Wang, Luo-Hao; Huang, Wei-Xi An efficient matrix factorization within the projection framework for ameliorating the surface tension time step constraint in interfacial flows. (English) Zbl 07797657 J. Comput. Phys. 498, Article ID 112678, 15 p. (2024). MSC: 76Mxx 76Dxx 65Mxx PDFBibTeX XMLCite \textit{L.-H. Wang} and \textit{W.-X. Huang}, J. Comput. Phys. 498, Article ID 112678, 15 p. (2024; Zbl 07797657) Full Text: DOI
Ménez, L.; Parnaudeau, P.; Beringhier, M.; Goncalves Da Silva, E. Assessment of volume penalization and immersed boundary methods for compressible flows with various thermal boundary conditions. (English) Zbl 07748051 J. Comput. Phys. 493, Article ID 112465, 23 p. (2023). MSC: 76Mxx 65Mxx 76Dxx PDFBibTeX XMLCite \textit{L. Ménez} et al., J. Comput. Phys. 493, Article ID 112465, 23 p. (2023; Zbl 07748051) Full Text: DOI
Funada, Masaya; Imamura, Taro High-order immersed boundary method for inviscid flows applied to flux reconstruction method on a hierarchical Cartesian grid. (English) Zbl 1521.76804 Comput. Fluids 265, Article ID 105986, 12 p. (2023). MSC: 76Q05 65M25 PDFBibTeX XMLCite \textit{M. Funada} and \textit{T. Imamura}, Comput. Fluids 265, Article ID 105986, 12 p. (2023; Zbl 1521.76804) Full Text: DOI
Llorente, Victor J.; Kou, Jiaqing; Valero, Eusebio; Ferrer, Esteban A modified equation analysis for immersed boundary methods based on volume penalization: applications to linear advection-diffusion equations and high-order discontinuous Galerkin schemes. (English) Zbl 1521.76348 Comput. Fluids 257, Article ID 105869, 16 p. (2023). MSC: 76M10 65M60 PDFBibTeX XMLCite \textit{V. J. Llorente} et al., Comput. Fluids 257, Article ID 105869, 16 p. (2023; Zbl 1521.76348) Full Text: DOI arXiv
Lai, Ming-Chih; Chang, Che-Chia; Lin, Wei-Syuan; Hu, Wei-Fan; Lin, Te-Sheng A shallow Ritz method for elliptic problems with singular sources. (English) Zbl 07592144 J. Comput. Phys. 469, Article ID 111547, 14 p. (2022). MSC: 65Nxx 35Jxx 76Mxx PDFBibTeX XMLCite \textit{M.-C. Lai} et al., J. Comput. Phys. 469, Article ID 111547, 14 p. (2022; Zbl 07592144) Full Text: DOI arXiv
Cao, Fujun; Yuan, Dongfang; Sheng, Zhiqiang; Yuan, Guangwei; He, Limin A finite difference method for elliptic problems with implicit jump condition. (English) Zbl 1513.65276 Int. J. Numer. Anal. Model. 19, No. 4, 439-457 (2022). MSC: 65N06 35R35 35J65 PDFBibTeX XMLCite \textit{F. Cao} et al., Int. J. Numer. Anal. Model. 19, No. 4, 439--457 (2022; Zbl 1513.65276) Full Text: Link
Laymuns, Genaro; Sánchez, Manuel A. Corrected finite element methods on unfitted meshes for Stokes moving interface problem. (English) Zbl 1524.65832 Comput. Math. Appl. 108, 159-174 (2022). MSC: 65N30 35J25 65N15 74F10 65N50 76D07 65M60 65M06 92C35 35Q92 74B10 76M10 74S05 35Q35 35Q74 PDFBibTeX XMLCite \textit{G. Laymuns} and \textit{M. A. Sánchez}, Comput. Math. Appl. 108, 159--174 (2022; Zbl 1524.65832) Full Text: DOI
Runnels, Brandon; Agrawal, Vinamra; Zhang, Weiqun; Almgren, Ann Massively parallel finite difference elasticity using block-structured adaptive mesh refinement with a geometric multigrid solver. (English) Zbl 07510250 J. Comput. Phys. 427, Article ID 110065, 17 p. (2021). MSC: 74-XX 65-XX PDFBibTeX XMLCite \textit{B. Runnels} et al., J. Comput. Phys. 427, Article ID 110065, 17 p. (2021; Zbl 07510250) Full Text: DOI arXiv
