Maestre, Jorge; Pallares, Jordi; Cuesta, Ildefonso; Scott, Michael A. A 3D isogeometric BE-FE analysis with dynamic remeshing for the simulation of a deformable particle in shear flows. (English) Zbl 1439.74446 Comput. Methods Appl. Mech. Eng. 326, 70-101 (2017). Summary: A three-dimensional isogeometric coupled boundary element and finite element approach based on analysis suitable T-splines is developed for the simulation of deformable capsules suspended in shear flows. Boundary element analysis is used to solve the fluid Stokes equation whereas the hydrodynamic membrane load is computed via isogeometric analysis under the assumption that the membrane is a hyper-elastic thin shell with negligible bending resistance. The smoothness of the T-spline basis functions accommodate large deformations of the capsule without the need for additional smoothing techniques, and can be used to accurately compute the membrane load. A balanced distribution of membrane elements can be constructed using an unstructured locally refined mesh. These properties are coupled with an adaptive temporal implicit integration scheme. Several benchmark examples are solved to illustrate the accuracy and potential of the method. The approach is then applied to simulate the dynamics of a capsule in a real geometry of a brain capillary. Cited in 6 Documents MSC: 74S05 Finite element methods applied to problems in solid mechanics 74S15 Boundary element methods applied to problems in solid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65D07 Numerical computation using splines 65N38 Boundary element methods for boundary value problems involving PDEs 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74K15 Membranes 76D07 Stokes and related (Oseen, etc.) flows Keywords:isogeometric analysis; BEM; FEM; T-spline; deformable capsule; dynamic refinement Software:BEMLIB PDFBibTeX XMLCite \textit{J. Maestre} et al., Comput. Methods Appl. Mech. Eng. 326, 70--101 (2017; Zbl 1439.74446) Full Text: DOI References: [1] Andrews, D. A.; Low, P. S., Role of red blood cells in thrombosis, Curr. Opin. Hematol., 6, 2, 76 (1999) [2] Bansode, S. S.; Banarjee, S. K.; Gaikwad, D. D.; Jadhav, S. L.; Thorat, R. M., Microencapsulation: a review, Int. J. Pharm. Sci. Rev. Res., 1, 2, 38-43 (2010) [3] Barthès-Biesel, D., Motion of a spherical microcapsule freely suspended in a linear shear flow, J. Fluid Mech., 100, 04, 831-853 (1980) · Zbl 0456.76038 [4] Barthès-Biesel, D.; Rallison, J. M., The time-dependent deformation of a capsule freely suspended in a linear shear flow, J. Fluid Mech., 113, 251-267 (1981) · Zbl 0493.76129 [5] Gao, T.; Hu, H. H.; Castañeda, P. P., Rheology of a suspension of elastic particles in a viscous shear flow, J. Fluid Mech., 687, 209 (2011) · Zbl 1241.76395 [6] Villone, M. M.; d’Avino, G.; Hulsen, M. A.; Maffettone, P. L., Dynamics of prolate spheroidal elastic particles in confined shear flow, Phys. Rev. E, 92, 6, 062303 (2015) [7] Sugiyama, K.; Ii, S.; Takeuchi, S.; Takagi, S.; Matsumoto, Y., A full Eulerian finite difference approach for solving fluid-structure coupling problems, J. Comput. Phys., 230, 3, 596-627 (2011) · Zbl 1283.74010 [8] Eggleton, C. D.; Popel, A. S., Large deformation of red blood cell ghosts in a simple shear flow, Phys. Fluids (1994-Present), 10, 8, 1834-1845 (1998) [9] Bagchi, P.; Johnson, P. C.; Popel, A. S., Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow, J. Biomech. Eng., 127, 7, 1070-1080 (2005) [10] Bagchi, P., Mesoscale simulation of blood flow in small vessels, Biophys. J., 92, 6, 1858-1877 (2007) [11] Song, C.; Shin, S. J.; Sung, H. J.; Chang, K.