Belyaev, V. A.; Bryndin, L. S.; Golushko, S. K.; Semisalov, B. V.; Shapeev, V. P. h-, p-, and hp-versions of the least-squares collocation method for solving boundary value problems for biharmonic equation in irregular domains and their applications. (English. Russian original) Zbl 07538076 Comput. Math. Math. Phys. 62, No. 4, 517-537 (2022); translation from Zh. Vychisl. Mat. Mat. Fiz. 62, No. 4, 531-552 (2022). MSC: 65N35 65N12 65N55 31A30 74K20 35Q74 PDF BibTeX XML Cite \textit{V. A. Belyaev} et al., Comput. Math. Math. Phys. 62, No. 4, 517--537 (2022; Zbl 07538076); translation from Zh. Vychisl. Mat. Mat. Fiz. 62, No. 4, 531--552 (2022) Full Text: DOI OpenURL
Singh, Swarn; Singh, Suruchi; Li, Zhilin A new patch up technique for elliptic partial differential equation with irregularities. (English) Zbl 07474394 J. Comput. Appl. Math. 407, Article ID 113975, 20 p. (2022). MSC: 65N35 65D07 65N12 35J25 PDF BibTeX XML Cite \textit{S. Singh} et al., J. Comput. Appl. Math. 407, Article ID 113975, 20 p. (2022; Zbl 07474394) Full Text: DOI OpenURL
Xie, Yaning; Li, Shuwang; Ying, Wenjun A fourth-order Cartesian grid method for multiple acoustic scattering on closely packed obstacles. (English) Zbl 1484.35165 J. Comput. Appl. Math. 406, Article ID 113885, 17 p. (2022). MSC: 35J05 65N38 65N06 65N30 PDF BibTeX XML Cite \textit{Y. Xie} et al., J. Comput. Appl. Math. 406, Article ID 113885, 17 p. (2022; Zbl 1484.35165) Full Text: DOI OpenURL
Chai, Shuqing; Zhang, Zhen; Zhang, Zhiwen A second order accuracy preserving method for moving contact lines with Stokes flow. (English) Zbl 07515862 J. Comput. Phys. 445, Article ID 110607, 18 p. (2021). MSC: 76Mxx 76Dxx 65Mxx PDF BibTeX XML Cite \textit{S. Chai} et al., J. Comput. Phys. 445, Article ID 110607, 18 p. (2021; Zbl 07515862) Full Text: DOI OpenURL
Jeon, Youngmok; Shin, Dongwook Immersed hybrid difference methods for elliptic boundary value problems by artificial interface conditions. (English) Zbl 07438936 Electron Res. Arch. 29, No. 5, 3361-3382 (2021). MSC: 65Nxx 65N06 65N50 PDF BibTeX XML Cite \textit{Y. Jeon} and \textit{D. Shin}, Electron Res. Arch. 29, No. 5, 3361--3382 (2021; Zbl 07438936) Full Text: DOI OpenURL
Gómez, Vicente; Pérez-Arancibia, Carlos On the regularization of Cauchy-type integral operators via the density interpolation method and applications. (English) Zbl 07325138 Comput. Math. Appl. 87, 107-119 (2021). MSC: 65-XX 41-XX PDF BibTeX XML Cite \textit{V. Gómez} and \textit{C. Pérez-Arancibia}, Comput. Math. Appl. 87, 107--119 (2021; Zbl 07325138) Full Text: DOI arXiv OpenURL
Xie, Yaning; Ying, Wenjun A fourth-order kernel-free boundary integral method for implicitly defined surfaces in three space dimensions. (English) Zbl 1440.65158 J. Comput. Phys. 415, Article ID 109526, 28 p. (2020). MSC: 65N06 65N38 PDF BibTeX XML Cite \textit{Y. Xie} and \textit{W. Ying}, J. Comput. Phys. 415, Article ID 109526, 28 p. (2020; Zbl 1440.65158) Full Text: DOI OpenURL
Egan, Raphael; Gibou, Frédéric xGFM: recovering convergence of fluxes in the ghost fluid method. (English) Zbl 1435.76050 J. Comput. Phys. 409, Article ID 109351, 22 p. (2020). MSC: 76M20 35J05 35R12 PDF BibTeX XML Cite \textit{R. Egan} and \textit{F. Gibou}, J. Comput. Phys. 409, Article ID 109351, 22 p. (2020; Zbl 1435.76050) Full Text: DOI OpenURL
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 07157292 Comput. Fluids 198, Article ID 104397, 14 p. (2020). MSC: 76-XX PDF BibTeX XML Cite \textit{Z. Qin} et al., Comput. Fluids 198, Article ID 104397, 14 p. (2020; Zbl 07157292) Full Text: DOI OpenURL
Marques, Alexandre Noll; Nave, Jean-Christophe; Rosales, Rodolfo Ruben Imposing jump conditions on nonconforming interfaces for the correction function method: a least squares approach. (English) Zbl 1453.65384 J. Comput. Phys. 397, Article ID 108869, 17 p. (2019). MSC: 65N06 35J05 35R05 PDF BibTeX XML Cite \textit{A. N. Marques} et al., J. Comput. Phys. 397, Article ID 108869, 17 p. (2019; Zbl 1453.65384) Full Text: DOI arXiv OpenURL
Xie, Yaning; Ying, Wenjun; Wang, Wei-Cheng A high-order kernel-free boundary integral method for the biharmonic equation on irregular domains. (English) Zbl 1428.65103 J. Sci. Comput. 80, No. 3, 1681-1699 (2019). MSC: 65N38 31A30 65N06 65T50 PDF BibTeX XML Cite \textit{Y. Xie} et al., J. Sci. Comput. 80, No. 3, 1681--1699 (2019; Zbl 1428.65103) Full Text: DOI OpenURL