Boustani, Jonathan; Barad, Michael F.; Kiris, Cetin C.; Brehm, Christoph An immersed boundary fluid-structure interaction method for thin, highly compliant shell structures. (English) Zbl 07505964 J. Comput. Phys. 438, Article ID 110369, 35 p. (2021). MSC: 76Mxx 65Mxx 74Sxx PDFBibTeX XMLCite \textit{J. Boustani} et al., J. Comput. Phys. 438, Article ID 110369, 35 p. (2021; Zbl 07505964) Full Text: DOI
Constant, Benjamin; Péron, Stéphanie; Beaugendre, Héloïse; Benoit, Christophe An improved immersed boundary method for turbulent flow simulations on Cartesian grids. (English) Zbl 07503726 J. Comput. Phys. 435, Article ID 110240, 21 p. (2021). MSC: 76Mxx 65Mxx 76Dxx PDFBibTeX XMLCite \textit{B. Constant} et al., J. Comput. Phys. 435, Article ID 110240, 21 p. (2021; Zbl 07503726) Full Text: DOI HAL
Vahab, Mehdi; Sussman, Mark; Shoele, Kourosh Fluid-structure interaction of thin flexible bodies in multi-material multi-phase systems. (English) Zbl 07500743 J. Comput. Phys. 429, Article ID 110008, 29 p. (2021). MSC: 76Mxx 76Txx 65Mxx PDFBibTeX XMLCite \textit{M. Vahab} et al., J. Comput. Phys. 429, Article ID 110008, 29 p. (2021; Zbl 07500743) Full Text: DOI
Wang, Weiyi; Tan, Zhijun A simple 3D immersed interface method for Stokes flow with singular forces on staggered grids. (English) Zbl 1473.65123 Commun. Comput. Phys. 30, No. 1, 227-254 (2021). MSC: 65M06 76D07 PDFBibTeX XMLCite \textit{W. Wang} and \textit{Z. Tan}, Commun. Comput. Phys. 30, No. 1, 227--254 (2021; Zbl 1473.65123) Full Text: DOI
Amiri, Farhad A.; Le, Guigao; Chen, Qing; Zhang, Junfeng Accuracy improvement for immersed boundary method using Lagrangian velocity interpolation. (English) Zbl 07508415 J. Comput. Phys. 423, Article ID 109800, 23 p. (2020). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{F. A. Amiri} et al., J. Comput. Phys. 423, Article ID 109800, 23 p. (2020; Zbl 07508415) Full Text: DOI
Becerra-Sagredo, Julián T.; Jeltsch, Rolf; Málaga, Carlos The collocation basis of compact finite differences for moment-preserving interpolations: review, extension and applications. (English) Zbl 1482.65018 Commun. Comput. Phys. 28, No. 4, 1245-1273 (2020). MSC: 65D05 65D07 41A05 76M23 PDFBibTeX XMLCite \textit{J. T. Becerra-Sagredo} et al., Commun. Comput. Phys. 28, No. 4, 1245--1273 (2020; Zbl 1482.65018) Full Text: DOI
Wang, Luohao; Xie, Chunmei; Huang, Weixi A monolithic projection framework for constrained FSI problems with the immersed boundary method. (English) Zbl 1506.74113 Comput. Methods Appl. Mech. Eng. 371, Article ID 113332, 36 p. (2020). MSC: 74F10 74S15 65M38 76D05 PDFBibTeX XMLCite \textit{L. Wang} et al., Comput. Methods Appl. Mech. Eng. 371, Article ID 113332, 36 p. (2020; Zbl 1506.74113) Full Text: DOI
Kwon, Chunsong; Tartakovsky, Daniel M. Modified immersed boundary method for flows over randomly rough surfaces. (English) Zbl 1453.76035 J. Comput. Phys. 406, Article ID 109195, 16 p. (2020). MSC: 76D05 76M20 35R60 65M06 76D07 PDFBibTeX XMLCite \textit{C. Kwon} and \textit{D. M. Tartakovsky}, J. Comput. Phys. 406, Article ID 109195, 16 p. (2020; Zbl 1453.76035) Full Text: DOI
Qin, Zhipeng; Riaz, Amir; Balaras, Elias A locally second order symmetric method for discontinuous solution of Poisson’s equation on uniform Cartesian grids. (English) Zbl 1519.76345 Comput. Fluids 198, Article ID 104397, 14 p. (2020). MSC: 76T99 65N06 PDFBibTeX XMLCite \textit{Z. Qin} et al., Comput. Fluids 198, Article ID 104397, 14 p. (2020; Zbl 1519.76345) Full Text: DOI
