ECE 715: INTRO.
TO
CEM FINITE ELEMENT METHOD
Galerkin Weak Formulation: Determine the trial function space:
1 u H0 0,
(
)
1 Associate with every trial function, u x H0 0, , a residual:
du x d R x := p x +q x u x f x dx dx
()
()
()
()
(
)
()()
()
Constru
Lecture 4: Characteristic Impedance
Calculations of Microstrip Transmission Lines Prof. Jin-Fa Lee http:/esl.eng.ohio-state.edu/~csg
Computation of Area x1 x 0 y1 y0 1 A = abs x 2 x 0 y2 y0 2 1 = ( x1 x 0 ) ( y2 y0 ) ( x 2 x 0 ) ( y1 y0 ) 2
Computation of
Lecture 3: Characteristic Impedance
Calculations of Microstrip Transmission Lines Prof. Jin-Fa Lee http:/esl.eng.ohio-state.edu/~csg
Compute Z c of the microstrip transmission line
C : the capacitance per unit length for the microstrip line C0 : the capac
Introduction to FEM: Lecture 2
Prof. Jin-Fa Lee http:/esl.eng.ohio-state.edu/~csg
0
1/2
1
x
Trial Function Space = Testing Function Space = h =Span cfw_ 0 , 1 , m 1
h FEM = 0 0 + 11 + + m 1 m 1 v = v0 0 + v11 + + vm 1 m 1
Application of FEM
Note: i x j =
Introduction to FEM: Lecture 1
Prof. Jin-Fa Lee http:/esl.eng.ohio-state.edu/~csg
0
1/2
1
x
Basis Functions
Galerkin Method
M=1
Avoid these difficulties
Finite Element Methods
Admissble Function Space
1.0
d d1 d d 2 R ( x ) = 1 1 r 2 r dx dx dx dx
1 , R
ECE 715: Introduction to Numerical Methods for Electromagnetics, 2010
Instructor: e-mail: Time: Text: References: Prof. Jin-Fa Lee lee.1863@osu.edu M, W, F. 1:30pm 2:20pm, DL 0264 None 1. G. F. Carey and J. T. Oden, Finite Elements: A Second Course, vol.