ES 105 Homework: February 20, 2009

Below you will find the discussion and relevant materials for the ES 105 homework assignment due on February 20, 2009.

Discussion

Our homework assignment for this week, Problem#44, asked us to solve the above system. We were provided: 1) an element file, 2) a node file, 3) a file with boundary nodes and their values, and 4) a README file with details on the problem set. I used LAPACK to perform certain parts of this homework. I compiled my program using GFORTRAN (e.g., gfortran hw6.f -o hw6.out -llapack).

 

 

 

 

 

Materials

Source Code

 

 

Plots

Solution using SOLVE.F

 

 

Vector Results using SOLVE.F

 

Solution using using LU decomposition with LAPACK'S DGSEV Routine

 

Vector Results using LAPACK'S DGSEV Routine

 

 

Solution using using SVD with LAPACK

 

Difference between LAPACK (i.e., DGSEV) and SOLVE.F direct LU

 

 

Current INPUT variation by +/- 50%

 

Current OUTPUT variation by +/- 40%

Ground variation by +/- 0.5 volts @ ~Length Scale=0

Ground variation by +/- 0.5 volts @ ~Length Scale=0.3

Ground variation by +/- 0.5 volts @ ~Length Scale=0.6

Composite variation

(INPUT +/- 50%, OUTPUT +/- 40%, and GROUND +/- 0.5 volts @ ~Length Scale=0.3)

 

Covariance of Voltage @ Node # 10

 

Covariance of Voltage @ Node # 493