Liu, Xiaoling; Song, Fangying; Xu, Chuanju An efficient spectral method for the inextensible immersed interface in incompressible flows. (English) Zbl 1473.65238 Commun. Comput. Phys. 25, No. 4, 1071-1096 (2019). MSC: 65M70 74F10 76N10 PDFBibTeX XMLCite \textit{X. Liu} et al., Commun. Comput. Phys. 25, No. 4, 1071--1096 (2019; Zbl 1473.65238) Full Text: DOI
Allen, T.; Zerroukat, M. A semi-Lagrangian semi-implicit immersed boundary method for atmospheric flow over complex terrain. (English) Zbl 1453.86021 J. Comput. Phys. 397, Article ID 108857, 13 p. (2019). MSC: 86A10 65M22 86-08 PDFBibTeX XMLCite \textit{T. Allen} and \textit{M. Zerroukat}, J. Comput. Phys. 397, Article ID 108857, 13 p. (2019; Zbl 1453.86021) Full Text: DOI
Ma, Yunfei; Cui, Jiahuan; Vadlamani, Nagabhushana Rao; Tucker, Paul Hierarchical geometry modelling using the immersed boundary method. (English) Zbl 1441.76066 Comput. Methods Appl. Mech. Eng. 355, 323-348 (2019). MSC: 76M10 65M60 PDFBibTeX XMLCite \textit{Y. Ma} et al., Comput. Methods Appl. Mech. Eng. 355, 323--348 (2019; Zbl 1441.76066) Full Text: DOI
Xu, Songzhe; Xu, Fei; Kommajosula, Aditya; Hsu, Ming-Chen; Ganapathysubramanian, Baskar Immersogeometric analysis of moving objects in incompressible flows. (English) Zbl 1519.76161 Comput. Fluids 189, 24-33 (2019). MSC: 76M10 65M60 74F10 76D05 PDFBibTeX XMLCite \textit{S. Xu} et al., Comput. Fluids 189, 24--33 (2019; Zbl 1519.76161) Full Text: DOI Link
Chen, Xiaohong; Li, Zhilin; Ruiz Álvarez, Juan A direct IIM approach for two-phase Stokes equations with discontinuous viscosity on staggered grids. (English) Zbl 1410.76281 Comput. Fluids 172, 549-563 (2018). MSC: 76M20 65N06 35Q35 35R05 65N22 76D07 PDFBibTeX XMLCite \textit{X. Chen} et al., Comput. Fluids 172, 549--563 (2018; Zbl 1410.76281) Full Text: DOI
Mittal, H. V. R.; Ray, Rajendra K. Solving immersed interface problems using a new interfacial points-based finite difference approach. (English) Zbl 1448.65195 SIAM J. Sci. Comput. 40, No. 3, A1860-A1883 (2018). MSC: 65N06 52B10 68U05 68U07 65D18 65D05 76M20 76D07 35Q35 35R05 PDFBibTeX XMLCite \textit{H. V. R. Mittal} and \textit{R. K. Ray}, SIAM J. Sci. Comput. 40, No. 3, A1860--A1883 (2018; Zbl 1448.65195) Full Text: DOI
Rowlatt, C. F.; Phillips, T. N. A spectral element formulation of the immersed boundary method for Newtonian fluids. (English) Zbl 1423.74949 Comput. Methods Appl. Mech. Eng. 298, 29-57 (2016). MSC: 74S25 74S05 74S15 65M70 65M60 74F10 PDFBibTeX XMLCite \textit{C. F. Rowlatt} and \textit{T. N. Phillips}, Comput. Methods Appl. Mech. Eng. 298, 29--57 (2016; Zbl 1423.74949) Full Text: DOI
Kumar, Manish; Roy, Somnath A sharp interface immersed boundary method for moving geometries with mass conservation and smooth pressure variation. (English) Zbl 1390.76585 Comput. Fluids 137, 15-35 (2016). MSC: 76M20 65M06 76D05 PDFBibTeX XMLCite \textit{M. Kumar} and \textit{S. Roy}, Comput. Fluids 137, 15--35 (2016; Zbl 1390.76585) Full Text: DOI
Feldman, Yuri; Gulberg, Yosef An extension of the immersed boundary method based on the distributed Lagrange multiplier approach. (English) Zbl 1351.76105 J. Comput. Phys. 322, 248-266 (2016). MSC: 76M12 65M08 76D05 PDFBibTeX XMLCite \textit{Y. Feldman} and \textit{Y. Gulberg}, J. Comput. Phys. 322, 248--266 (2016; Zbl 1351.76105) Full Text: DOI
Greene, Patrick T.; Eldredge, Jeff D.; Zhong, Xiaolin; Kim, John A high-order multi-zone cut-stencil method for numerical simulations of high-speed flows over complex geometries. (English) Zbl 1349.76467 J. Comput. Phys. 316, 652-681 (2016). MSC: 76M20 65M06 76K05 76N15 PDFBibTeX XMLCite \textit{P. T. Greene} et al., J. Comput. Phys. 316, 652--681 (2016; Zbl 1349.76467) Full Text: DOI