-S., Dynamic fluid-structure interaction of an elastic capsule in a viscous shear flow at moderate Reynolds number, J. Fluids Struct., 27, 3, 438-455 (2011) [12] Huang, W.-X.; Chang, C. B.; Sung, H. J., Three-dimensional simulation of elastic capsules in shear flow by the penalty immersed boundary method, J. Comput. Phys., 231, 8, 3340-3364 (2012) · Zbl 1404.74159 [13] Sui, Y.; Chew, Y.-T.; Roy, P.; Low, H.-T., A hybrid method to study flow-induced deformation of three-dimensional capsules, J. Comput. Phys., 227, 12, 6351-6371 (2008) · Zbl 1160.76028 [14] MacMeccan, R. M.; Clausen, J. R.; Neitzel, G. P.; Aidun, C. K., Simulating deformable particle suspensions using a coupled lattice-Boltzmann and finite-element method, J. Fluid Mech., 618, 13-39 (2009) · Zbl 1156.76455 [15] Sui, Y.; Chen, X. B.; Chew, Y. T.; Roy, P.; Low, H. T., Numerical simulation of capsule deformation in simple shear flow, Comput. & Fluids, 39, 2, 242-250 (2010) · Zbl 1242.76280 [16] Kilimnik, A.; Mao, W.; Alexeev, A., Inertial migration of deformable capsules in channel flow, Phys. Fluids (1994-Present), 23, 12, 123302 (2011) [17] Schot, S. H., Eighty years of Sommerfeld’s radiation condition, His. Math., 19, 4, 385-401 (1992) · Zbl 0763.01020 [18] Pozrikidis, C., Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow, J. Fluid Mech., 297, 123-152 (1995) · Zbl 0859.73053 [19] Ramanujan, S.; Pozrikidis, C., Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities, J. Fluid Mech., 361, 117-143 (1998) · Zbl 0921.76058 [20] Leyrat-Maurin, A.; Barthès-Biesel, D., Motion of a deformable capsule through a hyperbolic constriction, J. Fluid Mech., 279, 135-163 (1994) · Zbl 0826.76016 [21] Quéguiner, C.; Barthès-Biesel, D., Axisymmetric motion of capsules through cylindrical channels, J. Fluid Mech., 348, 349-376 (1997) · Zbl 0912.76089 [22] Diaz, A.; Pelekasis, N.; Barthès-Biesel, D., Transient response of a capsule subjected to varying flow conditions: effect of internal fluid viscosity and membrane elasticity, Phys. Fluids (1994-Present), 12, 5, 948-957 (2000) · Zbl 1149.76360 [23] Diaz, A.; Barthès-Biesel, D., Entrance of a bioartificial capsule in a pore, CMES Comput. Model. Eng. Sci., 3, 3, 321-338 (2001) · Zbl 1039.74034 [24] Lefebvre, Y.; Barthès-Biesel, D., Motion of a capsule in a cylindrical tube: effect of membrane pre-stress, J. Fluid Mech., 589, 157-181 (2007) · Zbl 1141.76367 [25] Lac, E.; Barthès-Biesel, D.; Pelekasis, N. A.; Tsamopoulos, J., Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling, J. Fluid Mech., 516, 303-334 (2004) · Zbl 1131.74306 [26] Lac, E.; Barthès-Biesel, D., Deformation of a capsule in simple shear flow: effect of membrane prestress, Phys. Fluids (1994-Present), 17, 7, 072105 (2005) · Zbl 1187.76290 [27] Dodson III, W. R.; Dimitrakopoulos, P., Spindles, cusps, and bifurcation for capsules in Stokes flow, Phys. Rev. Lett., 