Moldovan, Ionuţ Dragoş; Coutinho, Ana; Cismaşiu, Ildi Hybrid-Trefftz finite elements for non-homogeneous parabolic problems using a novel dual reciprocity variant. (English) Zbl 1464.74191 Eng. Anal. Bound. Elem. 106, 228-242 (2019). MSC: 74S05 65M70 PDF BibTeX XML Cite \textit{I. D. Moldovan} et al., Eng. Anal. Bound. Elem. 106, 228--242 (2019; Zbl 1464.74191) Full Text: DOI OpenURL
Elgindy, Kareem T. A high-order embedded domain method combining a predictor-corrector-Fourier-continuation-Gram method with an integral Fourier pseudospectral collocation method for solving linear partial differential equations in complex domains. (English) Zbl 1422.65426 J. Comput. Appl. Math. 361, 372-395 (2019). MSC: 65N35 65N85 PDF BibTeX XML Cite \textit{K. T. Elgindy}, J. Comput. Appl. Math. 361, 372--395 (2019; Zbl 1422.65426) Full Text: DOI OpenURL
Xie, Yaning; Ying, Wenjun A fourth-order kernel-free boundary integral method for the modified Helmholtz equation. (English) Zbl 1418.35094 J. Sci. Comput. 78, No. 3, 1632-1658 (2019); correction ibid. 78, No. 3, 1659 (2019). MSC: 35J05 35J25 65N38 65N06 65N30 PDF BibTeX XML Cite \textit{Y. Xie} and \textit{W. Ying}, J. Sci. Comput. 78, No. 3, 1632--1658 (2019; Zbl 1418.35094) Full Text: DOI OpenURL
Beale, J. Thomas; Ying, Wenjun Solution of the Dirichlet problem by a finite difference analog of the boundary integral equation. (English) Zbl 1411.31010 Numer. Math. 141, No. 3, 605-626 (2019). MSC: 31C20 35J05 65N06 65N12 PDF BibTeX XML Cite \textit{J. T. Beale} and \textit{W. Ying}, Numer. Math. 141, No. 3, 605--626 (2019; Zbl 1411.31010) Full Text: DOI arXiv OpenURL
Xu, Minqiang; Zhao, Zhihong; Niu, Jing; Guo, Li; Lin, Yingzhen A simplified reproducing kernel method for 1-D elliptic type interface problems. (English) Zbl 1409.65048 J. Comput. Appl. Math. 351, 29-40 (2019). MSC: 65L10 65L20 65L60 PDF BibTeX XML Cite \textit{M. Xu} et al., J. Comput. Appl. Math. 351, 29--40 (2019; Zbl 1409.65048) Full Text: DOI OpenURL
Ying, Wenjun A Cartesian grid-based boundary integral method for an elliptic interface problem on closely packed cells. (English) Zbl 1475.65210 Commun. Comput. Phys. 24, No. 4, 1196-1220 (2018). MSC: 65N38 35J05 65N06 PDF BibTeX XML Cite \textit{W. Ying}, Commun. Comput. Phys. 24, No. 4, 1196--1220 (2018; Zbl 1475.65210) Full Text: DOI Link OpenURL
Siraj-ul-Islam; Haider, Nadeem; Aziz, Imran Meshless and multi-resolution collocation techniques for parabolic interface models. (English) Zbl 1427.65303 Appl. Math. Comput. 335, 313-332 (2018). MSC: 65M70 35J25 PDF BibTeX XML Cite \textit{Siraj-ul-Islam} et al., Appl. Math. Comput. 335, 313--332 (2018; Zbl 1427.65303) Full Text: DOI OpenURL
Beams, Natalie N.; Klöckner, Andreas; Olson, Luke N. High-order finite element-integral equation coupling on embedded meshes. (English) Zbl 1416.65432 J. Comput. Phys. 375, 1295-1313 (2018). MSC: 65N30 65N85 65N15 65R20 35J05 PDF BibTeX XML Cite \textit{N. N. Beams} et al., J. Comput. Phys. 375, 1295--1313 (2018; Zbl 1416.65432) Full Text: DOI arXiv OpenURL
Jiang, Ying; Wang, Bo; Xu, Yuesheng A fully discrete fast Fourier-Galerkin method solving a boundary integral equation for the biharmonic equation. (English) Zbl 1401.31011 J. Sci. Comput. 76, No. 3, 1594-1632 (2018). MSC: 31A30 31A25 65N30 PDF BibTeX XML Cite \textit{Y. Jiang} et al., J. Sci. Comput. 76, No. 3, 1594--1632 (2018; Zbl 1401.31011) Full Text: DOI OpenURL
Ludvigsson, Gustav; Steffen, Kyle R.; Sticko, Simon; Wang, Siyang; Xia, Qing; Epshteyn, Yekaterina; Kreiss, Gunilla High-order numerical methods for 2D parabolic problems in single and composite domains. (English) Zbl 1395.65024 J. Sci. Comput. 76, No. 2, 812-847 (2018). MSC: 65M06 65M12 65M22 65M55 65M60 65M70 35K20 PDF BibTeX XML Cite \textit{G. Ludvigsson} et al., J. Sci. Comput. 76, No. 2, 812--847 (2018; Zbl 1395.65024) Full Text: DOI arXiv OpenURL
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 PDF BibTeX XML Cite \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 OpenURL
Towers, John D. A source term method for Poisson problems on irregular domains. (English) Zbl 1422.65327 J. Comput. Phys. 361, 424-441 (2018). MSC: 65N06 35J05 PDF BibTeX XML Cite \textit{J. D. Towers}, J. Comput. Phys. 361, 424--441 (2018; Zbl 1422.65327) Full Text: DOI OpenURL
Coco, Armando; Russo, Giovanni Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface. (English) Zbl 1422.65306 J. Comput. Phys. 361, 299-330 (2018). MSC: 65N06 35R05 65N55 65N15 PDF BibTeX XML Cite \textit{A. Coco} and \textit{G. Russo}, J. Comput. Phys. 361, 299--330 (2018; Zbl 1422.65306) Full Text: DOI Link OpenURL