Casquero, Hugo; Bona-Casas, Carles; Gomez, Hector A NURBS-based immersed methodology for fluid-structure interaction. (English) Zbl 1423.74261 Comput. Methods Appl. Mech. Eng. 284, 943-970 (2015). MSC: 74F10 65D17 65M60 74D10 76D99 PDFBibTeX XMLCite \textit{H. Casquero} et al., Comput. Methods Appl. Mech. Eng. 284, 943--970 (2015; Zbl 1423.74261) Full Text: DOI
Frisani, Angelo; Hassan, Yassin A. On the immersed boundary method: finite element versus finite volume approach. (English) Zbl 1390.65105 Comput. Fluids 121, 51-67 (2015). MSC: 65M60 65M08 76M10 76M12 PDFBibTeX XMLCite \textit{A. Frisani} and \textit{Y. A. Hassan}, Comput. Fluids 121, 51--67 (2015; Zbl 1390.65105) Full Text: DOI
Nicolaou, L.; Jung, S. Y.; Zaki, T. A. A robust direct-forcing immersed boundary method with enhanced stability for moving body problems in curvilinear coordinates. (English) Zbl 1390.76603 Comput. Fluids 119, 101-114 (2015). MSC: 76M20 65M06 76D05 PDFBibTeX XMLCite \textit{L. Nicolaou} et al., Comput. Fluids 119, 101--114 (2015; Zbl 1390.76603) Full Text: DOI Link
Benvenuti, Elena; Ventura, Giulio; Ponara, Nicola; Tralli, Antonio Accuracy of three-dimensional analysis of regularized singularities. (English) Zbl 1352.65080 Int. J. Numer. Methods Eng. 101, No. 1, 29-53 (2015). MSC: 65D30 PDFBibTeX XMLCite \textit{E. Benvenuti} et al., Int. J. Numer. Methods Eng. 101, No. 1, 29--53 (2015; Zbl 1352.65080) Full Text: DOI
Collin, Annabelle; Chapelle, Dominique; Moireau, Philippe A Luenberger observer for reaction-diffusion models with front position data. (English) Zbl 1349.76445 J. Comput. Phys. 300, 288-307 (2015). MSC: 76M20 35K58 35K20 35K57 65M06 94A08 PDFBibTeX XMLCite \textit{A. Collin} et al., J. Comput. Phys. 300, 288--307 (2015; Zbl 1349.76445) Full Text: DOI
Zhang, P.; Benard, A. Numerical simulation of particle motion using a combined MacCormack and immersed boundary method. (English) Zbl 1349.76560 J. Comput. Phys. 294, 524-546 (2015). MSC: 76M20 65M06 65M75 74F10 76Nxx 76T20 PDFBibTeX XMLCite \textit{P. Zhang} and \textit{A. Benard}, J. Comput. Phys. 294, 524--546 (2015; Zbl 1349.76560) Full Text: DOI
Li, Zhilin; Wang, Li; Aspinwall, Eric; Cooper, Racheal; Kuberry, Paul; Sanders, Ashley; Zeng, Ke Some new analysis results for a class of interface problems. (English) Zbl 1338.65197 Math. Methods Appl. Sci. 38, No. 18, 4530-4539 (2015). Reviewer: Maria Gousidou-Koutita (Thessaloniki) MSC: 65L10 34A36 65L20 34B16 PDFBibTeX XMLCite \textit{Z. Li} et al., Math. Methods Appl. Sci. 38, No. 18, 4530--4539 (2015; Zbl 1338.65197) Full Text: DOI Link
Li, Zhilin On convergence of the immersed boundary method for elliptic interface problems. (English) Zbl 1311.65133 Math. Comput. 84, No. 293, 1169-1188 (2015). MSC: 65N06 65N12 65N15 PDFBibTeX XMLCite \textit{Z. Li}, Math. Comput. 84, No. 293, 1169--1188 (2015; Zbl 1311.65133) Full Text: DOI
Cockburn, Bernardo; Qiu, Weifeng; Solano, Manuel A priori error analysis for HDG methods using extensions from subdomains to achieve boundary conformity. (English) Zbl 1290.65110 Math. Comput. 83, No. 286, 665-699 (2014). Reviewer: Petr Sváček (Praha) MSC: 65N30 35J25 65N12 PDFBibTeX XMLCite \textit{B. Cockburn} et al., Math. Comput. 83, No. 286, 665--699 (2014; Zbl 1290.65110) Full Text: DOI