101, 20, 208102 (2008) [28] Dodson, W. R.; Dimitrakopoulos, P., Dynamics of strain-hardening and strain-softening capsules in strong planar extensional flows via an interfacial spectral boundary element algorithm for elastic membranes, J. Fluid Mech., 641, 263-296 (2009) · Zbl 1183.76825 [29] Zhu, L.; Rabault, J.; Brandt, L., The dynamics of a capsule in a wall-bounded oscillating shear flow, Phys. Fluids (1994-Present), 27, 7, 071902 (2015) [30] Rorai, C.; Touchard, A.; Zhu, L.; Brandt, L., Motion of an elastic capsule in a constricted microchannel, Eur. Phys. J. E, 38, 5, 1-13 (2015) [31] Zarda, P. R.; Chien, S.; Skalak, R., Interaction of viscous incompressible fluid with an elastic body, Comput. Methods Fluid-Solid Interact. Probl., 65-82 (1977) · Zbl 0388.73048 [32] Skalak, R.; Tozeren, A.; Zarda, R. P.; Chien, S., Strain energy function of red blood cell membranes, Biophys. J., 13, 3, 245 (1973) [33] Skalak, R.; Ozkaya, N.; Skalak, T. C., Biofluid mechanics, Annu. Rev. Fluid Mech., 21, 1, 167-200 (1989) · Zbl 0662.76160 [34] Pieper, G.; Rehage, H.; Barthès-Biesel, D., Deformation of a capsule in a spinning drop apparatus, J. Colloid Interface Sci., 202, 2, 293-300 (1998) [35] Carin, M.; Barthès-Biesel, D.; Edwards-Lévy, F.; Postel, C.; Andrei, D. C., Compression of biocompatible liquid-filled HSA-alginate capsules: Determination of the membrane mechanical properties, Biotechnol. Bioeng., 82, 2, 207-212 (2003) [36] Husmann, M.; Rehage, H.; Dhenin, E.; Barthès-Biesel, D., Deformation and bursting of nonspherical polysiloxane microcapsules in a spinning-drop apparatus, J. Colloid Interface Sci., 282, 1, 109-119 (2005) [37] Pozrikidis, C., Numerical simulation of the flow-induced deformation of red blood cells, Ann. Biomed. Eng., 31, 10, 1194-1205 (2003) [38] Zhao, H.; Isfahani, A. H.; Olson, L. N.; Freund, J. B., A spectral boundary integral method for flowing blood cells, J. Comput. Phys., 229, 10, 3726-3744 (2010) · Zbl 1186.92013 [39] Peng, Z.; Asaro, R. J.; Zhu, Q., Multiscale simulation of erythrocyte membranes, Phys. Rev. E, 81, 031904 (2010) [40] Peng, Z.; Chen, Y.-L.; Lu, H.; Pan, Z.; Chang, H.-C., Mesoscale simulations of two model systems in biophysics: from red blood cells to DNAs, Comput. Part. Mech., 2, 4, 339-357 (2015) [41] Dupont, C.; Salsac, A.-V.; Barthès-Biesel, D.; Vidrascu, M.; Le Tallec, P., Influence of bending resistance on the dynamics of a spherical capsule in shear flow, Phys. Fluids (1994-Present), 27, 5, 051902 (2015) [42] Barthès-Biesel, D., Motion and deformation of elastic capsules and vesicles in flow, Annu. Rev. Fluid Mech., 48, 25-52 (2016) · Zbl 1356.76459 [43] Walter, J.; Salsac, A.-V.; Barthès-Biesel, D.; Le Tallec, P., Coupling of finite element and boundary integral methods for a capsule in a Stokes flow, Internat. J. Numer. Methods Engrg., 83, 7, 829-850 (2010) · Zbl 1197.74187 [44] Foessel, E.; Walter, J.; Salsac, A.-V.; Barthès-Biesel, D., Influence of internal viscosity on the large deformation and buckling of a spherical capsule in a simple shear flow, J. Fluid Mech., 672, 477-486 (2011) · Zbl 1225.74035 [45] Walter, J.; Salsac, A.-V.; Barthès-Biesel, D., Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes, J. Fluid Mech., 676, 318-347 (2011) · Zbl 1241.76127 [46] Hu, X.