10_PMCHWT - Modeling Homogeneous Penetrable Materials...

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Modeling Homogeneous Penetrable Materials --- *PMCHWT Formulation Donald R. Wilton *Poggio, Miller, Chang, Harrington, Wu, Tsai Scattering Notes, pp. 37,38
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Formulation of Problems Involving Piecewise Homogeneous Media ( ) () , , εμ ±± EH JM S are fields i.e., they are radiated by in a medium of parameters In each region, scattering from or incident fields from the other region incident homogeneous M J S are modeled by equivalent sources and placed on ( ) , ++ , ε μ ( ) , ( ) , -- , −− , S ˆ n
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Exterior Equivalence, Interior Null Field Conditions ;(, ) ; 0 , l im ;( , ) ; 0 , l i m mm + + < >+< > = < r r EJM E r HJM H r S S S S Tested null field conditions: 1) 2) ΛΛ ˆ = × J nH ( ) , JM ++ () , ε μ ( ) , EH , 00 , ˆ = × M En ˆ n
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Interior Equivalence, Exterior Null Field Conditions ;( , ) ; 0 , l im ;( , ) ; 0 , l i m mm < − − >+< > = < r r EJM E r HJM H r S S S S Tested null field conditions: 3) 4) ΛΛ ˆ = −× J nH ( ) , 00 ˆ = M En ˆ n ( ) , JM -- () , ε μ −− , EH ,
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The PMCHWT Equations ;(, ) ; 0 , l im ;( , ) ; 0 , l i m ;( , ) ; 0 , l , ) ; 0 , l i m mm + + <> + < > = + < > = <− > + < > = > + < > =∈ r r r r EJM E r HJM H r E r H r S S S S S S S S ΛΛ Tested null field conditions: 1) 2) 3) 4) Most common formulation is PM : lim ; ( , ) ; + < >+< > = < r r EH E S S S CHWT, obtained by equating 1) to 3) and 2) to 4); it yields a unique solution at all frequencies and is equivalent to enforcing continuity of tangential and at ) ; l i m; ( , ) ; l i ( , ) ; m m +− −− > + < > < < − − > r r E H H J M H S S ±± Λ Λ Any linear combination of 1) and 2) and of 3) and 4) constitutes a valid coupled
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This note was uploaded on 09/24/2009 for the course ECE 6350 taught by Professor Staff during the Spring '08 term at University of Houston.

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10_PMCHWT - Modeling Homogeneous Penetrable Materials...

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