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Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics. (English) Zbl 1442.76162
Summary: Standard approaches for uncertainty quantification in cardiovascular modeling pose challenges due to the large number of uncertain inputs and the significant computational cost of realistic three-dimensional simulations. We propose an efficient uncertainty quantification framework utilizing a multilevel multifidelity Monte Carlo (MLMF) estimator to improve the accuracy of hemodynamic quantities of interest while maintaining reasonable computational cost. This is achieved by leveraging three cardiovascular model fidelities, each with varying spatial resolution to rigorously quantify the variability in hemodynamic outputs. We employ two low-fidelity models (zero- and one-dimensional) to construct several different estimators. Our goal is to investigate and compare the efficiency of estimators built from combinations of these two low-fidelity model alternatives and our high-fidelity three-dimensional models. We demonstrate this framework on healthy and diseased models of aortic and coronary anatomy, including uncertainties in material property and boundary condition parameters. Our goal is to demonstrate that for this application it is possible to accelerate the convergence of the estimators by utilizing a MLMF paradigm. Therefore, we compare our approach to single fidelity Monte Carlo estimators and to a multilevel Monte Carlo approach based only on three-dimensional simulations, but leveraging multiple spatial resolutions. We demonstrate significant, on the order of 10 to 100 times, reduction in total computational cost with the MLMF estimators. We also examine the differing properties of the MLMF estimators in healthy versus diseased models, as well as global versus local quantities of interest. As expected, global quantities such as outlet pressure and flow show larger reductions than local quantities, such as those relating to wall shear stress, as the latter rely more heavily on the highest fidelity model evaluations. Similarly, healthy models show larger reductions than diseased models. In all cases, our workflow coupling Dakota’s MLMF estimators with the SimVascular cardiovascular modeling framework makes uncertainty quantification feasible for constrained computational budgets.
76Z05 Physiological flows
92C35 Physiological flow
76M10 Finite element methods applied to problems in fluid mechanics
DAKOTA; SimVascular
Full Text: DOI
[1] Global, regional, and national age-sex-specific mortality for 282 causes of death in 195 countries and territories, 1980-2017: a systematic analysis for the Global Burden of Disease Study 2017, Lancet, 392, 1736-1788 (2018)
[2] Heron, M., Deaths: Leading causes for 2016, Natl. Vital Stat. Rep., 67, 6 (2018)
[3] Taylor, C. A.; Hughes, T. J.; Zarins, C. K., Finite element modeling of blood flow in arteries, Comput. Methods Appl. Mech. Engrg., 158, 1, 155-196 (1998) · Zbl 0953.76058
[4] Benjamin, E. J.; Virani, S. S.; Callaway, C. W.; Chamberlain, A. M.; Chang, A. R., Heart disease and stroke statistics—2018 update: A report from the American Heart Association, Circulation, 137, 12, e67-e492 (2018)
[5] Taylor, C. A.; Fonte, T. A.; Min, J. K., Computational fluid dynamics applied to cardiac computed tomography for noninvasive quantification of fractional flow reserve: Scientific basis, J. Am. Coll. Cardiol., 61, 22, 2233-2241 (2013)