-Q.; Salsac, A.-V.; Barthès-Biesel, D., Flow of a spherical capsule in a pore with circular or square cross-section, J. Fluid Mech., 705, 176-194 (2012) · Zbl 1250.76194 [47] Omori, T.; Ishikawa, T.; Imai, Y.; Yamaguchi, T., Membrane tension of red blood cells pairwisely interacting in simple shear flow, J. Biomech., 46, 3, 548-553 (2013) [48] Dupont, C.; Delahaye, F.; Salsac, A.-V.; Barthès-Biesel, D., Off-plane motion of an oblate capsule in a simple shear flow, Comput. Methods Biomech. Biomed. Eng., 16, Suppl. 1, 4-5 (2013) · Zbl 1287.76246 [49] Hughes, T. J.R.; Cottrell, J. A.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 39-41, 4135-4195 (2005) · Zbl 1151.74419 [50] Bazilevs, Y.; Calo, V. M.; Zhang, Y.; Hughes, T. J.R., Isogeometric fluid-structure interaction analysis with applications to arterial blood flow, Comput. Mech., 38, 4-5, 310-322 (2006) · Zbl 1161.74020 [51] Zhang, Y.; Bazilevs, Y.; Goswami, S.; Bajaj, C. L.; Hughes, T. J.R., Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow, Comput. Methods Appl. Mech. Engrg., 196, 29, 2943-2959 (2007) · Zbl 1121.76076 [52] Bazilevs, Y.; Gohean, J. R.; Hughes, T. J.R.; Moser, R. D.; Zhang, Y., Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device, Comput. Methods Appl. Mech. Engrg., 198, 45, 3534-3550 (2009) · Zbl 1229.74096 [53] Chivukula, V.; Mousel, J.; Lu, J.; Vigmostad, S., Micro-scale blood particulate dynamics using a non-uniform rational B-spline-based isogeometric analysis, Int. J. Numer. Methods Biomed. Eng., 30, 12, 1437-1459 (2014) [54] Politis, C.; Ginnis, A.; Kaklis, P.; Belibassakis, K.; Feurer, C., An isogeometric BEM for exterior potential-flow problems in the plane, Joint Conf. Geom. Phys. Model., 349-354 (2009) [55] Simpson, R. N.; Bordas, S. P.A.; Trevelyan, J.; Rabczuk, T., A two-dimensional isogeometric boundary element method for elastostatic analysis, Comput. Methods Appl. Mech. Engrg., 209-212, 87-100 (2012) · Zbl 1243.74193 [56] Li, K.; Qian, X., Isogeometric analysis and shape optimization via boundary integral, Comput. Aided Des., 43, 11, 1427-1437 (2011) [57] Belibassakis, K.; Gerostathis, T.; Kostas, K.; Politis, C.; Kaklis, P.; Ginnis, A.; Feurer, C., A BEM-isogeometric method for the ship wave-resistance problem, Ocean Eng., 60, 53-67 (2013) [58] Peake, M. J.; Trevelyan, J.; Coates, G., Extended isogeometric boundary element method (XIBEM) for two-dimensional Helmholtz problems, Comput. Methods Appl. Mech. Engrg., 259, 93-102 (2013) · Zbl 1286.65176 [59] Politis, C.; Papagiannopoulos, A.; Belibassakis, K.; Kaklis, P.; Kostas, K.; Ginnis, A.; Gerostathis, T., An isogeometric BEM for exterior potential-flow problems around lifting bodies, (11th World Congress on Computational Mechanics, WCCM XI (2014), International Center for Numerical Methods in Engineering (CIMNE)), 2433-2444 [60] Peake, M. J.; Trevelyan, J.; Coates, G., Extended isogeometric boundary element method (XIBEM) for three-dimensional medium-wave acoustic scattering problems, Comput. Methods Appl. Mech. Engrg., 284, 762-780 (2015) · Zbl 1425.65202 [61] Aimi, A.; Diligenti, M.; Sampoli, M.; Sestini, A., Isogemetric analysis and symmetric Galerkin BEM: A 2D numerical study, Appl. Math. Comput., 272, 