Liu, Jiankang; Zheng, Zhoushun IIM-based ADI finite difference scheme for nonlinear convection-diffusion equations with interfaces. (English) Zbl 1352.65248 Appl. Math. Modelling 37, No. 3, 1196-1207 (2013). MSC: 65M06 65M12 65M85 PDFBibTeX XMLCite \textit{J. Liu} and \textit{Z. Zheng}, Appl. Math. Modelling 37, No. 3, 1196--1207 (2013; Zbl 1352.65248) Full Text: DOI
Gibou, Frédéric; Min, Chohong; Fedkiw, Ron High resolution sharp computational methods for elliptic and parabolic problems in complex geometries. (English) Zbl 1263.65093 J. Sci. Comput. 54, No. 2-3, 369-413 (2013). MSC: 65M50 35J05 35K05 80A22 65N50 35R35 65M06 PDFBibTeX XMLCite \textit{F. Gibou} et al., J. Sci. Comput. 54, No. 2--3, 369--413 (2013; Zbl 1263.65093) Full Text: DOI
Fang, Jiannong; Diebold, Marc; Higgins, Chad; Parlange, Marc B. Towards oscillation-free implementation of the immersed boundary method with spectral-like methods. (English) Zbl 1408.76412 J. Comput. Phys. 230, No. 22, 8179-8191 (2011). MSC: 76M28 65M70 65M85 76D05 PDFBibTeX XMLCite \textit{J. Fang} et al., J. Comput. Phys. 230, No. 22, 8179--8191 (2011; Zbl 1408.76412) Full Text: DOI Link
Chen, Kuan-Yu; Feng, Ko-An; Kim, Yongsam; Lai, Ming-Chih A note on pressure accuracy in immersed boundary method for Stokes flow. (English) Zbl 1416.76098 J. Comput. Phys. 230, No. 12, 4377-4383 (2011). MSC: 76M10 76D07 65N06 65N85 PDFBibTeX XMLCite \textit{K.-Y. Chen} et al., J. Comput. Phys. 230, No. 12, 4377--4383 (2011; Zbl 1416.76098) Full Text: DOI
Araújo, A.; Patrício, F.; Santos, José L. Optimal solution of a reaction–diffusion system with a control discrete source term. (English) Zbl 1210.65150 Int. J. Numer. Methods Biomed. Eng. 27, No. 2, 186-197 (2011). MSC: 65M06 35K57 65K10 65M12 49J20 PDFBibTeX XMLCite \textit{A. Araújo} et al., Int. J. Numer. Methods Biomed. Eng. 27, No. 2, 186--197 (2011; Zbl 1210.65150) Full Text: DOI
Gong, Zhao-xin; Lu, Chuan-jing; Huang, Hua-xiong Accuracy analysis of immersed boundary method using method of manufactured solutions. (English) Zbl 1410.76326 Appl. Math. Mech., Engl. Ed. 31, No. 10, 1197-1208 (2010). MSC: 76M25 65N12 76M15 PDFBibTeX XMLCite \textit{Z.-x. Gong} et al., Appl. Math. Mech., Engl. Ed. 31, No. 10, 1197--1208 (2010; Zbl 1410.76326) Full Text: DOI
Araújo, A.; Patrício, F.; Santos, José L. Optimal solution of a diffusion equation with a discrete source term. (English) Zbl 1204.65100 Int. J. Numer. Methods Biomed. Eng. 26, No. 9, 1176-1187 (2010). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 65M12 35K05 PDFBibTeX XMLCite \textit{A. Araújo} et al., Int. J. Numer. Methods Biomed. Eng. 26, No. 9, 1176--1187 (2010; Zbl 1204.65100) Full Text: DOI Link
Zahedi, Sara; Tornberg, Anna-Karin Delta function approximations in level set methods by distance function extension. (English) Zbl 1186.65018 J. Comput. Phys. 229, No. 6, 2199-2219 (2010). MSC: 65D15 PDFBibTeX XMLCite \textit{S. Zahedi} and \textit{A.-K. Tornberg}, J. Comput. Phys. 229, No. 6, 2199--2219 (2010; Zbl 1186.65018) Full Text: DOI
Yang, Xiaolei; Zhang, Xing; Li, Zhilin; He, Guo-Wei A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations. (English) Zbl 1391.76590 J. Comput. Phys. 228, No. 20, 7821-7836 (2009). MSC: 76M25 65N99 PDFBibTeX XMLCite \textit{X. Yang} et al., J. Comput. Phys. 228, No. 20, 7821--7836 (2009; Zbl 1391.76590) Full Text: DOI
Griffith, Boyce E. An accurate and efficient method for the incompressible Navier-Stokes equations using the projection method as a preconditioner. (English) Zbl 1391.76474 J. Comput. Phys. 228, No. 20, 7565-7595 (2009). MSC: 76M20 65M06 76D05 PDFBibTeX XMLCite \textit{B. E. Griffith}, J. Comput. Phys. 228, No. 20, 7565--7595 (2009; Zbl 1391.76474) Full Text: DOI