Aziz, Imran; Siraj-ul-Islam; Haider, Nadeem Meshless and multi-resolution collocation techniques for steady state interface models. (English) Zbl 1404.65067 Int. J. Comput. Methods 15, No. 1, Article ID 1750073, 37 p. (2018). MSC: 65L10 65L60 PDF BibTeX XML Cite \textit{I. Aziz} et al., Int. J. Comput. Methods 15, No. 1, Article ID 1750073, 37 p. (2018; Zbl 1404.65067) Full Text: DOI OpenURL
Martin, Bradley; Fornberg, Bengt Using radial basis function-generated finite differences (RBF-FD) to solve heat transfer equilibrium problems in domains with interfaces. (English) Zbl 1403.80035 Eng. Anal. Bound. Elem. 79, 38-48 (2017). MSC: 80M20 65M06 80A20 PDF BibTeX XML Cite \textit{B. Martin} and \textit{B. Fornberg}, Eng. Anal. Bound. Elem. 79, 38--48 (2017; Zbl 1403.80035) Full Text: DOI OpenURL
Askham, T.; Cerfon, A. J. An adaptive fast multipole accelerated Poisson solver for complex geometries. (English) Zbl 1380.65413 J. Comput. Phys. 344, 1-22 (2017). MSC: 65N85 35J05 65D30 PDF BibTeX XML Cite \textit{T. Askham} and \textit{A. J. Cerfon}, J. Comput. Phys. 344, 1--22 (2017; Zbl 1380.65413) Full Text: DOI arXiv OpenURL
Moroney, Timothy J.; Lusmore, Dylan R.; McCue, Scott W.; McElwain, D. L. Sean Extending fields in a level set method by solving a biharmonic equation. (English) Zbl 1380.65029 J. Comput. Phys. 343, 170-185 (2017). MSC: 65D05 65-04 35A35 35R37 PDF BibTeX XML Cite \textit{T. J. Moroney} et al., J. Comput. Phys. 343, 170--185 (2017; Zbl 1380.65029) Full Text: DOI arXiv OpenURL
Li, Zhilin; Qin, Fangfang An augmented method for 4th order PDEs with discontinuous coefficients. (English) Zbl 1381.65088 J. Sci. Comput. 73, No. 2-3, 968-979 (2017). MSC: 65N06 35J30 35J05 35R05 PDF BibTeX XML Cite \textit{Z. Li} and \textit{F. Qin}, J. Sci. Comput. 73, No. 2--3, 968--979 (2017; Zbl 1381.65088) Full Text: DOI OpenURL
Marques, Alexandre Noll; Nave, Jean-Christophe; Rosales, Rodolfo Ruben High order solution of Poisson problems with piecewise constant coefficients and interface jumps. (English) Zbl 1380.65224 J. Comput. Phys. 335, 497-515 (2017). MSC: 65M30 35J05 35R05 PDF BibTeX XML Cite \textit{A. N. Marques} et al., J. Comput. Phys. 335, 497--515 (2017; Zbl 1380.65224) Full Text: DOI arXiv OpenURL
Cao, Yin; Wang, Bao; Xia, Kelin; Wei, Guowei Finite volume formulation of the MIB method for elliptic interface problems. (English) Zbl 1366.65096 J. Comput. Appl. Math. 321, 60-77 (2017). MSC: 65N08 35J25 65N35 65N12 PDF BibTeX XML Cite \textit{Y. Cao} et al., J. Comput. Appl. Math. 321, 60--77 (2017; Zbl 1366.65096) Full Text: DOI arXiv OpenURL
Albright, Jason; Epshteyn, Yekaterina; Medvinsky, Michael; Xia, Qing High-order numerical schemes based on difference potentials for 2D elliptic problems with material interfaces. (English) Zbl 1353.65110 Appl. Numer. Math. 111, 64-91 (2017). MSC: 65N06 35J25 65Y05 PDF BibTeX XML Cite \textit{J. Albright} et al., Appl. Numer. Math. 111, 64--91 (2017; Zbl 1353.65110) Full Text: DOI OpenURL
Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan A new weak Galerkin finite element method for elliptic interface problems. (English) Zbl 1380.65383 J. Comput. Phys. 325, 157-173 (2016). MSC: 65N30 65M12 65M15 PDF BibTeX XML Cite \textit{L. Mu} et al., J. Comput. Phys. 325, 157--173 (2016; Zbl 1380.65383) Full Text: DOI OpenURL
Frolkovič, Peter; Logashenko, Dmitriy; Wehner, Christian Flux-based level-set method for two-phase flows on unstructured grids. (English) Zbl 1360.76159 Comput. Vis. Sci. 18, No. 1, 31-52 (2016). MSC: 76M12 76T10 65M08 PDF BibTeX XML Cite \textit{P. Frolkovič} et al., Comput. Vis. Sci. 18, No. 1, 31--52 (2016; Zbl 1360.76159) Full Text: DOI OpenURL
Zheng, Xiaoming; Lowengrub, John An interface-fitted adaptive mesh method for elliptic problems and its application in free interface problems with surface tension. (English) Zbl 1357.65271 Adv. Comput. Math. 42, No. 5, 1225-1257 (2016). Reviewer: Tomas Vejchodsky (Praha) MSC: 65N30 35J25 35R05 76D07 76M10 65N12 92C17 PDF BibTeX XML Cite \textit{X. Zheng} and \textit{J. Lowengrub}, Adv. Comput. Math. 42, No. 5, 1225--1257 (2016; Zbl 1357.65271) Full Text: DOI OpenURL
Moldovan, I. D.; Radu, L. Trefftz-based dual reciprocity method for hyperbolic boundary value problems. (English) Zbl 1352.76063 Int. J. Numer. Methods Eng. 106, No. 13, 1043-1070 (2016). MSC: 76M10 65M60 76Q05 PDF BibTeX XML Cite \textit{I. D. Moldovan} and \textit{L. Radu}, Int. J. Numer. Methods Eng. 106, No. 13, 1043--1070 (2016; Zbl 1352.76063) Full Text: DOI OpenURL