[6] Ramachandra, A. B.; Kahn, A. M.; Marsden, A. L., Patient-specific simulations reveal significant differences in mechanical stimuli in venous and arterial coronary grafts, J. Cardiovasc. Transl. Res., 9, 4, 279-290 (2016)
[7] Kung, E.; Baretta, A.; Baker, C.; Arbia, G.; Biglino, G., Predictive modeling of the virtual hemi-fontan operation for second stage single ventricle palliation: Two patient-specific cases, J. Biomech., 46, 2, 423-429 (2013)
[8] Schiavazzi, D.; Kung, E.; Marsden, A.; Baker, C.; Pennati, G., Hemodynamic effects of left pulmonary artery stenosis after superior cavopulmonary connection: A patient-specific multiscale modeling study, J. Thorac. Cardiovasc. Surg., 149, 3, 689-696.e3 (2015)
[9] Verma, A.; Esmaily, M.; Shang, J.; Figliola, R.; Feinstein, J. A.; Hsia, T.-Y.; Marsden, A. L., Optimization of the assisted bidirectional glenn procedure for first stage single ventricle repair, World J. Pediatr. Congenit. Heart Surg., 9, 2, 157-170 (2018)
[10] Sengupta, D.; Kahn, A. M.; Burns, J. C.; Sankaran, S.; Shadden, S. C.; Marsden, A. L., Image-based modeling of hemodynamics in coronary artery aneurysms caused by Kawasaki disease, Biomech. Model. Mechanobiol., 11, 6, 915-932 (2012)
[11] Gutierrez, N. G.; Shirinsky, O.; Gagarina, N.; Lyskina, G.; Fukazawa, R., Assessment of coronary artery aneurysms caused by Kawasaki disease using transluminal attenuation gradient analysis of computerized tomography angiograms, Am. J. Cardiol., 120, 4, 556-562 (2017)
[12] Grande Gutierrez, N.; Mathew, M.; W. McCrindle, B.; Tran, J.; M. Kahn, A., Hemodynamic variables in aneurysms are associated with thrombotic risk in children with Kawasaki disease, Int. J. Cardiol., 281 (2019)
[13] Yang, W.; Marsden, A. L.; Ogawa, M. T.; Sakarovitch, C.; Hall, K. K., Right ventricular stroke work correlates with outcomes in pediatric pulmonary arterial hypertension, Pulm. Circ., 8, 3 (2018)
[14] Yang, W.; Dong, M.; Rabinovitch, M.; Chan, F. P.; Marsden, A. L.; Feinstein, J. A., Evolution of hemodynamic forces in the pulmonary tree with progressively worsening pulmonary arterial hypertension in pediatric patients, Biomech. Model. Mechanobiol., 18, 3, 779-796 (2019)
[15] Suh, G.-Y.; Les, A. S.; Tenforde, A. S.; Shadden, S. C.; Spilker, R. L., Quantification of particle residence time in abdominal aortic aneurysms using magnetic resonance imaging and computational fluid dynamics, Ann. Biomed. Eng., 39, 2, 864-883 (2011)
[16] Arzani, A.; Shadden, S., Characterization of the transport topology in patient-specific abdominal aortic aneurysm models, Phys. Fluids, 24, 8, Article 81901 pp. (2012)
[17] Piccinelli, M.; Veneziani, A.; Steinman, D. A.; Remuzzi, A.; Antiga, L., A framework for geometric analysis of vascular structures: Application to cerebral aneurysms, IEEE Trans. Med. Imaging, 28, 8, 1141-1155 (2009)
[18] Cebral, J.; Mut, F.; Weir, J.; Putman, C., Association of hemodynamic characteristics and cerebral aneurysm rupture, AJNR Am. J. Neuroradiol., 32, 2, 264-270 (2011)
[19] Cebral, J. R.; Castro, M. A.; Burgess, J. E.; Pergolizzi, R. S.; Sheridan, M. J.; Putman, C. M., Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynamics models, AJNR Am. J. Neuroradiol., 26, 10, 2550-2559 (2005)
[20] Hughes, T. J.; Lubliner, J., On the one-dimensional theory of blood flow in the larger vessels, Math. Biosci., 18, 1, 161-170 (1973) · Zbl 0262.92004
[21] Mirramezani, M.; Diamond, S.; Litt, H.; Shadden, S., Reduced order models for transstenotic pressure drop in the coronary arteries, J. Biomech. Eng., 141, 031005-031011 (2019)
