Green’s Functions and Matlab’s cond function

1. Green’s Functions and Matlab’s cond function Wienand Drenth 11 December 2001

2. Overview • What are Green’s functions • Example • Implementation in MatLab • Improvements to the design • Future and NumLab

3. What are Green’s functions

4. Example Instead of looking at globally defined continuous Green’s functions, we aim at constructing locally defined discrete Green’s functions. globallocal

5. Implementation in Matlab(1D, no details, only features) • Standard Matlab routines • Assembly of stiffness matrix for applying Green’s functions to • Construction of Green’s functions requires solution of small linear system

6. Improvements to the design • Use sparse matrix instead of default full:Gain in speed, but computation of condition number (by condest) is now an estimate • Use routine condest for condition number instead of cond:Global behaviour of condition number remains the same This is shown next

7. Comparison of computational times

8. Comparison of condition numbers

9. Future • Investigation of 2 dimensional Green’s functions • Making the Matlab routines work within the NumLab environment