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

Outline1. Coercive and semicoercive contact model problem2. Variational formulation3. Dual formulation4. FETI-DP5. Theory for scalability of FETI-DP for coercive problem6. Theory for scalability of FETI-DP for semicoercive

problem7. QP algorithm8. Numerical experiments - evidence of scalability9. Remarks and conclusions

Model contact problems

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Numerical scalability

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Numerical experiments-Conforming FE

H 1/2 1/4 1/8

H/h=4 200/33/10 800/161/42 3200/705/154

17 21 27

H/h=8 648/73/10 2592/369/42 10365/1633/154

22 36 38

H/h=16 2312/153/10 9248/785/42 36992/3489/154

27 48 51

H 1/2 1/4 1/8

H/h=4 200/33/10 800/161/42 3200/705/154

24 24 31

H/h=8 648/73/10 2592/369/42 10365/1633/154

27 39 46

H/h=16 2312/153/10 9248/785/42 36992/3489/154

41 57 -

Numerical experiments-mortar FEN1 N2 1x2 1x3 2x4 2x5 4x8 4x11

H1/h1=4 242/23x35/6 840/122x140/25 3616/620x662/97

H2/h2=7 15 x 41 34 x 52 49 x 65

H1/h1=7 203/26x23/6 762/125x116/25 3616/581x566/97

H2/h2=4 28 x 23 43 x 38 56 x 50

H1/h1=8 750/47x69/6 2608/256x288/25 11216/1298x1374/97

H2/h2=13 29 x 48 49 x 68 59 x 88

H1/h1=13 635/52x49/6 2378/261x248/25 9836/1233x1214/97

H2/h2=8 37 x 36 58 x 51 71 x 65

H1/h1=16 2606/95x137/6 9072/524x584/25 38992/2654x2798/97

H2/h2=25 33 x 60 57 x 87 78 x 125

H1/h1=25 2219/104x101/6 8298/533x512/25 34348/2537x2510/97

H2/h2=16 41 x 41 67 x 63 94 x 90

N1 N2 1x2 1x3 2x4 2x5 4x8 4x11

H1/h1=4 242/23x35/6 840/122x140/25 3616/620x662/97

H2/h2=7 20 x 45 37 x 60 52 x 80

H1/h1=7 203/26x23/6 762/125x116/25 3616/581x566/97

H2/h2=4 29 x 28 56 x 44 60 x 53

H1/h1=8 750/47x69/6 2608/256x288/25 11216/1298x1374/97

H2/h2=13 36 x 54 56 x 76 70 x 112

H1/h1=13 635/52x49/6 2378/261x248/25 9836/1233x1214/97

H2/h2=8 44 x 38 68 x 56 86 x 71

H1/h1=16 2606/95x137/6 9072/524x584/25 38992/2654x2798/97

H2/h2=25 39 x 82 65 x 100 - x -

H1/h1=25 2219/104x101/6 8298/533x512/25 34348/2537x2510/97

H2/h2=16 47 x 48 91 x 68 - x -

21 xonNonmortars cc

Numerical experiments-mortar FEnormalized BI x nonnormalized BI

N1 N2 1x1 1x1 2x2 2x2 4x4 4x4

H1/h1=4 89/5/0 356/44/10 1424/230/42

H2/h2=7 6 x 8 20 x 48 28 x 106

H1/h1=8 277/9/0 1108/92/10 4432/486/42

H2/h2=13 11 x 14 26 x 118 46 x 263

H1/h1=16 965/17/0 3860/188/10 15440/998/42

H2/h2=25 16 x 25 31 x 268 60 x 743

Conclusion1. x2. x3. x4. x5. x