Guzmán, Johnny; Sánchez, Manuel A.; Sarkis, Marcus On the accuracy of finite element approximations to a class of interface problems. (English) Zbl 1342.65218 Math. Comput. 85, No. 301, 2071-2098 (2016). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N15 65N50 35J25 PDF BibTeX XML Cite \textit{J. Guzmán} et al., Math. Comput. 85, No. 301, 2071--2098 (2016; Zbl 1342.65218) Full Text: DOI Link OpenURL
Liu, Jie A second-order stable explicit interface advancing scheme for FSI with both rigid and elastic structures and its application to fish swimming simulations. (English) Zbl 1390.76956 Comput. Fluids 118, 274-292 (2015). MSC: 76Z10 74F10 76M10 92C05 PDF BibTeX XML Cite \textit{J. Liu}, Comput. Fluids 118, 274--292 (2015; Zbl 1390.76956) Full Text: DOI OpenURL
Moldovan, I. D. A new particular solution strategy for hyperbolic boundary value problems using hybrid-Trefftz displacement elements. (English) Zbl 1352.74410 Int. J. Numer. Methods Eng. 102, No. 6, 1293-1315 (2015). MSC: 74S05 74S15 65M60 65M70 74H15 78M10 78M15 PDF BibTeX XML Cite \textit{I. D. Moldovan}, Int. J. Numer. Methods Eng. 102, No. 6, 1293--1315 (2015; Zbl 1352.74410) Full Text: DOI OpenURL
Guittet, Arthur; Lepilliez, Mathieu; Tanguy, Sebastien; Gibou, Frédéric Solving elliptic problems with discontinuities on irregular domains – the Voronoi interface method. (English) Zbl 1349.65579 J. Comput. Phys. 298, 747-765 (2015). MSC: 65N08 65N50 PDF BibTeX XML Cite \textit{A. Guittet} et al., J. Comput. Phys. 298, 747--765 (2015; Zbl 1349.65579) Full Text: DOI OpenURL
Leguèbe, M.; Poignard, C.; Weynans, L. A second-order Cartesian method for the simulation of electropermeabilization cell models. (English) Zbl 1349.78093 J. Comput. Phys. 292, 114-140 (2015). MSC: 78M20 65M06 65M12 PDF BibTeX XML Cite \textit{M. Leguèbe} et al., J. Comput. Phys. 292, 114--140 (2015; Zbl 1349.78093) Full Text: DOI Link OpenURL
Zhang, Ran; Zhai, Qilong A weak Galerkin finite element scheme for the biharmonic equations by using polynomials of reduced order. (English) Zbl 1331.65163 J. Sci. Comput. 64, No. 2, 559-585 (2015). MSC: 65N30 65N15 65N12 74N20 35B45 35J50 35J35 PDF BibTeX XML Cite \textit{R. Zhang} and \textit{Q. Zhai}, J. Sci. Comput. 64, No. 2, 559--585 (2015; Zbl 1331.65163) Full Text: DOI arXiv OpenURL
Beale, J. Thomas Uniform error estimates for Navier-Stokes flow with an exact moving boundary using the immersed interface method. (English) Zbl 1326.76078 SIAM J. Numer. Anal. 53, No. 4, 2097-2111 (2015). MSC: 76M20 65N06 65N12 74F10 76D05 76D27 35R05 PDF BibTeX XML Cite \textit{J. T. Beale}, SIAM J. Numer. Anal. 53, No. 4, 2097--2111 (2015; Zbl 1326.76078) Full Text: DOI arXiv OpenURL
Albright, Jason; Epshteyn, Yekaterina; Steffen, Kyle R. High-order accurate difference potentials methods for parabolic problems. (English) Zbl 1326.65103 Appl. Numer. Math. 93, 87-106 (2015). MSC: 65M06 65M12 65Y05 PDF BibTeX XML Cite \textit{J. Albright} et al., Appl. Numer. Math. 93, 87--106 (2015; Zbl 1326.65103) Full Text: DOI Link OpenURL
Epshteyn, Yekaterina; Phippen, Spencer High-order difference potentials methods for 1D elliptic type models. (English) Zbl 1326.65142 Appl. Numer. Math. 93, 69-86 (2015). MSC: 65N06 65Y05 PDF BibTeX XML Cite \textit{Y. Epshteyn} and \textit{S. Phippen}, Appl. Numer. Math. 93, 69--86 (2015; Zbl 1326.65142) Full Text: DOI Link OpenURL
Bozorgnia, Farid; Bazarganzadeh, Mahmoudreza Numerical schemes for multi phase quadrature domains. (English) Zbl 07485176 Int. J. Numer. Anal. Model. 11, No. 4, 726-744 (2014). MSC: 35J70 65M06 PDF BibTeX XML Cite \textit{F. Bozorgnia} and \textit{M. Bazarganzadeh}, Int. J. Numer. Anal. Model. 11, No. 4, 726--744 (2014; Zbl 07485176) Full Text: Link OpenURL
Xia, Kelin; Wei, Guo-Wei A Galerkin formulation of the MIB method for three dimensional elliptic interface problems. (English) Zbl 1362.65130 Comput. Math. Appl. 68, No. 7, 719-745 (2014). MSC: 65N30 35J25 35R05 92D20 PDF BibTeX XML Cite \textit{K. Xia} and \textit{G.-W. Wei}, Comput. Math. Appl. 68, No. 7, 719--745 (2014; Zbl 1362.65130) Full Text: DOI OpenURL
Shu, Yu-Chen; Chern, I-Liang; Chang, Chien C. Accurate gradient approximation for complex interface problems in 3D by an improved coupling interface method. (English) Zbl 1349.82029 J. Comput. Phys. 275, 642-661 (2014). MSC: 82B80 65N06 82B24 PDF BibTeX XML Cite \textit{Y.-C. Shu} et al., J. Comput. Phys. 275, 642--661 (2014; Zbl 1349.82029) Full Text: DOI OpenURL