[22] Quarteroni, A.; Veneziani, A.; Vergara, C., Geometric multiscale modeling of the cardiovascular system, between theory and practice, Comput. Methods Appl. Mech. Engrg., 302, 193-252 (2016) · Zbl 1423.76528
[23] Moghadam, M. E.; Vignon-Clementel, I. E.; Figliola, R.; Marsden, A. L., A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations, J. Comput. Phys., 244, 63-79 (2013) · Zbl 1377.76041
[24] Quarteroni, A.; Ragni, S.; Veneziani, A., Coupling between lumped and distributed models for blood flow problems, Comput. Vis. Sci., 4, 2, 111-124 (2001) · Zbl 1097.76615
[25] Migliavacca, F.; Pennati, G.; Dubini, G.; Fumero, R.; Pietrabissa, R., Modeling of the norwood circulation: effects of shunt size, vascular resistances, and heart rate, Am. J. Physiol. Heart Circ. Physiol., 280, 5, H2076-H2086 (2001)
[26] Esmaily, M. M.; Migliavacca, F.; Vignon-Clementel, I.; Hsia, T.; Marsden, A., Optimization of shunt placement for the norwood surgery using multi-domain modeling, J. Biomech. Eng., 134, 051002-0510013 (2012)
[27] Schiavazzi, D.; Arbia, G.; Baker, C.; Hlavacek, A.; Y Hsia, T.; Marsden, A.; Vignon-Clementel, I.; The Modeling Of Congenital Hearts Alliance Mocha Investigators, Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation, Int. J. Numer. Methods Biomed. Eng., 32, 3, Article e02737 pp. (2015)
[28] Sankaran, S.; Kim, H. J.; Choi, G.; Taylor, C. A., Uncertainty quantification in coronary blood flow simulations: Impact of geometry, boundary conditions and blood viscosity, J. Biomech., 49, 12, 2540-2547 (2016)
[29] Schiavazzi, D.; Doostan, A.; Iaccarino, G.; Marsden, A., A generalized multi-resolution expansion for uncertainty propagation with application to cardiovascular modeling, Comput. Methods Appl. Mech. Engrg., 314, 196-221 (2017) · Zbl 1439.74213
[30] Tran, J. S.; Schiavazzi, D. E.; Kahn, A. M.; Marsden, A. L., Uncertainty quantification of simulated biomechanical stimuli in coronary artery bypass grafts, Comput. Methods Appl. Mech. Engrg., 345, 402-428 (2019) · Zbl 1440.74233
[31] Chen, P.; Quarteroni, A.; Rozza, G., Simulation-based uncertainty quantification of human arterial network hemodynamics, Int. J. Numer. Methods Biomed. Eng., 29, 6, 698-721 (2013)
[32] Sankaran, S.; Marsden, A. L., The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow, Phys. Fluids, 22, 12, Article 121902 pp. (2010)
[33] Eck, V.; Sturdy, J.; Hellevik, L., Effects of arterial wall models and measurement uncertainties on cardiovascular model predictions, J. Biomech., 50, 188-194 (2017)
[34] Tran, J. S.; Schiavazzi, D. E.; Ramachandra, A. B.; Kahn, A. M.; Marsden, A. L., Automated tuning for parameter identification and uncertainty quantification in multi-scale coronary simulations, Comput. Fluids, 142, 128-138 (2017) · Zbl 1390.76945
[35] Schiavazzi, D. E.; Baretta, A.; Pennati, G.; Hsia, T.-Y.; Marsden, A. L., Patient-specific parameter estimation in single-ventricle lumped circulation models under uncertainty, Int. J. Numer. Methods Biomed. Eng., 33, 3, Article e02799 pp. (2017)
[36] Biehler, J.; Wall, W. A., The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms, Int. J. Numer. Methods Biomed. Eng., 34, 2, Article e2922 pp. (2017)
[37] Marquis, A. D.; Arnold, A.; Dean-Bernhoft, C.; Carlson, B. E.; Olufsen, M. S., Practical identifiability and uncertainty quantification of a pulsatile cardiovascular model, Math. Biosci., 304, 9-24 (2018) · Zbl 1409.92072
[38] Brault, A.; Dumas, L.; Lucor, D., Uncertainty quantification of inflow boundary condition and proximal arterial stiffness-coupled effect on pulse wave propagation in a vascular network, Int. J. Numer. Methods Biomed. Eng., 33, 10, Article e2859 pp. (2017)
