1. Introduction to Scientific Computing II
Institut für
Informatik
Scientific Computing
In Computer Science
Introduction to Scientific Computing II
Gaussian Elimination
Dr. Miriam Mehl

2. Typical SLE
sparse
band structure

3. Example

4. Gaussian Elimination

5. Gaussian Elimination

6. Gaussian Elimination

7. Gaussian Elimination

8. Gaussian Elimination

9. Gaussian Elimination

10. Gaussian Elimination

11. Gaussian Elimination

12. Gaussian Elimination (LU)

13. Gaussian Elimination (LU)

14. Gaussian Elimination (LU)

15. Gaussian Elimination (LU)

16. Gaussian Elimination (LU)

17. Gaussian Elimination (LU)

18. Gaussian Elimination (LU)

19. Gaussian Elimination (LU)

20. Gaussian Elimination (LU)

21. Gaussian Elimination – Costs

22. Gaussian Elimination – Costs
O(1/h)2

23. Gaussian Elimination – Costs
O(1/h)2*(1/h)2

24. Gaussian Elimination – Costs
O(1/h)2*(1/h)2 + O(1/h)

25. Gaussian Elimination – Costs
O(1/h)2*(1/h)2 + O(1/h)*(1/h)2

26. Gaussian Elimination – Costs
O(1/h)2*(1/h)2 + O(1/h)*(1/h)2 + O(1/h)

27. Gaussian Elimination – Costs
O(1/h)2*(1/h)2 + O(1/h)*(1/h)2 + O(1/h)*(1/h)2

28. Gaussian Elimination – Costs
2D: O(1/h)4
3D: O(1/h)7

29. Gaussian Elimination – Costs 2Dh
runtime (33 TFlop/s)
2-7
0.03 sec
2-8
0.5 sec
2-9
8.3 sec
2-10
2 min 23 sec
2-11
35 min 32 sec
2-12
9 h 28 min 38 sec
2-13
6 d 7 h 28 min 10 sec
hallo

30. Gaussian Elimination – Costs 3D
hallo h
runtime (33 TFlop/s)
2-6
8 min 53 sec
2-7
18 h 57 min 26 sec
2-8
100 d 26 h 10 min 53 sec
2-9
35 a 156 d 57 h 53 min 04 sec

31. hallo

32. Relaxation Methods – Gauss-Seidel

33. Relaxation Methods – Jacobi