Xia, Kelin; Zhan, Meng; Wei, Guo-Wei MIB Galerkin method for elliptic interface problems. (English) Zbl 1294.65103 J. Comput. Appl. Math. 272, 195-220 (2014). MSC: 65N30 35J25 35R05 65N12 PDF BibTeX XML Cite \textit{K. Xia} et al., J. Comput. Appl. Math. 272, 195--220 (2014; Zbl 1294.65103) Full Text: DOI OpenURL
Ying, Wenjun; Wang, Wei-Cheng A kernel-free boundary integral method for implicitly defined surfaces. (English) Zbl 1349.65662 J. Comput. Phys. 252, 606-624 (2013). MSC: 65N38 PDF BibTeX XML Cite \textit{W. Ying} and \textit{W.-C. Wang}, J. Comput. Phys. 252, 606--624 (2013; Zbl 1349.65662) Full Text: DOI OpenURL
Coco, Armando; Russo, Giovanni Finite-difference ghost-point multigrid methods on Cartesian grids for elliptic problems in arbitrary domains. (English) Zbl 1349.65555 J. Comput. Phys. 241, 464-501 (2013). MSC: 65N06 65N55 35Jxx PDF BibTeX XML Cite \textit{A. Coco} and \textit{G. Russo}, J. Comput. Phys. 241, 464--501 (2013; Zbl 1349.65555) Full Text: DOI OpenURL
Mu, Lin; Wang, Junping; Wei, Guowei; Ye, Xiu; Zhao, Shan Weak Galerkin methods for second order elliptic interface problems. (English) Zbl 1349.65472 J. Comput. Phys. 250, 106-125 (2013). MSC: 65M60 35J15 PDF BibTeX XML Cite \textit{L. Mu} et al., J. Comput. Phys. 250, 106--125 (2013; Zbl 1349.65472) Full Text: DOI arXiv Link OpenURL
Jin, Shi; Qi, Peng \(l^1\)-error estimates on the immersed interface upwind scheme for linear convection equations with piecewise constant coefficients: a simple proof. (English) Zbl 1305.65202 Sci. China, Math. 56, No. 12, 2773-2782 (2013). MSC: 65M15 65M06 35L02 35L81 PDF BibTeX XML Cite \textit{S. Jin} and \textit{P. Qi}, Sci. China, Math. 56, No. 12, 2773--2782 (2013; Zbl 1305.65202) Full Text: DOI OpenURL
Hou, Songming; Song, Peng; Wang, Liqun; Zhao, Hongkai A weak formulation for solving elliptic interface problems without body fitted grid. (English) Zbl 1314.65147 J. Comput. Phys. 249, 80-95 (2013). MSC: 65N30 35J99 PDF BibTeX XML Cite \textit{S. Hou} et al., J. Comput. Phys. 249, 80--95 (2013; Zbl 1314.65147) Full Text: DOI OpenURL
Bukshtynov, Vladislav; Protas, Bartosz Optimal reconstruction of material properties in complex multiphysics phenomena. (English) Zbl 1427.80016 J. Comput. Phys. 242, 889-914 (2013). MSC: 80A23 80A20 80M50 65K10 76D05 65M32 65J20 65M55 PDF BibTeX XML Cite \textit{V. Bukshtynov} and \textit{B. Protas}, J. Comput. Phys. 242, 889--914 (2013; Zbl 1427.80016) Full Text: DOI arXiv OpenURL
Wang, Liqun; Shi, Liwei Numerical method for solving matrix coefficient elliptic equation on irregular domains with sharp-edged boundaries. (English) Zbl 1292.65129 Adv. Numer. Anal. 2013, Article ID 967342, 10 p. (2013). MSC: 65N30 35J25 65N50 65Y20 65N12 65N15 PDF BibTeX XML Cite \textit{L. Wang} and \textit{L. Shi}, Adv. Numer. Anal. 2013, Article ID 967342, 10 p. (2013; Zbl 1292.65129) Full Text: DOI OpenURL
Fang, Xufa; Han, Danfu; Hu, Xianliang A second order isoparametric finite element method for elliptic interface problems. (English) Zbl 1289.65257 Appl. Math., Ser. B (Engl. Ed.) 28, No. 1, 57-74 (2013). MSC: 65N30 65N50 65N38 35J25 PDF BibTeX XML Cite \textit{X. Fang} et al., Appl. Math., Ser. B (Engl. Ed.) 28, No. 1, 57--74 (2013; Zbl 1289.65257) Full Text: DOI OpenURL
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 PDF BibTeX XML Cite \textit{F. Gibou} et al., J. Sci. Comput. 54, No. 2--3, 369--413 (2013; Zbl 1263.65093) Full Text: DOI Link OpenURL
Xia, Kelin; Zhan, Meng; Wan, Decheng; Wei, Guo-Wei Adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients. (English) Zbl 1242.65229 J. Comput. Phys. 231, No. 4, 1440-1461 (2012). MSC: 65N22 65N50 35J25 PDF BibTeX XML Cite \textit{K. Xia} et al., J. Comput. Phys. 231, No. 4, 1440--1461 (2012; Zbl 1242.65229) Full Text: DOI Link OpenURL
Aksoylu, Burak; Yeter, Zuhal Robust multigrid preconditioners for the high-contrast biharmonic plate equation. (English) Zbl 1265.74055 Numer. Linear Algebra Appl. 18, No. 4, 733-750 (2011). MSC: 74K20 65F08 65N30 65N55 PDF BibTeX XML Cite \textit{B. Aksoylu} and \textit{Z. Yeter}, Numer. Linear Algebra Appl. 18, No. 4, 733--750 (2011; Zbl 1265.74055) Full Text: DOI arXiv OpenURL
Rüberg, Thomas; Cirak, Fehmi An immersed finite element method with integral equation correction. (English) Zbl 1235.76071 Int. J. Numer. Methods Eng. 86, No. 1, 93-114 (2011). MSC: 76M10 76D05 70E99 PDF BibTeX XML Cite \textit{T. Rüberg} and \textit{F. Cirak}, Int. J. Numer. Methods Eng. 86, No. 1, 93--114 (2011; Zbl 1235.76071) Full Text: DOI Link OpenURL