[39] Boccadifuoco, A.; Mariotti, A.; Celi, S.; Martini, N.; Salvetti, M., Impact of uncertainties in outflow boundary conditions on the predictions of hemodynamic simulations of ascending thoracic aortic aneurysms, Comput. Fluids, 165, 96-115 (2018) · Zbl 1390.76932
[40] Xiu, D.; Karniadakis, G., The Wiener-Askey polynomial chaos for stochastic differential equations, SIAM J. Sci. Comput., 24, 2, 619-644 (2002) · Zbl 1014.65004
[41] Babuška, I.; Nobile, F.; Tempone, R., A stochastic collocation method for elliptic partial differential equations with random input data, SIAM J. Numer. Anal., 45, 3, 1005-1034 (2007) · Zbl 1151.65008
[42] Metropolis, N.; Ulam, S., The Monte Carlo method, J. Am. Stat. Assoc., 44, 247, 335-341 (1949) · Zbl 0033.28807
[43] Giles, M., Multilevel Monte Carlo methods, Acta Numer., 24, 259-328 (2015) · Zbl 1316.65010
[44] Peherstorfer, B.; Willcox, K.; Gunzburger, M., Optimal model management for multifidelity Monte Carlo estimation, SIAM J. Sci. Comput., 38, 5, A3163-A3194 (2016) · Zbl 1351.65009
[45] Nobile, F.; Tesei, F., A multi level Monte Carlo method with control variate for elliptic PDEs with log-normal coefficients, Stoch. Partial Differ. Equ. Anal. Comput., 3, 3, 398-444 (2015) · Zbl 1334.60133
[46] Geraci, G.; Eldred, M.; Iaccarino, G., A Multifidelity Control Variate Approach for the Multilevel Monte Carlo Technique, 169-181 (2015), Center for Turbulence Research, Stanford University
[47] Geraci, G.; Eldred, M. S.; Iaccarino, G., A multifidelity multilevel Monte Carlo method for uncertainty propagation in aerospace applications, (19th AIAA Non-Deterministic Approaches Conference (2017), American Institute of Aeronautics and Astronautics: American Institute of Aeronautics and Astronautics Grapvine, Texas)
[48] Fairbanks, H. R.; Doostan, A.; Ketelsen, C.; Iaccarino, G., A low-rank control variate for multilevel Monte Carlo simulation of high-dimensional uncertain systems, J. Comput. Phys., 341 (2016)
[49] Updegrove, A.; Wilson, N.; Merkow, J.; Lan, H.; Marsden, A.; Shadden, S., SimVascular: An open source pipeline for cardiovascular simulation, Ann. Biomed. Eng., 45, 3, 525-541 (2016)
[50] Adams, B.; Ebeida, M.; Eldred, M.; Geraci, G.; Jakeman, J., Dakota, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.6 User’s ManualSandia Technical Report SAND2014-4633 (2014), Updated May 2017
[51] Formaggia, L.; Nobile, F.; Quarteroni, A.; Veneziani, A., Multiscale modelling of the circulatory system: a preliminary analysis, Comput. Vis. Sci., 2, 2, 75-83 (1999) · Zbl 1067.76624
[52] Vignon-Clementel, I. E.; Figueroa, C. A.; Jansen, K. E.; Taylor, C. A., Outflow boundary conditions for three-dimensional finite element modeling of blood flow and pressure in arteries, Comput. Methods Appl. Mech. Engrg., 195, 29, 3776-3796 (2006) · Zbl 1175.76098
[53] Esmaily Moghadam, M.; Bazilevs, Y.; Hsia, T.-Y.; Vignon-Clementel, I. E.; Marsden, A. L.; The Modeling of Congenital Hearts Alliance (MOCHA), S., A comparison of outlet boundary treatments for prevention of backflow divergence with relevance to blood flow simulations, Comput. Mech., 48, 3, 277-291 (2011) · Zbl 1398.76102
[54] Esmaily-Moghadam, M.; Bazilevs, Y.; Marsden, A. L., A bi-partitioned iterative algorithm for solving linear systems arising from incompressible flow problems, Comput. Methods Appl. Mech. Engrg., 286, 40-62 (2015) · Zbl 1423.76228
[55] Jansen, K. E.; Whiting, C. H.; Hulbert, G. M., A generalized-\( \alpha\) method for integrating the filtered Navier-Stokes equations with a stabilized finite element method, Comput. Methods Appl. Mech. Engrg., 190, 3, 305-319 (2000) · Zbl 0973.76048
