1. Scalable FETI-DP based algorithms for variational inequalities Zdeněk DOSTÁL, David Horák, Dan Stefanica Department of Applied Math., FEI–VŠB Technical University Ostrava Baruch College, City University of New York New York, January 2005, DDM 16 http://www.am.vsb.cz

2. Outline 1.Coercive and semicoercive contact model problem 2.Variational formulation 3.Dual formulation 4.FETI-DP 5.Theory for scalability of FETI-DP for coercive problem 6.Theory for scalability of FETI-DP for semicoercive problem 7.QP algorithm 8.Numerical experiments - evidence of scalability 9.Remarks and conclusions

3. Model contact problems Coercive problem Semicoercive problem

4. Variational formulation and domain decomposition

5. Discretized primal problem

6. Conforming and mortar FE discretization of contact interface Conforming Nonconforming mortars

7. Coercive FETI-DP problem

8. Semicoercive FETI-DP problem

9. Mortar FE–Importance of normalization of B I –rows

10. QP with modified proportioning and gradient projection

11. Numerical scalability

12. Numerical experiments-Conforming FE H1/21/41/8 H/h=4 200/33/10800/161/423200/705/154 172127 H/h=8 648/73/102592/369/4210365/1633/154 223638 H/h=16 2312/153/109248/785/4236992/3489/154 274851 H1/21/41/8 H/h=4 200/33/10800/161/423200/705/154 24 31 H/h=8 648/73/102592/369/4210365/1633/154 273946 H/h=16 2312/153/109248/785/4236992/3489/154 4157-

13. Numerical experiments-mortar FE N 1 N 2 1x2 1x32x4 2x54x8 4x11 H 1 /h 1 =4 242/23x35/6840/122x140/253616/620x662/97 H 2 /h 2 =715 x 4134 x 5249 x 65 H 1 /h 1 =7 203/26x23/6762/125x116/253616/581x566/97 H 2 /h 2 =428 x 2343 x 3856 x 50 H 1 /h 1 =8 750/47x69/62608/256x288/2511216/1298x1374/97 H 2 /h 2 =1329 x 4849 x 6859 x 88 H 1 /h 1 =13 635/52x49/62378/261x248/259836/1233x1214/97 H 2 /h 2 =837 x 3658 x 5171 x 65 H 1 /h 1 =16 2606/95x137/69072/524x584/2538992/2654x2798/97 H 2 /h 2 =2533 x 6057 x 8778 x 125 H 1 /h 1 =25 2219/104x101/68298/533x512/2534348/2537x2510/97 H 2 /h 2 =1641 x 4167 x 6394 x 90 N 1 N 2 1x2 1x32x4 2x54x8 4x11 H 1 /h 1 =4 242/23x35/6840/122x140/253616/620x662/97 H 2 /h 2 =720 x 4537 x 6052 x 80 H 1 /h 1 =7 203/26x23/6762/125x116/253616/581x566/97 H 2 /h 2 =429 x 2856 x 4460 x 53 H 1 /h 1 =8 750/47x69/62608/256x288/2511216/1298x1374/97 H 2 /h 2 =1336 x 5456 x 7670 x 112 H 1 /h 1 =13 635/52x49/62378/261x248/259836/1233x1214/97 H 2 /h 2 =844 x 3868 x 5686 x 71 H 1 /h 1 =16 2606/95x137/69072/524x584/2538992/2654x2798/97 H 2 /h 2 =2539 x 8265 x 100- x - H 1 /h 1 =25 2219/104x101/68298/533x512/2534348/2537x2510/97 H 2 /h 2 =1647 x 4891 x 68- x -

14. Numerical experiments-mortar FE normalized B I x nonnormalized B I N 1 N 2 1x1 2x2 4x4 H 1 /h 1 =4 89/5/0356/44/101424/230/42 H 2 /h 2 =76 x 820 x 4828 x 106 H 1 /h 1 =8 277/9/01108/92/104432/486/42 H 2 /h 2 =1311 x 1426 x 11846 x 263 H 1 /h 1 =16 965/17/03860/188/1015440/998/42 H 2 /h 2 =2516 x 2531 x 26860 x 743

15. Conclusion 1.x 2.x 3.x 4.x 5.x