173-186 (2016) · Zbl 1410.65468 [62] Joneidi, A.; Verhoosel, C.; Anderson, P., Isogeometric boundary integral analysis of drops and inextensible membranes in isoviscous flow, Comput. & Fluids, 109, 49-66 (2015) · Zbl 1390.76651 [63] Heltai, L.; Arroyo, M.; DeSimone, A., Nonsingular isogeometric boundary element method for Stokes flows in 3D, Comput. Methods Appl. Mech. Engrg., 268, 514-539 (2014) · Zbl 1295.76022 [64] Heltai, L.; Kiendl, J.; DeSimone, A.; Reali, A., A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling, Comput. Methods Appl. Mech. Engrg., 316, 522-546 (2017) · Zbl 1439.74108 [65] Sederberg, T. W.; Zheng, J.; Bakenov, A.; Nasri, A., T-splines and T-NURCCs, ACM Trans. Graph., 22, 3, 477-484 (2003) [66] Scott, M. A.; Li, X.; Sederberg, T. W.; Hughes, T. J.R., Local refinement of analysis-suitable T-splines, Comput. Methods Appl. Mech. Engrg., 213, 206-222 (2012) · Zbl 1243.65030 [67] Li, X.; Zheng, J.; Sederberg, T. W.; Hughes, T. J.R.; Scott, M. A., On linear independence of T-spline blending functions, Comput. Aided Geom. Design, 29, 1, 63-76 (2012) · Zbl 1251.65012 [68] Borden, M. J.; Scott, M. A.; Evans, J. A.; Hughes, T. J.R., Isogeometric finite element data structures based on Bézier extraction of NURBS, Internat. J. Numer. Methods Engrg., 87, 1-5, 15-47 (2011) · Zbl 1242.74097 [69] Scott, M. A.; Borden, M. J.; Verhoosel, C. V.; Sederberg, T. W.; Hughes, T. J.R., Isogeometric finite element data structures based on Bézier extraction of T-splines, Internat. J. Numer. Methods Engrg., 88, 2, 126-156 (2011) · Zbl 1242.65243 [70] Scott, M. A.; Simpson, R. N.; Evans, J. A.; Lipton, S.; Bordas, S. P.A.; Hughes, T. J.R.; Sederberg, T. W., Isogeometric boundary element analysis using unstructured T-splines, Comput. Methods Appl. Mech. Engrg., 254, 0, 197-221 (2013) · Zbl 1297.74156 [71] Dimitri, R.; De Lorenzis, L.; Scott, M. A.; Wriggers, P.; Taylor, R. L.; Zavarise, G., Isogeometric large deformation frictionless contact using T-splines, Comput. Methods Appl. Mech. Engrg., 269, 394-414 (2014) · Zbl 1296.74071 [72] Simpson, R. N.; Scott, M. A.; Taus, M.; Thomas, D. C.; Lian, H., Acoustic isogeometric boundary element analysis, Comput. Methods Appl. Mech. Engrg., 269, 265-290 (2014) · Zbl 1296.65175 [73] Kostas, K. V.; Ginnis, A. I.; Politis, C. G.; Kaklis, P. D., Ship-hull shape optimization with a T-spline based BEM-isogeometric solver, Comput. Methods Appl. Mech. Engrg., 284, 611-622 (2015) · Zbl 1425.65201 [74] Maestre, J.; Cuesta, I.; Pallares, J., An unsteady 3d isogeometrical boundary element analysis applied to nonlinear gravity waves, Comput. Methods Appl. Mech. Engrg., 310, 112-133 (2016) · Zbl 1439.76118 [75] Bazilevs, Y.; Calo, V. M.; Cottrell, J. A.; Evans, J. A.; Hughes, T. J.R.; Lipton, S.; Scott, M. A.; Sederberg, T. W., Isogeometric analysis using T-splines, Comput. Methods Appl. Mech. Engrg., 199, 5-8, 229-263 (2010) · Zbl 1227.74123 [76] Schillinger, D.; Dedè, L.; Scott, M. A.; Evans, J. A.; Borden, M. J.; Rank, E.; Hughes, T. J.R., An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces, Comput. Methods Appl. Mech. Engrg., 249-252, 116-150 (2012) · Zbl 1348.65055 [77] Benson, D. J.; Bazilevs, Y.; de