[56] Esmaily-Moghadam, M.; Bazilevs, Y.; Marsden, A. L., A new preconditioning technique for implicitly coupled multidomain simulations with applications to hemodynamics, Comput. Mech., 52, 5, 1141-1152 (2013) · Zbl 1388.76130
[57] Seo, J.; Schiavazzi, D. E.; Marsden, A. L., Performance of preconditioned iterative linear solvers for cardiovascular simulations in rigid and deformable vessels, Comput. Mech. (2019) · Zbl 07099898
[58] Chatzizisis, Y.; Coskun, A.; Jonas, M.; Edelman, E.; Feldman, C.; Stone, P., Role of endothelial shear stress in the natural history of coronary atherosclerosis and vascular remodeling: molecular, cellular, and vascular behavior, J. Am. Coll. Cardiol., 49, 25, 2379-2393 (2007)
[59] Figueroa, A.; Vignon-Clementel, I.; Jansen, K.; Hughes, T.; Taylor, C., A coupled momentum method for modeling blood flow in three-dimensional deformable arteries, Comput. Methods Appl. Mech. Engrg., 195, 41, 5685-5706 (2006) · Zbl 1126.76029
[60] Euler, L., Principia pro motu sanguinis per arterias determinando, (Opera posthuma mathematica et physica anno 1844 detecta 2 (1775)), 814-823, ediderunt PH Fuss et N Fuss Petropoli; Apund Eggers et Socios
[61] Vignon, I.; Taylor, C., Outflow boundary conditions for one-dimensional finite element modeling of blood flow and pressure waves in arteries, Wave Motion, 39, 4, 361-374 (2004) · Zbl 1163.74453
[62] Vignon, I., A Coupled Multidomain Method for Computational Modeling of Blood Flow (2006), Stanford University, (Ph.D. thesis)
[63] Wan, J.; Steele, B.; Spicer, S. A.; Strohband, S.; Feijóo, G. R.; Hughes, T. J.; Taylor, C. A., A one-dimensional finite element method for simulation-based medical planning for cardiovascular disease, Comput. Methods Biomech. Biomed. Eng., 5, 195-206 (2002)
[64] Steele, B.; Taylor, C.; Wan, J.; Ku, J.; Hughes, T., In vivo validation of a one-dimensional finite element method for simulation-based medical planning for cardiovascular bypass surgery, IEEE Trans. Biomed. Engin, 1, 120-123 (2001)
[65] Milišić, V.; Quarteroni, A., Analysis of lumped parameter models for blood flow simulations and their relation with 1D models, ESAIM Math. Model. Numer. Anal., 38, 4, 613-632 (2004) · Zbl 1079.76053
[66] Migliavacca, F.; Balossino, R.; Pennati, G.; Dubini, G.; Hsia, T.-Y., Multiscale modelling in biofluidynamics: Application to reconstructive paediatric cardiac surgery, J. Biomech., 39, 1010-1020 (2006)
[67] Corsini, C.; Cosentino, D.; Pennati, G.; Dubini, G.; Hsia, T.-Y.; Migliavacca, F., Multiscale models of the hybrid palliation for hypoplastic left heart syndrome, J. Biomech., 44, 767-770 (2011)
[68] Pasupathy, R.; Schmeiser, B. W.; Taaffe, M. R.; Wang, J., Control-variate estimation using estimated control means, IIE Trans., 44, 5, 381-385 (2012)
[69] Ng, L.; Willcox, K., Multifidelity approaches for optimization under uncertainty, Int. J. Numer. Methods Eng., 100, 10, 746-772 (2014) · Zbl 1352.74230
[70] Rubinstein, R. Y.; Marcus, R., Efficiency of multivariate control variates in Monte Carlo simulation, Oper. Res., 33, 3, 661-677 (1985) · Zbl 0606.65100
[71] Gorodetsky, A. A.; Geraci, G.; Eldred, M.; Jakeman, J. D., A generalized approximate control variate framework for multifidelity uncertainty quantification, J. Comput. Phys., Article 109257 pp. (2020)
