[理学]CEM-IEMFast_Methods.ppt

Integral Equation Methods and Fast Algorithms in Computational Electromagnetics Great Thanks to Prof. C. H. Chan in CityU, HK and Prof. J. M. Jin in UIUC, USA Review of Important Theorems and Concepts Duality is an important concept that once we obtain an equation for a field quantity, we can obtain its dual counterpart by replacing that field quantity with its dual quantity Duality Uniqueness Theorem A solution is said to be unique when it is the only one possible among a given class of solutions Consider two possible solutions These difference fields satisfy the complex Poynting Theorem that for a lossy medium Uniqueness Theorem Uniqueness Theorem Image Theory The Equivalent Principle Two sources producing the same field within a region of space are said to be equivalent within that region The Equivalent Principle The Equivalent Principle The Induction Theorem The Induction Theorem Reciprocity Theorem The reciprocity theorem states that a response of a system to a source is unchanged when the source and the measurer are interchanged Use of Reciprocity Theorem J on PEC does not radiate Use of Reciprocity Theorem The Method of Moments Lf = g where L is a linear operator replace f by a set of basis functions Inner Product An inner product is defined as: Matrix Equation Method of Moments is the n-th moment of f , when xn is replaced by wn, we continue to call the integral a moment of f it is also called the Method of Weighted residuals note that is only an approximation to the exact f a residual R can be defined as these weighted residuals are forced to be zero by adjusting the values of a’s this procedure can also be called the method of projection Method of Moments an adjoint operator can be defined as if L= La then this operator is self-adjoint and the domain of La is that of L if wi is chosen such that wi =fi, this is called the Galerkin’s method an