Chen, Zhan; Baker, Nathan A.; Wei, G. W. Differential geometry based solvation model II: Lagrangian formulation. (English) Zbl 1284.92025 J. Math. Biol. 63, No. 6, 1139-1200 (2011). MSC: 92C40 35J61 35Q92 PDF BibTeX XML Cite \textit{Z. Chen} et al., J. Math. Biol. 63, No. 6, 1139--1200 (2011; Zbl 1284.92025) Full Text: DOI Link OpenURL
Marques, Alexandre Noll; Nave, Jean-Christophe; Rosales, Rodolfo Ruben A correction function method for Poisson problems with interface jump conditions. (English) Zbl 1453.35054 J. Comput. Phys. 230, No. 20, 7567-7597 (2011). MSC: 35J05 35R05 65N06 PDF BibTeX XML Cite \textit{A. N. Marques} et al., J. Comput. Phys. 230, No. 20, 7567--7597 (2011; Zbl 1453.35054) Full Text: DOI arXiv OpenURL
Kropinski, Mary Catherine A.; Quaife, Bryan D. Fast integral equation methods for Rothe’s method applied to the isotropic heat equation. (English) Zbl 1221.65279 Comput. Math. Appl. 61, No. 9, 2436-2446 (2011). MSC: 65M99 45L05 PDF BibTeX XML Cite \textit{M. C. A. Kropinski} and \textit{B. D. Quaife}, Comput. Math. Appl. 61, No. 9, 2436--2446 (2011; Zbl 1221.65279) Full Text: DOI OpenURL
Zheng, Qiong; Chen, Duan; Wei, Guo-Wei Second-order Poisson-Nernst-Planck solver for ion transport. (English) Zbl 1222.82073 J. Comput. Phys. 230, No. 13, 5239-5262 (2011). Reviewer: Guy Jumarie (Montréal) MSC: 82C70 82C24 35Q82 82-08 PDF BibTeX XML Cite \textit{Q. Zheng} et al., J. Comput. Phys. 230, No. 13, 5239--5262 (2011; Zbl 1222.82073) Full Text: DOI OpenURL
Xia, Kelin; Zhan, Meng; Wei, Guo-Wei MIB method for elliptic equations with multi-material interfaces. (English) Zbl 1220.65150 J. Comput. Phys. 230, No. 12, 4588-4615 (2011). MSC: 65N06 PDF BibTeX XML Cite \textit{K. Xia} et al., J. Comput. Phys. 230, No. 12, 4588--4615 (2011; Zbl 1220.65150) Full Text: DOI Link OpenURL
Simeonov, Julian A.; Calantoni, Joseph A pressure boundary integral method for direct fluid-particle simulations on Cartesian grids. (English) Zbl 1391.76247 J. Comput. Phys. 230, No. 5, 1749-1765 (2011). MSC: 76F65 76M25 74F10 PDF BibTeX XML Cite \textit{J. A. Simeonov} and \textit{J. Calantoni}, J. Comput. Phys. 230, No. 5, 1749--1765 (2011; Zbl 1391.76247) Full Text: DOI OpenURL
Geng, Weihua; Wei, G. W. Multiscale molecular dynamics using the matched interface and boundary method. (English) Zbl 1246.82028 J. Comput. Phys. 230, No. 2, 435-457 (2011). MSC: 82B24 78A70 82-08 92C40 PDF BibTeX XML Cite \textit{W. Geng} and \textit{G. W. Wei}, J. Comput. Phys. 230, No. 2, 435--457 (2011; Zbl 1246.82028) Full Text: DOI Link OpenURL
Chen, Duan; Wei, Guo-Wei Modeling and simulation of electronic structure, material interface and random doping in nano-electronic devices. (English) Zbl 1191.82113 J. Comput. Phys. 229, No. 12, 4431-4460 (2010). MSC: 82D37 82D80 82C70 82B24 35Q55 PDF BibTeX XML Cite \textit{D. Chen} and \textit{G.-W. Wei}, J. Comput. Phys. 229, No. 12, 4431--4460 (2010; Zbl 1191.82113) Full Text: DOI Link OpenURL
Zhang, Qinghai; Liu, Philip L.-F. Handling solid-fluid interfaces for viscous flows: explicit jump approximation vs. ghost cell approaches. (English) Zbl 1334.76117 J. Comput. Phys. 229, No. 11, 4225-4246 (2010). MSC: 76M25 65M06 PDF BibTeX XML Cite \textit{Q. Zhang} and \textit{P. L. F. Liu}, J. Comput. Phys. 229, No. 11, 4225--4246 (2010; Zbl 1334.76117) Full Text: DOI OpenURL
Colella, Phillip; Norgaard, Peter C. Controlling self-force errors at refinement boundaries for AMR-PIC. (English) Zbl 1185.82054 J. Comput. Phys. 229, No. 4, 947-957 (2010). Reviewer: Iván Abonyi (Budapest) MSC: 82D10 65N75 65N30 PDF BibTeX XML Cite \textit{P. Colella} and \textit{P. C. Norgaard}, J. Comput. Phys. 229, No. 4, 947--957 (2010; Zbl 1185.82054) Full Text: DOI OpenURL
Karagiozis, K.; Kamakoti, R.; Pantano, C. A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations. (English) Zbl 1253.76027 J. Comput. Phys. 229, No. 3, 701-727 (2010). MSC: 76D05 65M06 76M20 PDF BibTeX XML Cite \textit{K. Karagiozis} et al., J. Comput. Phys. 229, No. 3, 701--727 (2010; Zbl 1253.76027) Full Text: DOI OpenURL
Layton, Anita T. Using integral equations and the immersed interface method to solve immersed boundary problems with stiff forces. (English) Zbl 1237.76123 Comput. Fluids 38, No. 2, 266-272 (2009). MSC: 76M25 76D05 PDF BibTeX XML Cite \textit{A. T. Layton}, Comput. Fluids 38, No. 2, 266--272 (2009; Zbl 1237.76123) Full Text: DOI OpenURL
Ditkowski, Adi; Harness, Yuval High-order embedded finite difference schemes for initial boundary value problems on time dependent irregular domains. (English) Zbl 1203.65133 J. Sci. Comput. 39, No. 3, 394-440 (2009). MSC: 65M06 80A22 PDF BibTeX XML Cite \textit{A. Ditkowski} and \textit{Y. Harness}, J. Sci. Comput. 39, No. 3, 394--440 (2009; Zbl 1203.65133) Full Text: DOI OpenURL