[72] Maniaci, D. C.; Frankel, A. L.; Geraci, G.; Blaylock, M. L.; Eldred, M. S., Multilevel uncertainty quantification of a wind turbine large eddy simulation model, (6th European Conference on Computational Mechanics—7th European Conference on Computational Fluid Dynamics (2018), International Centre for Numerical Methods in Engineering: International Centre for Numerical Methods in Engineering Glasgow, UK), 2747-2758
[73] Fleeter, C. M.; Geraci, G.; Schiavazzi, D. E.; Kahn, A. M.; Eldred, M. S.; Marsden, A. L., Multilevel multifidelity approaches for cardiovascular flow under uncertainty, (Sandia Center for Computing Research Summer Proceedings 2017, Technical Report SAND2018-2780O (2018), Sandia National Laboratories), 27-50
[74] Schiavazzi, D.; Fleeter, C. M.; Geraci, G.; Marsden, A. L., Multifidelity approaches for cardiovascular hemodynamics, (6th European Conference on Computational Mechanics—7th European Conference on Computational Fluid Dynamics (2018), International Centre for Numerical Methods in Engineering: International Centre for Numerical Methods in Engineering Glasgow, UK), 2759-2770
[75] Fleeter, C., Dakota-simvascular cardiovascular UQ interface (2019), Github Repository, Zenodo
[76] Kent, K. C., Abdominal aortic aneurysms, N. Engl. J. Med., 371, 22, 2101-2108 (2014)
[77] Giannoglou, G. D.; Antoniadis, A. P.; Chatzizisis, Y. S.; Louridas, G. E., Difference in the topography of atherosclerosis in the left versus right coronary artery in patients referred for coronary angiography, BMC Cardiovasc. Disord., 10, 1, 26 (2010)
[78] Peiró, J.; Veneziani, A., Reduced models of the cardiovascular system, (Formaggia, L.; Quarteroni, A.; Veneziani, A., Cardiovascular Mathematics: Modeling and Simulation of the Circulatory System (2009), Springer Milan: Springer Milan Milano), 347-394
[79] Zhou, Y.; Kassab, G.; Molloi, S., On the design of the coronary arterial tree: a generalization of Murray’s law, Phys. Med. Biol., 44, 12, 2929-2945 (1999)
[80] Les, A. S.; Shadden, S. C.; Figueroa, C. A.; Park, J. M.; Tedesco, M. M., Quantification of hemodynamics in abdominal aortic aneurysms during rest and exercise using magnetic resonance imaging and computational fluid dynamics, Ann. Biomed. Eng., 38, 4, 1288-1313 (2010)
[81] Coogan, J.; Humphrey, J.; Figueroa, C., Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodeling in response to distal aortic coarctation, Biomech. Model. Mechanobiol., 12, 1, 79-93 (2013)
[82] Roccabianca, S.; Figueroa, C.; Tellides, G.; Humphrey, J., Quantification of regional differences in aortic stiffness in the aging human, J. Mech. Behav. Biomed. Mater., 29, 618-634 (2014)
[83] Zambrano, B. A.; Gharahi, H.; Lim, C.; Jaberi, F. A.; Choi, J.; Lee, W.; Baek, S., Association of intraluminal thrombus, hemodynamic forces, and abdominal aortic aneurysm expansion using longitudinal CT images, Ann. Biomed. Eng., 44, 1502-1514 (2015)
[84] Geraci, G.; Eldred, M. S.; Gorodetsky, A. A.; Jakeman, J. D., Leveraging active directions for efficient multifidelity UQ, (6th European Conference on Computational Mechanics—7th European Conference on Computational Fluid Dynamics (2018), International Centre for Numerical Methods in Engineering: International Centre for Numerical Methods in Engineering Glasgow, UK), 2735-2746
[85] Blonigan, P. J.; Geraci, G.; Rizzi, F.; Eldred, M. S.; Carlberg, K., On-line Generation and Error Handling for Surrogate Models within Multifidelity Uncertainty QuantificationSandia Technical Report SAND2019-11427R (2019)
[86] P.J. Blonigan, G. Geraci, F. Rizzi, M.S. Eldred, Towards an integrated and efficient framework for leveraging reduced order models for multifidelity uncertainty quantification, in: AIAA Scitech 2020 Forum, 2020.