Hsu, Chia-Yu; Dillon, Robert A 3D motile rod-shaped monotrichous bacterial model. (English) Zbl 1168.92015 Bull. Math. Biol. 71, No. 5, 1228-1263 (2009). MSC: 92C37 76D05 74F10 65C20 PDFBibTeX XMLCite \textit{C.-Y. Hsu} and \textit{R. Dillon}, Bull. Math. Biol. 71, No. 5, 1228--1263 (2009; Zbl 1168.92015) Full Text: DOI
Towers, John D. Discretizing delta functions via finite differences and gradient normalization. (English) Zbl 1167.65007 J. Comput. Phys. 228, No. 10, 3816-3836 (2009). Reviewer: Martin D. Buhmann (Gießen) MSC: 65D15 46F10 PDFBibTeX XMLCite \textit{J. D. Towers}, J. Comput. Phys. 228, No. 10, 3816--3836 (2009; Zbl 1167.65007) Full Text: DOI
Liu, Hailiang; Wang, Zhongming Superposition of multi-valued solutions in high frequency wave dynamics. (English) Zbl 1203.65141 J. Sci. Comput. 35, No. 2-3, 192-218 (2008). MSC: 65M06 35F20 76M25 PDFBibTeX XMLCite \textit{H. Liu} and \textit{Z. Wang}, J. Sci. Comput. 35, No. 2--3, 192--218 (2008; Zbl 1203.65141) Full Text: DOI
Ramière, Isabelle Convergence analysis of the \(\mathcal {Q}_{1}\)-finite element method for elliptic problems with non-boundary-fitted meshes. (English) Zbl 1195.65154 Int. J. Numer. Methods Eng. 75, No. 9, 1007-1052 (2008). MSC: 65N12 65N15 65N30 PDFBibTeX XMLCite \textit{I. Ramière}, Int. J. Numer. Methods Eng. 75, No. 9, 1007--1052 (2008; Zbl 1195.65154) Full Text: DOI
Newren, Elijah P.; Fogelson, Aaron L.; Guy, Robert D.; Kirby, Robert M. A comparison of implicit solvers for the immersed boundary equations. (English) Zbl 1158.76409 Comput. Methods Appl. Mech. Eng. 197, No. 25-28, 2290-2304 (2008). MSC: 76M25 74F10 76D05 76M20 65M06 65N22 PDFBibTeX XMLCite \textit{E. P. Newren} et al., Comput. Methods Appl. Mech. Eng. 197, No. 25--28, 2290--2304 (2008; Zbl 1158.76409) Full Text: DOI
Layton, Anita T. An efficient numerical method for the two-fluid Stokes equations with a moving immersed boundary. (English) Zbl 1158.76381 Comput. Methods Appl. Mech. Eng. 197, No. 25-28, 2147-2155 (2008). MSC: 76M20 76M25 76D07 35R05 65M12 65N06 PDFBibTeX XMLCite \textit{A. T. Layton}, Comput. Methods Appl. Mech. Eng. 197, No. 25--28, 2147--2155 (2008; Zbl 1158.76381) Full Text: DOI
Liehr, Florian; Preusser, Tobias; Rumpf, Martin; Sauter, Stefan; Schwen, Lars Ole Composite finite elements for 3D image based computing. (English) Zbl 1512.65036 Comput. Vis. Sci. 12, No. 4, 171-188 (2009). MSC: 65D18 68U10 92C55 94A08 PDFBibTeX XMLCite \textit{F. Liehr} et al., Comput. Vis. Sci. 12, No. 4, 171--188 (2008; Zbl 1512.65036) Full Text: DOI
Tan, Zhijun; Le, D. V.; Li, Zhilin; Lim, K. M.; Khoo, B. C. An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane. (English) Zbl 1317.76064 J. Comput. Phys. 227, No. 23, 9955-9983 (2008). MSC: 76M25 74F10 74H15 76Z05 65N30 PDFBibTeX XMLCite \textit{Z. Tan} et al., J. Comput. Phys. 227, No. 23, 9955--9983 (2008; Zbl 1317.76064) Full Text: DOI
Wang, Zeli; Fan, Jianren; Luo, Kun Parallel computing strategy for the simulation of particulate flows with immersed boundary method. (English) Zbl 1143.76049 Sci. China, Ser. E 51, No. 8, 1169-1176 (2008). MSC: 76M25 76T20 65Y05 PDFBibTeX XMLCite \textit{Z. Wang} et al., Sci. China, Ser. E 51, No. 8, 1169--1176 (2008; Zbl 1143.76049) Full Text: DOI
