain (DGTD), Maxwell's equations.

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Section: Cgtd Versus Dgtd: the Cdgtd Methodsmentioning

confidence: 99%

A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations

Angulo

Alvarez

Teixeira

et al. 2015

IEEE Trans. Microwave Theory Techn.

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“…, = − − and Z m is the intrinsic impedance in the element. In order to inject the defined surface currents in (10) to the DGTD calculations, one needs to calculate the tangential fields on the elements using the following modified relation [47] Thus a discontinuous field is added to the DGTD results, which is equal to the radiation field outside the element and zero inside. By following the presented procedure, the radiated field of charges outside the containing element is calculated and propagated.…”

Section: J R N H R M R N E R R T T T T S ( )mentioning

confidence: 99%

Field-based DGTD/PIC technique for general and stable simulation of interaction between light and electron bunches

Fallahi¹,

Kärtner²

2014

J. Phys. B: At. Mol. Opt. Phys.

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We introduce a hybrid technique based on the discontinuous Galerkin time domain (DGTD) and the particle in cell (PIC) simulation methods for the analysis of interaction between light and charged particles. The DGTD algorithm is a three-dimensional, dual-field and fully explicit method for efficiently solving Maxwell equations in the time domain on unstructured grids. On the other hand, the PIC algorithm is a versatile technique for the simulation of charged particles in an electromagnetic field. This paper introduces a novel strategy for combining both methods to solve for the electron motion and field distribution when an optical beam interacts with an electron bunch in a very general geometry. The developed software offers a complete and stable numerical solution of the problem for arbitrary charge and field distributions in the time domain on unstructured grids. For this purpose, an advanced search algorithm is developed for fast calculation of field data at charge points and for later importing to the PIC simulations. In addition, we propose a field-based coupling between the two methods resulting in a stable and precise time marching scheme for both fields and charged particle motion. To benchmark the solver, some examples are numerically solved and compared with analytical solutions. Eventually, the developed software is utilized to simulate the field emission from a flat metal plate and a silicon nano-tip. In the future, we will use this technique for the simulation and design of ultrafast compact x-ray sources.

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“…This is because the DG-FETD method is not only globally explicit, but also capable of dealing with arbitrarily-shaped and inhomogeneously-filled objects. The NDA is important for understanding the effect of spatial discretization and field expansion on the accuracy of the DG-FETD method [27], [28]. To the best of the authors' knowledge, however, the detailed dispersion analysis in the 3-D DG-FETD method has not been reported yet.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

2015

IEEE Trans. Antennas Propagat.

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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 zerothorder 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.Index Terms-Brick elements, discontinuous Galerkin (DG) approach, finite-element time-domain (FETD) method, numerical dispersion, tetrahedral elements, vector basis functions.

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A Spurious-Free Discontinuous Galerkin Time-Domain Method for the Accurate Modeling of Microwave Filters

Cited by 50 publications

References 26 publications

A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations

A Nodal Continuous-Discontinuous Galerkin Time-Domain Method for Maxwell's Equations

Field-based DGTD/PIC technique for general and stable simulation of interaction between light and electron bunches

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

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