A High-Order Ultra-Weak Variational Formulation for Electromagnetic Waves Utilizing Curved Elements
IEEE Transactions on Antennas and Propagation(2023)
摘要
The Ultra Weak Variational Formulation (UWVF) is a special Trefftz
discontinuous Galerkin method, here applied to the time-harmonic Maxwell's
equations. The method uses superpositions of plane waves to represent solutions
element-wise on a finite element mesh. We focus on our parallel UWVF
implementation, called ParMax, emphasizing high-order solutions in the presence
of scatterers with piecewise smooth boundaries. We explain the incorporation of
curved surface triangles into the UWVF, necessitating quadrature for system
matrix assembly. We also show how to implement a total field and scattered
field approach, together with the transmission conditions across an interface
to handle resistive sheets. We note also that a wide variety of element shapes
can be used, that the elements can be large compared to the wavelength of the
radiation, and that a low memory version is easy to implement (although
computationally costly). Our contributions are illustrated through numerical
examples demonstrating the efficiency enhancement achieved by curved elements
in the UWVF. The method accurately handles resistive screens, as well as
perfect electric conductor and penetrable scatterers. By employing large curved
elements and the low memory approach, we successfully simulated X-band
frequency scattering from an aircraft. These innovations demonstrate the
practicality of the UWVF for industrial applications.
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关键词
Maxwell equations,Simulation software,Numerical analysis,Frequency domain analysis
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