Liang, An; Jing, Xiaodong; Sun, Xiaofeng Constructing spectral schemes of the immersed interface method via a global description of discontinuous functions. (English) Zbl 1147.65098 J. Comput. Phys. 227, No. 18, 8341-8366 (2008). MSC: 65N35 35J25 65N06 65L60 65L12 34B05 PDFBibTeX XMLCite \textit{A. Liang} et al., J. Comput. Phys. 227, No. 18, 8341--8366 (2008; Zbl 1147.65098) Full Text: DOI
Mori, Yoichiro Convergence proof of the velocity field for a Stokes flow immersed boundary method. (English) Zbl 1171.76042 Commun. Pure Appl. Math. 61, No. 9, 1213-1263 (2008). Reviewer: Tomislav Zlatanovski (Skopje) MSC: 76M22 76M20 76D07 74F10 65M12 65N12 PDFBibTeX XMLCite \textit{Y. Mori}, Commun. Pure Appl. Math. 61, No. 9, 1213--1263 (2008; Zbl 1171.76042) Full Text: DOI
Boffi, Daniele; Gastaldi, Lucia; Heltai, Luca Numerical stability of the finite element immersed boundary method. (English) Zbl 1186.76661 Math. Models Methods Appl. Sci. 17, No. 10, 1479-1505 (2007). Reviewer: Titus Petrila (Cluj-Napoca) MSC: 76M10 76D05 74F10 65N12 65N30 PDFBibTeX XMLCite \textit{D. Boffi} et al., Math. Models Methods Appl. Sci. 17, No. 10, 1479--1505 (2007; Zbl 1186.76661) Full Text: DOI
Wen, Xin High order numerical methods to a type of delta function integrals. (English) Zbl 1125.65024 J. Comput. Phys. 226, No. 2, 1952-1967 (2007). MSC: 65D32 41A55 41A63 PDFBibTeX XMLCite \textit{X. Wen}, J. Comput. Phys. 226, No. 2, 1952--1967 (2007; Zbl 1125.65024) Full Text: DOI
Hou, Thomas Y.; Li, Ruo Computing nearly singular solutions using pseudo-spectral methods. (English) Zbl 1310.76127 J. Comput. Phys. 226, No. 1, 379-397 (2007). MSC: 76M22 65M70 PDFBibTeX XMLCite \textit{T. Y. Hou} and \textit{R. Li}, J. Comput. Phys. 226, No. 1, 379--397 (2007; Zbl 1310.76127) Full Text: DOI arXiv Link
Zhong, Xiaolin A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity. (English) Zbl 1343.65130 J. Comput. Phys. 225, No. 1, 1066-1099 (2007). MSC: 65N06 76M20 76T99 PDFBibTeX XMLCite \textit{X. Zhong}, J. Comput. Phys. 225, No. 1, 1066--1099 (2007; Zbl 1343.65130) Full Text: DOI
Newren, Elijah P.; Fogelson, Aaron L.; Guy, Robert D.; Kirby, Robert M. Unconditionally stable discretizations of the immersed boundary equations. (English) Zbl 1158.74350 J. Comput. Phys. 222, No. 2, 702-719 (2007). MSC: 74F10 65M12 76D05 76M20 PDFBibTeX XMLCite \textit{E. P. Newren} et al., J. Comput. Phys. 222, No. 2, 702--719 (2007; Zbl 1158.74350) Full Text: DOI
Towers, John D. Two methods for discretizing a delta function supported on a level set. (English) Zbl 1115.65028 J. Comput. Phys. 220, No. 2, 915-931 (2007). Reviewer: Manfred Tasche (Rostock) MSC: 65D32 58C35 46F10 41A55 PDFBibTeX XMLCite \textit{J. D. Towers}, J. Comput. Phys. 220, No. 2, 915--931 (2007; Zbl 1115.65028) Full Text: DOI
Xu, Sheng; Wang, Z. Jane An immersed interface method for simulating the interaction of a fluid with moving boundaries. (English) Zbl 1220.76058 J. Comput. Phys. 216, No. 2, 454-493 (2006). MSC: 76M25 65M60 74F10 76M20 PDFBibTeX XMLCite \textit{S. Xu} and \textit{Z. J. Wang}, J. Comput. Phys. 216, No. 2, 454--493 (2006; Zbl 1220.76058) Full Text: DOI
Smereka, Peter The numerical approximation of a delta function with application to level set methods. (English) Zbl 1086.65503 J. Comput. Phys. 211, No. 1, 77-90 (2006). MSC: 65D15 65L10 34B05 35J05 65N06 PDFBibTeX XMLCite \textit{P. Smereka}, J. Comput. Phys. 211, No. 1, 77--90 (2006; Zbl 1086.65503) Full Text: DOI