Khattar, Dinesh; Singh, Swarn; Mohanty, R. K. A new coupled approach high accuracy numerical method for the solution of 3D non-linear biharmonic equations. (English) Zbl 1180.65137 Appl. Math. Comput. 215, No. 8, 3036-3044 (2009). MSC: 65N06 35J66 65N15 PDF BibTeX XML Cite \textit{D. Khattar} et al., Appl. Math. Comput. 215, No. 8, 3036--3044 (2009; Zbl 1180.65137) Full Text: DOI OpenURL
Chen, Duan; Wei, Guowei; Cong, Wenxiang; Wang, Ge Computational methods for optical molecular imaging. (English) Zbl 1180.92051 Commun. Numer. Methods Eng. 25, No. 12, 1137-1161 (2009). MSC: 92C55 35Q92 65C20 PDF BibTeX XML Cite \textit{D. Chen} et al., Commun. Numer. Methods Eng. 25, No. 12, 1137--1161 (2009; Zbl 1180.92051) Full Text: DOI Link OpenURL
Oevermann, M.; Scharfenberg, C.; Klein, R. A sharp interface finite volume method for elliptic equations on Cartesian grids. (English) Zbl 1169.65343 J. Comput. Phys. 228, No. 14, 5184-5206 (2009). MSC: 65N30 35J25 65N12 PDF BibTeX XML Cite \textit{M. Oevermann} et al., J. Comput. Phys. 228, No. 14, 5184--5206 (2009; Zbl 1169.65343) Full Text: DOI OpenURL
Lui, S. H. Spectral domain embedding for elliptic PDEs in complex domains. (English) Zbl 1160.65346 J. Comput. Appl. Math. 225, No. 2, 541-557 (2009). MSC: 65N35 35J25 65N12 65N55 PDF BibTeX XML Cite \textit{S. H. Lui}, J. Comput. Appl. Math. 225, No. 2, 541--557 (2009; Zbl 1160.65346) Full Text: DOI OpenURL
Tlupova, Svetlana; Cortez, Ricardo Boundary integral solutions of coupled Stokes and Darcy flows. (English) Zbl 1188.76232 J. Comput. Phys. 228, No. 1, 158-179 (2009). Reviewer: Titus Petrila (Cluj-Napoca) MSC: 76M15 76D07 76S05 PDF BibTeX XML Cite \textit{S. Tlupova} and \textit{R. Cortez}, J. Comput. Phys. 228, No. 1, 158--179 (2009; Zbl 1188.76232) Full Text: DOI OpenURL
Huh, Jae-Seok; Sethian, James A. Exact subgrid interface correction schemes for elliptic interface problems. (English) Zbl 1205.74158 Proc. Natl. Acad. Sci. USA 105, No. 29, 9874-9879 (2008). MSC: 74S05 PDF BibTeX XML Cite \textit{J.-S. Huh} and \textit{J. A. Sethian}, Proc. Natl. Acad. Sci. USA 105, No. 29, 9874--9879 (2008; Zbl 1205.74158) Full Text: DOI OpenURL
Lai, Ming-Chih; Tseng, Hsiao-Chieh A simple implementation of the immersed interface methods for Stokes flows with singular forces. (English) Zbl 1194.76179 Comput. Fluids 37, No. 2, 99-106 (2008). MSC: 76M20 76D07 PDF BibTeX XML Cite \textit{M.-C. Lai} and \textit{H.-C. Tseng}, Comput. Fluids 37, No. 2, 99--106 (2008; Zbl 1194.76179) Full Text: DOI OpenURL
Beale, J. Thomas; Layton, Anita T. A velocity decomposition approach for moving interfaces in viscous fluids. (English) Zbl 1160.76327 J. Comput. Phys. 228, No. 9, 3358-3367 (2009). MSC: 76D05 65N06 35R05 74F10 PDF BibTeX XML Cite \textit{J. T. Beale} and \textit{A. T. Layton}, J. Comput. Phys. 228, No. 9, 3358--3367 (2008; Zbl 1160.76327) Full Text: DOI Link OpenURL
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 PDF BibTeX XML Cite \textit{A. T. Layton}, Comput. Methods Appl. Mech. Eng. 197, No. 25--28, 2147--2155 (2008; Zbl 1158.76381) Full Text: DOI OpenURL
Min, Chohong; Gibou, Frédéric Robust second-order accurate discretizations of the multi-dimensional Heaviside and Dirac delta functions. (English) Zbl 1153.65014 J. Comput. Phys. 227, No. 22, 9686-9695 (2008). MSC: 65D15 PDF BibTeX XML Cite \textit{C. Min} and \textit{F. Gibou}, J. Comput. Phys. 227, No. 22, 9686--9695 (2008; Zbl 1153.65014) Full Text: DOI OpenURL
Chen, Guo; Li, Zhilin; Lin, Ping A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow. (English) Zbl 1241.76324 Adv. Comput. Math. 29, No. 2, 113-133 (2008). MSC: 76M20 65N06 35Q35 76D07 PDF BibTeX XML Cite \textit{G. Chen} et al., Adv. Comput. Math. 29, No. 2, 113--133 (2008; Zbl 1241.76324) Full Text: DOI OpenURL
Rutka, Vita A staggered grid-based explicit jump immersed interface method for two-dimensional Stokes flows. (English) Zbl 1140.76028 Int. J. Numer. Methods Fluids 57, No. 10, 1527-1543 (2008). MSC: 76M20 76D07 PDF BibTeX XML Cite \textit{V. Rutka}, Int. J. Numer. Methods Fluids 57, No. 10, 1527--1543 (2008; Zbl 1140.76028) Full Text: DOI OpenURL
Towers, John D. A convergence rate theorem for finite difference approximations to delta functions. (English) Zbl 1155.65016 J. Comput. Phys. 227, No. 13, 6591-6597 (2008). Reviewer: Vasilis Dimitriou (Chania) MSC: 65D15 PDF BibTeX XML Cite \textit{J. D. Towers}, J. Comput. Phys. 227, No. 13, 6591--6597 (2008; Zbl 1155.65016) Full Text: DOI OpenURL