Luycker, E.; Hsu, M. C.; Scott, M. A.; Hughes, T. J.R.; Belytschko, T., A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM, Internat. J. Numer. Methods Engrg., 83, 6, 765-785 (2010) · Zbl 1197.74177 [78] Verhoosel, C. V.; Scott, M. A.; De Borst, R.; Hughes, T. J.R., An isogeometric approach to cohesive zone modeling, Internat. J. Numer. Methods Engrg., 87, 1-5, 336-360 (2011) · Zbl 1242.74169 [79] Verhoosel, C. V.; Scott, M. A.; Hughes, T. J.R.; de Borst, R., An isogeometric analysis approach to gradient damage models, Internat. J. Numer. Methods Engrg., 86, 1, 115-134 (2011) · Zbl 1235.74320 [80] Borden, M. J.; Verhoosel, C. V.; Scott, M. A.; Hughes, T. J.R.; Landis, C. M., A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Engrg., 217-220, 77-95 (2012) · Zbl 1253.74089 [81] Ghorashi, S. S.; Valizadeh, N.; Mohammadi, S.; Rabczuk, T., T-spline based XIGA for fracture analysis of orthotropic media, Comput. Struct., 147, 138-146 (2015) [82] Bazilevs, Y.; Hsu, M. C.; Scott, M. A., Isogeometric fluid-structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines, Comput. Methods Appl. Mech. Engrg., 249-252, 28-41 (2012) · Zbl 1348.74094 [83] Hsu, M.-C.; Kamensky, D.; Xu, F.; Kiendl, J.; Wang, C.; Wu, M.; Mineroff, J.; Reali, A.; Bazilevs, Y.; Sacks, M., Dynamic and fluidstructure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models, Comput. Mech., 55, 6, 1211-1225 (2015) · Zbl 1325.74048 [84] Buffa, A.; Sangalli, G.; Vázquez, R., Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations, J. Comput. Phys., 257, PB, 1291-1320 (2014) · Zbl 1351.78036 [85] Lorenzo, G.; Scott, M. A.; Tew, K.; Hughes, T. J.R.; Gomez, H., Hierarchically refined and coarsened splines for moving interface problems, with particular application to phase-field models of prostate tumor growth, Comput. Methods Appl. Mech. Engrg. (2017) · Zbl 1439.74203 [86] Deng, J.; Chen, F.; Li, X.; Hu, C.; Tong, W.; Yang, Z.; Feng, Y., Polynomial splines over hierarchical T-meshes, Graph. Models, 70, 4, 76-86 (2008) [87] Scott, M. A.; Thomas, D. C.; Evans, E. J., Isogeometric spline forests, Comput. Methods Appl. Mech. Engrg., 269, 222-264 (2014) · Zbl 1296.65023 [88] Evans, E. J.; Scott, M. A.; Li, X.; Thomas, D. C., Hierarchical T-splines: Analysis-suitability, Bézier extraction, and application as an adaptive basis for isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 284, 1-20 (2015) · Zbl 1425.65025 [89] Giannelli, C.; Jüttler, B.; Speleers, H., THB-splines: The truncated basis for hierarchical splines, Comput. Aided Geom. Design, 29, 7, 485-498 (2012) · Zbl 1252.65030 [90] Hennig, P.; Müller, S.; Kästner, M., Bézier extraction and adaptive refinement of truncated hierarchical NURBS, Comput. Methods Appl. Mech. Engrg., 305, 316-339 (2016) · Zbl 1425.65031 [91] Wei, X.; Zhang, Y.; Hughes, T. J.R.; Scott, M. A., Truncated hierarchical Catmull-Clark subdivision with local refinement, Comput. Methods Appl. Mech. Engrg., 291, 1-20 (2015) · Zbl 1425.65028 [92] Boey, S. K.; Boal, D. H.; Discher, D. E., Simulations of the erythrocyte cytoskeleton at large deformation. I. Microscopic models, Biophys. J., 75, 3, 1573-1583 (1998) [93] Discher, D. E.; Boal, D. H.; Boey, S. K., Simulations of the erythrocyte cytoskeleton at large deformation. II. Micropipette aspiration, Biophys. J., 