Engquist, Björn; Tornberg, Anna-Karin; Tsai, Richard Discretization of Dirac delta functions in level set methods. (English) Zbl 1074.65025 J. Comput. Phys. 207, No. 1, 28-51 (2005). Reviewer: Nácere Hayek (La Laguna) MSC: 65D20 46F10 PDFBibTeX XMLCite \textit{B. Engquist} et al., J. Comput. Phys. 207, No. 1, 28--51 (2005; Zbl 1074.65025) Full Text: DOI
Linnick, Mark N.; Fasel, Hermann F. A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. (English) Zbl 1143.76538 J. Comput. Phys. 204, No. 1, 157-192 (2005). MSC: 76M25 65M06 PDFBibTeX XMLCite \textit{M. N. Linnick} and \textit{H. F. Fasel}, J. Comput. Phys. 204, No. 1, 157--192 (2005; Zbl 1143.76538) Full Text: DOI
Kandilarov, Juri D.; Vulkov, Lubin G. The immersed interface method for a nonlinear chemical diffusion equation with local sites of reactions. (English) Zbl 1074.65102 Numer. Algorithms 36, No. 4, 285-307 (2004). Reviewer: Marek Brandner (Plzeň) MSC: 65M06 35K57 80A32 80M20 PDFBibTeX XMLCite \textit{J. D. Kandilarov} and \textit{L. G. Vulkov}, Numer. Algorithms 36, No. 4, 285--307 (2004; Zbl 1074.65102) Full Text: DOI
Tornberg, Anna-Karin; Engquist, Björn Numerical approximations of singular source terms in differential equations. (English) Zbl 1115.76392 J. Comput. Phys. 200, No. 2, 462-488 (2004). MSC: 76M25 74S30 65N99 PDFBibTeX XMLCite \textit{A.-K. Tornberg} and \textit{B. Engquist}, J. Comput. Phys. 200, No. 2, 462--488 (2004; Zbl 1115.76392) Full Text: DOI
Berthelsen, Petter Andreas A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions. (English) Zbl 1052.65100 J. Comput. Phys. 197, No. 1, 364-386 (2004). MSC: 65N06 35J25 35R05 PDFBibTeX XMLCite \textit{P. A. Berthelsen}, J. Comput. Phys. 197, No. 1, 364--386 (2004; Zbl 1052.65100) Full Text: DOI
Givelberg, Edward; Bunn, Julian A comprehensive three-dimensional model of the cochlea. (English) Zbl 1024.92005 J. Comput. Phys. 191, No. 2, 377-391 (2003). MSC: 92C30 65Y05 92-08 65C20 92C05 PDFBibTeX XMLCite \textit{E. Givelberg} and \textit{J. Bunn}, J. Comput. Phys. 191, No. 2, 377--391 (2003; Zbl 1024.92005) Full Text: DOI arXiv
Calhoun, Donna A Cartesian grid method for solving the two-dimensional streamfunction-vorticity equations in irregular regions. (English) Zbl 1130.76371 J. Comput. Phys. 176, No. 2, 231-275 (2002). MSC: 76M12 76M20 76D05 65N06 PDFBibTeX XMLCite \textit{D. Calhoun}, J. Comput. Phys. 176, No. 2, 231--275 (2002; Zbl 1130.76371) Full Text: DOI Link
Gibou, Frederic; Fedkiw, Ronald P.; Cheng, Li-Tien; Kang, Myungjoo A second-order-accurate symmetric discretization of the Poisson equation on irregular domains. (English) Zbl 0996.65108 J. Comput. Phys. 176, No. 1, 205-227 (2002). MSC: 65N06 65M06 35K05 35R35 35J05 80M20 80A22 PDFBibTeX XMLCite \textit{F. Gibou} et al., J. Comput. Phys. 176, No. 1, 205--227 (2002; Zbl 0996.65108) Full Text: DOI Link
Roma, Alexandre M.; Peskin, Charles S.; Berger, Marsha J. An adaptive version of the immersed boundary method. (English) Zbl 0953.76069 J. Comput. Phys. 153, No. 2, 509-534 (1999). MSC: 76M20 76D05 65M55 74F10 PDFBibTeX XMLCite \textit{A. M. Roma} et al., J. Comput. Phys. 153, No. 2, 509--534 (1999; Zbl 0953.76069) Full Text: DOI Link
Waldén, Johan On the approximation of singular source terms in differential equations. (English) Zbl 0938.65112 Numer. Methods Partial Differ. Equations 15, No. 4, 503-520 (1999). Reviewer: L.G.Vulkov (Russe) MSC: 65M12 65N12 35R05 35J05 35K05 PDFBibTeX XMLCite \textit{J. Waldén}, Numer. Methods Partial Differ. Equations 15, No. 4, 503--520 (1999; Zbl 0938.65112) Full Text: DOI