scalable feti-dp based algorithms for variational inequalities zdeněk dostÁl, david horák, dan...
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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
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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
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H/h=8 648/73/10 2592/369/42 10365/1633/154
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H/h=16 2312/153/10 9248/785/42 36992/3489/154
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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 -
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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
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