75, 3, 1584-1597 (1998) [94] Pozrikidis, C., Numerical simulation of the flow-induced deformation of red blood cells, Ann. Biomed. Eng., 31, 10, 1194-1205 (2003) [95] Pozrikidis, C., Numerical simulation of cell motion in tube flow, Ann. Biomed. Eng., 33, 2, 165-178 (2005) [96] Pivkin, I. V.; Karniadakis, G. E., Accurate coarse-grained modeling of red blood cells, Phys. Rev. Lett., 101, 11, 118105 (2008) [97] Fedosov, D. A.; Caswell, B.; Karniadakis, G. E., A multiscale red blood cell model with accurate mechanics, rheology, and dynamics, Biophys. J., 98, 10, 2215-2225 (2010) [98] Zhao, H.; Isfahani, A. H.; Olson, L. N.; Freund, J. B., A spectral boundary integral method for flowing blood cells, J. Comput. Phys., 229, 10, 3726-3744 (2010) · Zbl 1186.92013 [99] Li, X.; Peng, Z.; Lei, H.; Dao, M.; Karniadakis, G. E., Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model, Phil. Trans. R. Soc. A, 372, 2021, 20130389 (2014) · Zbl 1353.92037 [100] Barthès-Biesel, D.; Diaz, A.; Dhenin, E., Effect of constitutive laws for two-dimensional membranes on flow-induced capsule deformation, J. Fluid Mech., 460, 211-222 (2002) · Zbl 1066.74023 [101] Li, X.; Scott, M. A., Analysis-suitable T-splines: characterization, refineability, and approximation, Math. Models Methods Appl. Sci., 24, 06, 1141-1164 (2014) · Zbl 1292.41004 [102] Taus, M.; Rodin, G. J.; Hughes, T. J., Isogeometric analysis of boundary integral equations: High-order collocation methods for the singular and hyper-singular equationsac, Math. Models Methods Appl. Sci., 26, 08, 1447-1480 (2016) · Zbl 1343.65143 [103] Takacs, T.; Jüttler, B., Existence of stiffness matrix integrals for singularly parameterized domains in isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 200, 49, 3568-3582 (2011) · Zbl 1239.65014 [104] Hu, S.-M., Conversion between triangular and rectangular Bézier patches, Comput. Aided Geom. Design, 18, 7, 667-671 (2001) · Zbl 0983.68216 [105] Yan, L.; Han, X.; Liang, J., Conversion between triangular Bézier patches and rectangular Bézier patches, Appl. Math. Comput., 232, 469-478 (2014) · Zbl 1410.65059 [106] Pozrikidis, C., A Practical Guide to Boundary Element Methods with the Software Library BEMLIB (2002), CRC Press · Zbl 1019.65097 [107] Mantic, V., A new formula for the C-matrix in the Somigliana identity, J. Elasticity, 33, 3, 191-201 (1993) · Zbl 0801.73015 [108] Brebbia, C. A.; Domínguez, J., Boundary Elements: An Introductory Course (1992), WIT Press, Computational Mechanics · Zbl 0780.73002 [109] Lachat, J. C.; Watson, J. O., Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics, Internat. J. Numer. Methods Engrg., 10, 5, 991-1005 (1976) · Zbl 0332.73022 [110] Dominguez, J., Boundary Elements in Dynamics (1993), Wit Press · Zbl 0790.73003 [111] Auricchio, F.; Calabrò, F.; Hughes, T.; Reali, A.; Sangalli, G., A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 249-252, 15-27 (2012) · Zbl 1348.65059 [112] Hughes, T.; Reali, A.; Sangalli, G., Efficient quadrature for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 199, 5-8, 301-313 (2010) · Zbl 1227.65029 [113] Cruse, T.; Aithal, R., Non-singular boundary integral equation implementation, Internat. J. Numer. Methods Engrg., 36, 2, 237-254 (1993) [114] Huang, Q.; Cruse, T., Some notes on singular integral techniques in boundary element analysis, Internat. J. Numer. Methods Engrg., 36, 15, 2643-2659 (1993) · Zbl 0781.73076 [115] Johnston, P. R.; Elliott, D., A sinh transformation for evaluating nearly singular boundary element integrals, Internat. J. Numer. Methods Engrg., 62, 4, 564-578 (2005) · Zbl 1119.65318 [116] Lekner, J., Viscous flow through pipes of various cross-sections, Eur. J. Phys., 28, 3, 521 (2007) · Zbl 1116.76020 [117] Sederberg, T.; Cardon, D.; Zheng, J.; Lyche, T., T-spline simplification and local refinement, (SIGGRAPH 2004 (2004), ACM), 276-283 [118] Thomas, D. C.; Scott, M. A.; Evans, J. A.; Tew, K.; Evans, E. J., Bézier projection: A unified approach for local projection and quadrature-free refinement and coarsening of NURBS and T-splines with particular application to isogeometric design and analysis, Comput. Methods Appl. Mech. Engrg., 284, 55-105 (2015), Isogeometric Analysis Special Issue · Zbl 1425.65035 [119] Pozrikidis, C., Effect of membrane bending stiffness on the deformation of capsules in simple shear flow, J. Fluid Mech., 440, 269-291 (2001) · Zbl 1107.74307 [120] Wang, Y.; Dimitrakopoulos, P., A three-dimensional spectral boundary element algorithm for interfacial dynamics in Stokes flow, Phys. Fluids (1994-Present), 18, 8, 082106 (2006) · Zbl 1185.76515 [121] Chwang, A. T.; Wu, T. Y.-T., Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows, J. Fluid Mech., 67, 04, 787-815 (1975) · Zbl 0309.76016 [122] Bentley, B. J.; Leal, L. G., An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows, J. Fluid Mech., 167, 241-283 (1986) · Zbl 0611.76117 [123] Avtan, S. M.; Kaya, M.; Orhan, N.; Arslan, A.; Arican, N.; Toklu, A. S.; Gürses, C.; Elmas, I.; Kucuk, M.; Ahishali, B., The effects of hyperbaric oxygen therapy on blood-brain barrier permeability in septic rats, Brain Res., 1412, 63-72 (2011) [124] H.L. Goldsmith, Red cell motions and wall interactions in tube flow, in: Federation Proceedings, vol. 30, 1971, pp. 1578-1590.; H.L. Goldsmith, Red cell motions and wall interactions in tube flow, in: Federation Proceedings, vol. 30, 1971, pp. 1578-1590. [125] Helmy, A.; Barthès-Biesel, D., Migration of a spherical capsule freely suspended in an unbounded parabolic flow, J. Mec. Theor. Appl., 1, 5, 859-880 (1982) · Zbl 0517.76107 [126] Coupier, G.; Kaoui, B.; Podgorski, T.; Misbah, C., Noninertial lateral migration of vesicles in bounded Poiseuille flow, Phys. Fluids (1994-Present), 20, 11, 111702 (2008) · Zbl 1182.76164 [127] Doddi, S. K.; Bagchi, P., Lateral migration of a capsule in a plane Poiseuille flow in a channel, Int. J. Multiph. Flow., 34, 10, 966-986 (2008) [128] Shi, L.; Pan, T.-W.; Glowinski, R., Numerical simulation of lateral migration of red blood cells in Poiseuille flows, Internat. J. Numer. Methods Fluids, 68, 11, 1393-1408 (2012) · Zbl 1302.92021 [129] Singh, R. K.; Li, X.; Sarkar, K., Lateral migration of a capsule in plane shear near a wall, J. Fluid Mech., 739, 421-443 (2014) [130] Hu, S.-M., Conversion of a triangular Bézier patch into three rectangular Bézier patches, Comput. Aided Geom. Design, 13, 3, 219-226 (1996) · Zbl 0900.68406 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.