[87] Perotto, S.; Ern, A.; Veneziani, A., Hierarchical local model reduction for elliptic problems: A domain decomposition approach, Multiscale Model. Simul., 8 (2010) · Zbl 1206.65251
[88] Perotto, S.; Veneziani, A., Coupled model and grid adaptivity in hierarchical reduction of elliptic problems, J. Sci. Comput., 60, 505-536 (2013) · Zbl 1307.65155
[89] Aletti, M. C.; Perotto, S.; Veneziani, A., Himod reduction of advection—diffusion—reaction problems with general boundary conditions, J. Sci. Comput., 76, 1, 89-119 (2018) · Zbl 1397.65248
[90] MansillaAlvarez, L.; Blanco, P.; Bulant, C.; Dari, E.; Veneziani, A.; Feijóo, R., Transversally enriched pipe element method (TEPEM): An effective numerical approach for blood flow modeling, Int. J. Numer. Methods Biomed. Eng., 33, 4, Article e2808 pp. (2017), e2808 cnm.2808
[91] Blanco, P.; Alvarez, L. M.; Feijóo, R., Hybrid element-based approximation for the Navier-Stokes equations in pipe-like domains, Comput. Methods Appl. Mech. Engrg., 283, 971-993 (2015) · Zbl 1423.76516
[92] Alvarez, A.; Blanco, P.; Feijóo, R., An efficient method for the numerical solution of blood flow in 3D bifurcated regions, (Proceeding Series of the Brazilian Society of Applied and Computational Mathematics, vol. 6 (2018))
[93] Guzzetti, S.; Alvarez, L. M.; Blanco, P.; Carlberg, K.; Veneziani, A., Propagating uncertainties in large-scale hemodynamics models via network uncertainty quantification and reduced-order modeling, Comput. Methods Appl. Mech. Engrg., 358, Article 112626 pp. (2020) · Zbl 1441.76147
[94] Dal Santo, N.; Deparis, S.; Pegolotti, L., Data driven approximation of parametrized PDEs by reduced basis and neural networks (2019), arXiv preprint arXiv:1908.04875
[95] G. Geraci, M.S. Eldred, A. Gorodetsky, J. Jakeman, Recent advancements in Multilevel-Multifidelity techniques for forward UQ in the DARPA Sequoia project, in: AIAA Scitech 2019 Forum, San Diego, CA, 2019.
[96] Gorodetsky, A. A.; Geraci, G.; Eldred, M. S.; Jakeman, J. D., Latent variable networks for multifidelity uncertainty quantification and data fusion, (6th European Conference on Computational Mechanics—7th European Conference on Computational Fluid Dynamics (2018), International Centre for Numerical Methods in Engineering: International Centre for Numerical Methods in Engineering Glasgow, UK)
[97] Towns, J.; Cockerill, T.; Dahan, M.; Foster, I.; Gaither, K., XSEDE: Accelerating scientific discovery, Comput. Sci. Eng., 16, 5, 62-74 (2014)
[98] Wilkins-Diehr, N.; Sanielevici, S.; Alameda, J.; Cazes, J.; Crosby, L.; Pierce, M.; Roskies, R., An overview of the XSEDE extended collaborative support program, (High Performance Computer Applications - 6th International Conference, ISUM 2015, Revised Selected Papers. High Performance Computer Applications - 6th International Conference, ISUM 2015, Revised Selected Papers, Communications in Computer and Information Science, vol. 595 (2016), Springer Verlag: Springer Verlag Germany), 3-13
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