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By Andrew F. Peterson
The method-of-moments resolution of the electrical box and magnetic box imperative equations (EFIE and MFIE) is prolonged to accomplishing gadgets modeled with curved cells. those suggestions are very important for electromagnetic scattering, antenna, radar signature, and instant conversation purposes. Vector foundation capabilities of the divergence-conforming and curl-conforming varieties are defined, and particular interpolatory and hierarchical foundation capabilities are reviewed. systems for mapping those foundation features from a reference area to a curved telephone, whereas retaining the specified continuity homes on curved cells, are mentioned intimately. For representation, effects are offered for examples that hire divergence-conforming foundation capabilities with the EFIE and curl-conforming foundation capabilities with the MFIE. The meant viewers contains electromagnetic engineers with a few prior familiarity with numerical suggestions.
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Extra resources for Mapped vector basis functions for electromagnetic integral equations
Example text
In addition, the tangential-vector continuity must be maintained by the mapping to curvilinear cells. Curl-conforming functions do not usually maintain the continuity of the normal component of the vector unknown at cell boundaries, and a representation therefore exhibits jump discontinuities in the normal components at cell edges. The coefficients of the preceding basis functions have an obvious physical interpretation: they are the field or current density component at the cell edge, tangential to that edge.
The philosophy underlying the Nedelec spaces suggests that, for a general problem where the leading order derivative in an equation is a divergence operator, the best accuracy will be obtained by consistently using the first 4 degrees of freedom (Nedelec p = 0), or the first 12 (Nedelec p = 1), or the first 24 (Nedelec p = 2). 2: Hierarchical Divergence-Conforming Vector Bases for Quadrilateral Cells p=0 ˆ − u) u(1 Four edge-based functions uˆ (1 + u) vˆ (1 − v) p = 1, edge vˆ (1 + v) Total degree of freedom = 4 uˆ (1 − u)v Four edge-based functions uˆ (1 + u)v vˆ u (1 − v) p = 1, cell vˆ u (1 + v) Total degrees of freedom = 8 uˆ (u − 1) Four cell-based functions 2 uˆ (u 2 − 1)v vˆ (v2 − 1) p = 2, edge vˆ u (v2 − 1) Total degrees of freedom = 12 uˆ (1 − u)v Four edge-based functions 2 uˆ (1 + u)v2 vˆ u 2 (1 − v) p = 2, cell vˆ u 2 (1 + v) Total degrees of freedom = 16 uˆ (u − 1)v Eight cell-based functions 2 2 uˆ (u 3 − u) uˆ (u 3 − u)v uˆ (u 3 − u)v 2 ˆ 2 (v 2 − 1) vu vˆ (v3 − v) ˆ (v3 − v) vu ˆ 2 (v3 − v) vu Total degrees of freedom = 24 Note.
14), multiplied by shifted Silvester polynomials to zero the result at the other interpolation points. 39) However, only two of these are linearly independent functions, so one must be discarded. 39) each have an identically zero normal component at all three of the cell edges. 45) are normalized so that the outward component is unity at the interpolation point. cls 44 December 28, 2005 19:47 MAPPED VECTOR BASIS FUNCTIONS analogous functions in adjacent cells to ensure normal-vector continuity at cell boundaries.