Fast Methods
Donald R. Wilton Vikram Jandhyala
1
Why Are Fast Methods Needed for Large MoM Problems?
Matrix Memory Requirements for Direct Solvers
1.E+0 6
Memory in [GB]
1.E+0 4 1.E+0 2 1.E+0 0 1.E- 0 2 1.E- 0 4 1.E- 0 6 1.E+0 0
slope = 6 decades = 2 N 2
ECE 6350
Introduction to Finite Difference Time
Domain (FDTD) Solution of Transmission
Lines and Maxwells Equations
D. R. Wilton
University of Houston
Time-domain Transmission line Solution
vg ( , t )
+
R0
=0
1
In
I n 1
I n +1
+
2
n 1
Vn
n
Time domain
TX
ECE 6350
Brief Review of Numerical Methods
D. R. Wilton
University of Houston
http:/www.egr.uh.edu/courses/ece/ece6350/
Some Numerical Considerations
Interpolation
Numerical Integration
Singular Integrals
Large and small numbers
Loss of accuracy resu
ECE 6350
Brief Introduction to Fortran 90/95
D. R. Wilton
University of Houston
High Level Overview of an O/O F90 Program
ModuleFilename.f90
Program
starts here
aMODULE ModuleName
Module data
CONTAINS
Module procedures
(Subroutines, functions)
END MODULE
ELEE 6350
Spring 2013
Homework Set #1
Due Tuesday, January 29, 2013
1. Write the appropriate linear transformation for transforming the interval
x (a, b) to the interval
(0,1) with the correspondence a 1 , b 0 ,
(opposite to that presented in the notes).
ECE 6350
Solution of Transmission Line Currents
Introduction to FEM
D. R. Wilton
University of Houston
Transmission Line with Per Unit Length
Voltage Sources
vg ( ) +
I( )
Z0
+
V( )
L, C
=0
dV
= j L I vg
d
dI
= j C V
d
eliminate V
ZL
=L
d 2I
+ j L I = vg
ECE 6350
Review of Field Representation Via
Potential Integrals
D. R. Wilton
University of Houston
Ref: Scattering Notes, p. 2
Maxwells Equations
Maxwell's equations in frequency domain with e jt time
convention factor assumed and suppressed :
= jB
(Fara
Finite Element Solution of Helmholtz
Equation for Inhomogeneously Filled
Cylindrical Waveguide -TMz Solution
D. R. Wilton
University of Houston
Important Cylindrical Waveguide Properties
Homogeneously filled
guides:
Inhomogeneously filled
guides:
Frequen
ECE 6350
3D Electrostatic Potential
Integral Equation
D. R. Wilton
University of Houston
New Features of Static 3D Potential
Integral Equation
3D geometry and Greens function
Triangular elements
- Data structure
- Local coordinate system
(area coordinat
ECE 6350
2D Poissons Equation
D. R. Wilton
University of Houston
Poissons Equation for Cylindrical
Conducting Tube with z-Independent Charge
Density
z
Infinite
Cylinder
r ()
q ()
xx + yy
Poissons' Eq. in 2D :
= xx + yy = ( x, y )
2D
z = 0
D = E = r 0
Coupled Finite and Boundary Element Formulation
Donald R. Wilton
Scattering notes, pp. 39-41 3D-FEM pp. 41-43, hybrid FEM/BEM
Strong and Weak Forms of the 3-D Helmholtz Equation
( 0 , 0 )
n
(E , H )
i i
( r (r), r (r) )
J-
Strong form :
S
r1 E k02 r E =
Thin Wire Modeling
Donald R. Wilton Nathan Champagne
Thin Wire Assumptions
E
i
Current has only an axial component
I2
Current is azimuthally invariant
+ V0
2a
I3 I1
a 0.01
Kirchhoffs law applies at junctions: I1 = I 2 + I 3 Current vanishes at wire en
ELEE 6350
Spring 2013
Homework Set #2
Due Tuesday, Feb. 19, 2013
1. Most of the terminology of the transmission line problems we considered is common
to all finite element (PDE) and even to boundary element (integral equation) methods.
Hence it is worthwh