Scalable FETI-DP based algorithms for variational inequalities

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Scalable FETI-DP based algorithms for variational
inequalities

• Zdenek DOSTÁL, David Horák, Dan Stefanica 
• Department of Applied Math., FEIVŠB Technical
  University Ostrava
• Baruch College, City University of New York
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• New York, January 2005, DDM 16

http//www.am.vsb.cz
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Outline

• Coercive and semicoercive contact model problem
• Variational formulation
• Dual formulation
• FETI-DP
• Theory for scalability of FETI-DP for coercive
  problem
• Theory for scalability of FETI-DP for
  semicoercive problem
• QP algorithm
• Numerical experiments - evidence of scalability
• Remarks and conclusions

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Model contact problems
Coercive problem
Semicoercive problem
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Variational formulation and domain decomposition
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Discretized primal problem
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Conforming and mortar FE discretization of
contact interface
Conforming
Nonconforming mortars
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Coercive FETI-DP problem
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Semicoercive FETI-DP problem
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Mortar FEImportance of normalization of BIrows
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QP with modified proportioning and gradient
projection
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Numerical scalability
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Numerical experiments-Conforming FE
H 1/2 1/4 1/8
H/h4 200/33/10 800/161/42 3200/705/154
17 21 27
H/h8 648/73/10 2592/369/42 10365/1633/154
22 36 38
H/h16 2312/153/10 9248/785/42 36992/3489/154
27 48 51
H 1/2 1/4 1/8
H/h4 200/33/10 800/161/42 3200/705/154
24 24 31
H/h8 648/73/10 2592/369/42 10365/1633/154
27 39 46
H/h16 2312/153/10 9248/785/42 36992/3489/154
41 57 -
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Numerical experiments-mortar FE
N1 N2 1x2 1x3 2x4 2x5 4x8 4x11
H1/h14 242/23x35/6 840/122x140/25 3616/620x662/97
H2/h27 15 x 41 34 x 52 49 x 65
H1/h17 203/26x23/6 762/125x116/25 3616/581x566/97
H2/h24 28 x 23 43 x 38 56 x 50
H1/h18 750/47x69/6 2608/256x288/25 11216/1298x1374/97
H2/h213 29 x 48 49 x 68 59 x 88
H1/h113 635/52x49/6 2378/261x248/25 9836/1233x1214/97
H2/h28 37 x 36 58 x 51 71 x 65
H1/h116 2606/95x137/6 9072/524x584/25 38992/2654x2798/97
H2/h225 33 x 60 57 x 87 78 x 125
H1/h125 2219/104x101/6 8298/533x512/25 34348/2537x2510/97
H2/h216 41 x 41 67 x 63 94 x 90
N1 N2 1x2 1x3 2x4 2x5 4x8 4x11
H1/h14 242/23x35/6 840/122x140/25 3616/620x662/97
H2/h27 20 x 45 37 x 60 52 x 80
H1/h17 203/26x23/6 762/125x116/25 3616/581x566/97
H2/h24 29 x 28 56 x 44 60 x 53
H1/h18 750/47x69/6 2608/256x288/25 11216/1298x1374/97
H2/h213 36 x 54 56 x 76 70 x 112
H1/h113 635/52x49/6 2378/261x248/25 9836/1233x1214/97
H2/h28 44 x 38 68 x 56 86 x 71
H1/h116 2606/95x137/6 9072/524x584/25 38992/2654x2798/97
H2/h225 39 x 82 65 x 100 - x -
H1/h125 2219/104x101/6 8298/533x512/25 34348/2537x2510/97
H2/h216 47 x 48 91 x 68 - x -
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Numerical experiments-mortar FEnormalized BI x
nonnormalized BI
N1 N2 1x1 1x1 2x2 2x2 4x4 4x4
H1/h14 89/5/0 356/44/10 1424/230/42
H2/h27 6 x 8 20 x 48 28 x 106
H1/h18 277/9/0 1108/92/10 4432/486/42
H2/h213 11 x 14 26 x 118 46 x 263
H1/h116 965/17/0 3860/188/10 15440/998/42
H2/h225 16 x 25 31 x 268 60 x 743
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Conclusion

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