Xu, Sheng The immersed interface method for simulating prescribed motion of rigid objects in an incompressible viscous flow. (English) Zbl 1388.76280 J. Comput. Phys. 227, No. 10, 5045-5071 (2008). MSC: 76M25 76D05 PDF BibTeX XML Cite \textit{S. Xu}, J. Comput. Phys. 227, No. 10, 5045--5071 (2008; Zbl 1388.76280) Full Text: DOI OpenURL
Beale, J. Thomas A proof that a discrete delta function is second-order accurate. (English) Zbl 1136.65017 J. Comput. Phys. 227, No. 4, 2195-2197 (2008). MSC: 65D15 46F10 PDF BibTeX XML Cite \textit{J. T. Beale}, J. Comput. Phys. 227, No. 4, 2195--2197 (2008; Zbl 1136.65017) Full Text: DOI OpenURL
Ying, Wenjun; Henriquez, Craig S. A kernel-free boundary integral method for elliptic boundary value problems. (English) Zbl 1128.65102 J. Comput. Phys. 227, No. 2, 1046-1074 (2007). MSC: 65N38 35J25 65N12 65N06 65N30 PDF BibTeX XML Cite \textit{W. Ying} and \textit{C. S. Henriquez}, J. Comput. Phys. 227, No. 2, 1046--1074 (2007; Zbl 1128.65102) Full Text: DOI Link OpenURL
Yu, Sining; Wei, G. W. Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities. (English) Zbl 1128.65103 J. Comput. Phys. 227, No. 1, 602-632 (2007). MSC: 65N38 35J25 35R05 PDF BibTeX XML Cite \textit{S. Yu} and \textit{G. W. Wei}, J. Comput. Phys. 227, No. 1, 602--632 (2007; Zbl 1128.65103) Full Text: DOI OpenURL
Min, Chohong; Gibou, Frédéric Geometric integration over irregular domains with application to level-set methods. (English) Zbl 1125.65021 J. Comput. Phys. 226, No. 2, 1432-1443 (2007). MSC: 65D32 41A55 41A63 PDF BibTeX XML Cite \textit{C. Min} and \textit{F. Gibou}, J. Comput. Phys. 226, No. 2, 1432--1443 (2007; Zbl 1125.65021) Full Text: DOI OpenURL
Chern, I-Liang; Shu, Yu-Chen A coupling interface method for elliptic interface problems. (English) Zbl 1123.65108 J. Comput. Phys. 225, No. 2, 2138-2174 (2007). MSC: 65N06 35J25 35R05 65F10 65N55 65N12 PDF BibTeX XML Cite \textit{I-L. Chern} and \textit{Y.-C. Shu}, J. Comput. Phys. 225, No. 2, 2138--2174 (2007; Zbl 1123.65108) Full Text: DOI OpenURL
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 PDF BibTeX XML Cite \textit{X. Zhong}, J. Comput. Phys. 225, No. 1, 1066--1099 (2007; Zbl 1343.65130) Full Text: DOI OpenURL
Chen, Han; Min, Chohong; Gibou, Frédéric A supra-convergent finite difference scheme for the Poisson and heat equations on irregular domains and non-graded adaptive Cartesian grids. (English) Zbl 1120.65113 J. Sci. Comput. 31, No. 1-2, 19-60 (2007). MSC: 65N06 35J05 65M06 35K05 65N12 65M12 PDF BibTeX XML Cite \textit{H. Chen} et al., J. Sci. Comput. 31, No. 1--2, 19--60 (2007; Zbl 1120.65113) Full Text: DOI OpenURL
Yu, Sining; Zhou, Yongcheng; Wei, G. W. Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces. (English) Zbl 1120.65333 J. Comput. Phys. 224, No. 2, 729-756 (2007). MSC: 65N06 65N12 35J05 PDF BibTeX XML Cite \textit{S. Yu} et al., J. Comput. Phys. 224, No. 2, 729--756 (2007; Zbl 1120.65333) Full Text: DOI Link OpenURL
Klapper, I.; Shaw, T. A large jump asymptotic framework for solving elliptic and parabolic equations with interfaces and strong coefficient discontinuities. (English) Zbl 1115.65101 Appl. Numer. Math. 57, No. 5-7, 657-671 (2007). MSC: 65M60 PDF BibTeX XML Cite \textit{I. Klapper} and \textit{T. Shaw}, Appl. Numer. Math. 57, No. 5--7, 657--671 (2007; Zbl 1115.65101) Full Text: DOI OpenURL
Mayo, Anita; Greenbaum, Anne Fourth order accurate evaluation of integrals in potential theory on exterior 3D regions. (English) Zbl 1109.65028 J. Comput. Phys. 220, No. 2, 900-914 (2007). MSC: 65D32 41A55 41A63 PDF BibTeX XML Cite \textit{A. Mayo} and \textit{A. Greenbaum}, J. Comput. Phys. 220, No. 2, 900--914 (2007; Zbl 1109.65028) Full Text: DOI OpenURL
Rutka, Vita; Wiegmann, Andreas Explicit jump immersed interface method for virtual material design of the effective elastic moduli of composite materials. (English) Zbl 1150.74095 Numer. Algorithms 43, No. 4, 309-330 (2006). MSC: 74S20 74Q05 65N06 PDF BibTeX XML Cite \textit{V. Rutka} and \textit{A. Wiegmann}, Numer. Algorithms 43, No. 4, 309--330 (2006; Zbl 1150.74095) Full Text: DOI Link OpenURL
Min, Chohong; Gibou, Frédéric; Ceniceros, Hector D. A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids. (English) Zbl 1106.65093 J. Comput. Phys. 218, No. 1, 123-140 (2006). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 65N06 65N12 65N50 35J05 PDF BibTeX XML Cite \textit{C. Min} et al., J. Comput. Phys. 218, No. 1, 123--140 (2006; Zbl 1106.65093) Full Text: DOI Link OpenURL