Research Of DGTD Method Based On Curvilinear Hexahedrons

Among various methods in the field of computational electromagnetic, high ordertime domain method can long term, long distance and accurately simulate the procedureof wave propagation. Methods based on unstructured meshes can accurately reconstructcomplicated geometry and have good versatility. Discontinuous Galerkin Time Domainmethod combined the above two kinds of methods very well. DGTD method usedunstructured meshes to conform to geometry which has complicated surfaces. Thenhigh order polynomials were used to approximate the element’s electromagnetic fieldfunction, numerical dispersion error is lower, that can simulate the propagation at lowcell sampling density. Based on above advantages, this paper aims at extending theapplications of Hexahedral DGTD method, mainly research the basic theory ofHex-DGTD and the meshes generation technology, the work can be summarized asfollows:Firstly, introduced the local coordinate theory and the Jacobian matrix obtained bycoordinate transformation. Then rewrite the Maxwell equation in local coordinate. Thenintroduced high order interpolation based on Chebyshev and Legendre points,Runge-Kutta method in the time integration scheme. Then through applyingdiscontinuous Galerkin method to solve the weak form of Maxwell equation, weobtained the Hex-DGTD equation in each hexahedron.Secondly, introduced the upwind numerical conditions between two hexahedrons’boundary, then introduced the perfect electric conductor, analytic absorbing boundarycondition, uniaxial anisotropic perfectly matched layer in Hex-DGTD method.Numerical results verified the above boundary equation theory.Thirdly, take extending the application range of Hex-DGTD method as target.Combined with currently existing meshes generation software, this paper studied thehexahedrons generation strategy and calculated some complicated geometries’electromagnetic scattering characteristic. In addition, because currently existing meshesgeneration software can only export low order hexahedrons which cannot conform tothe geometry very well, this paper put forward an arbitrary high order hexahedronsgeneration technology through Gordon-Hall transfinite blending function. Numericalresults verified this technology can achieve high precision of Hex-DGTD method bylow meshes density, which can save much computation resources.Lastly, summarized the whole paper, and pointed out the next direction of researchand work efforts.