Weighted least-squares finite elements based on particle imaging velocimetry data

Journal of Computational Physics

Volumn 229, Issue 1, 2010, Pages 107-118

  Heys, J J ^a   Manteuffel, T A ^b   McCormick, S F ^b   Milano, M ^c   Westerdale, J ^c   Belohlavek, M ^d  

^a Idaho National Laboratory   (United States)

^b UNIVERSITY OF COLORADO   (United States)

^c Arizona State University   (United States)

^d MAYO CLINIC   (United States)

Author keywords

Data assimilation; Finite element; Least squares; Particle imaging velocimetry

Indexed keywords

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; GAUSSIAN NOISE (ELECTRONIC); LEAST SQUARES APPROXIMATIONS; VELOCIMETERS; VELOCITY MEASUREMENT; VISCOUS FLOW;

DATA ASSIMILATION; ELEMENT-BASED; FINITE ELEMENT; LEAST SQUARE; LEAST SQUARES FINITE ELEMENT METHODS; LEAST-SQUARES FINITE ELEMENTS; NAVIER-STOKES EQUATION; PARTICLE IMAGING VELOCIMETRY; TEST PROBLEM; WEIGHTED LEAST-SQUARES;

NAVIER STOKES EQUATIONS;

EID: 70350377794     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.09.016     Document Type: Article

References (25)

1. Anderson J. An ensemble adjustment kalman filter for data assimilation. Mon. Weath. Rev. 129 (2001) 2884-2903
2. Bochev P. Analysis of least-squares finite element methods for the Navier-Stokes equations. SIAM J. Numer. Anal. 34 5 (1997) 1817-1844
3. Bochev P., and Gunzburger M. Accuracy of least-squares methods for the Navier-Stokes equations. Comput. Fluids 22 4/5 (1993) 549-563
4. Bochev P., and Gunzburger M. Finite element methods of least-squares type. SIAM Rev. 40 4 (1998) 789-837
5. Box G., and Muller M. A note on the generation of random normal deviates. Annal. Math. Stat. 29 (1958) 610-611
6. Cai Z., Mantueffel T.A., and McCormick S.F. First-order system least squares for second-order partial differential equations: Part ii. SIAM J. Numer. Anal. 34 2 (1997) 425-545
7. Carrol R., and Ruppert D. Transformation and Weighting in Regression. Monographs on Statistics and Applied Probability vol. 30 (1988), Chapman & Hall, New York
8. Carroll R., Wu C., and Ruppert D. The effect of estimating weights in weighted least squares. J. Am. Stat. Assoc. 83 404 (1988) 1045-1054
9. Ciarlet P. The Finite Element Method for Elliptic Problems. Classics in Applied Mathematics (2002), SIAM, Philadelphia
10. Ford M., Nikolov H., Milner J., Lownie S., DeMont E., Kalata W., Loth F., Holdsworth D.W., and Steinman D.A. Piv-measured versus cfd-predicted flow dynamics in anatomically realistic cerebral aneurysm models. J. Biomech. Eng. 130 2 (2008) 021015
11. Gharib M., Rambod E., Kheradvar A., Sahn D., and Dabiri J. Optimal vortex formation as an index of cardiac health. Proc. Nat. Acad. Sci. 103 16 (2006) 6305-6308
12. Gresho P., and Sani R. Incompressible Flow and the Finite Element Method. Advection-Diffusion and Isothermal Laminar Flow (1998), John Wiley and Sons, New York
13. Heys J., Manteuffel T., McCormick S., and Olson L. Algebraic multigrid for higher-order finite elements. J. Comput. Phys. 204 2 (2005) 520-532
14. Heys J.J., DeGroff C.G., Manteuffel T.A., and McCormick S. First-order system least-squares (fosls) for modeling blood flow. Med. Eng. Phys. 28 6 (2006) 495-503
15. Heys J.J., Lee E., Manteuffel T.A., and McCormick S.F. An alternative least-squares formulation of the Navier-Stokes equations with improved mass conservation. J. Comput. Phys. 226 1 (2007) 994-1006
16. HINSCH K. 3-Dimensional particle velocimetry. Meas. Sci. Technol. 6 6 (1995) 742-753
17. Jiang B. The Least-Squares Finite Element Method (1998), Springer, Berlin
18. Ku D. Blood flow in arteries. Ann. Rev. Fluid Mech. 29 (1997) 399-434
19. Lee E., Manteuffel T., and Westphal C. Weighted-norm first-order system least squares for problems with corner singularities. SIAM J. Numer. Anal. 44 (2006) 1974-1996
20. Lee E., Manteuffel T., and Westphal C. Weighted-norm first order system least squares for problems with three dimensional edge singularities. SIAM J. Numer. Anal. 46 (2008) 1619-1639
21. Mavriplis D. 3-Dimensional multigrid Reynolds-averaged Navier-Stokes solver for unstructured meshes. AIAA J. 33 3 (1995) 445-453
22. T. Ryan, Modern Regression Methods, Wiley Series In Probability and Statistics, John Wiley, New York, NY, 1997.
23. Sengupta P., Khandheria B., Korinek J., Jahangir A., Yoshifuku S., Milosevic I., and Belohlavek M. Left ventricular isovolumic flow sequence during sinus and paced rhythms: new insights from use of high-resolution doppler and ultrasonic digital particle imaging velocimetry. J. Am. Coll. Cardiol. 49 8 (2007) 899-908
24. Sengupta P.P., Krishnamoorthy V.K., Korinek J., Narula J., Vannan M.A., Lester S.J., Tajik J.A., Seward J.B., Khandheria B.K., and Belohlavek M. Left ventricular form and function revisited: applied translational science to cardiovascular ultrasound imaging. J. Am. Soc. Echocard. 20 5 (2007) 539-551
25. van Ertbruggen C., Corieri P., Theunissen R., Riethmuller M., and Darquenne C. Validation of cfd predictions of flow in a 3d alveolated bend with experimental data. J. Biomech. 41 (2008) 399-405