{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T02:04:44Z","timestamp":1777082684685,"version":"3.51.4"},"reference-count":86,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,1,10]],"date-time":"2018-01-10T00:00:00Z","timestamp":1515542400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004359","name":"Vetenskapsr\u00e5det","doi-asserted-by":"publisher","award":["2014-6088"],"award-info":[{"award-number":["2014-6088"]}],"id":[{"id":"10.13039\/501100004359","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001728","name":"Swedish Foundation for International Cooperation in Research and Higher Education","doi-asserted-by":"publisher","award":["STINT-IB2016-6512"],"award-info":[{"award-number":["STINT-IB2016-6512"]}],"id":[{"id":"10.13039\/501100001728","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Uppsala University, Department of Information Technology"},{"name":"University of Utah, Department of Mathematics"},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["415673"],"award-info":[{"award-number":["415673"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,8]]},"DOI":"10.1007\/s10915-017-0637-y","type":"journal-article","created":{"date-parts":[[2018,1,10]],"date-time":"2018-01-10T15:01:58Z","timestamp":1515596518000},"page":"812-847","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["High-Order Numerical Methods for 2D Parabolic Problems in Single and Composite Domains"],"prefix":"10.1007","volume":"76","author":[{"given":"Gustav","family":"Ludvigsson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kyle R.","family":"Steffen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simon","family":"Sticko","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siyang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qing","family":"Xia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yekaterina","family":"Epshteyn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gunilla","family":"Kreiss","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,1,10]]},"reference":[{"key":"637_CR1","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1006\/jcph.1997.5653","volume":"133","author":"S Abarbanel","year":"1997","unstructured":"Abarbanel, S., Ditkowski, A.: Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes. J. Comput. Phys. 133, 279\u2013288 (1997). https:\/\/doi.org\/10.1006\/jcph.1997.5653","journal-title":"J. Comput. Phys."},{"issue":"2","key":"637_CR2","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1137\/S1064827501389849","volume":"24","author":"L Adams","year":"2002","unstructured":"Adams, L., Li, Z.: The immersed interface\/multigrid methods for interface problems. SIAM J. Sci. Comput. 24(2), 463\u2013479 (2002). https:\/\/doi.org\/10.1137\/S1064827501389849","journal-title":"SIAM J. Sci. Comput."},{"key":"637_CR3","unstructured":"Albright, J.: Numerical Methods Based on Difference Potentials for Models with Material Interfaces. Ph.D. thesis, University of Utah (2016)"},{"key":"637_CR4","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.apnum.2016.08.017","volume":"111","author":"J Albright","year":"2017","unstructured":"Albright, J., Epshteyn, Y., Medvinsky, M., Xia, Q.: High-order numerical schemes based on difference potentials for 2D elliptic problems with material interfaces. Appl. Numer. Math. 111, 64\u201391 (2017). https:\/\/doi.org\/10.1016\/j.apnum.2016.08.017","journal-title":"Appl. Numer. Math."},{"key":"637_CR5","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.apnum.2014.08.002","volume":"93","author":"J Albright","year":"2015","unstructured":"Albright, J., Epshteyn, Y., Steffen, K.R.: High-order accurate difference potentials methods for parabolic problems. Appl. Numer. Math. 93, 87\u2013106 (2015). https:\/\/doi.org\/10.1016\/j.apnum.2014.08.002","journal-title":"Appl. Numer. Math."},{"issue":"4","key":"637_CR6","doi-asserted-by":"publisher","first-page":"985","DOI":"10.4310\/CMS.2017.v15.n4.a4","volume":"15","author":"J Albright","year":"2017","unstructured":"Albright, J., Epshteyn, Y., Xia, Q.: High-order accurate methods based on difference potentials for 2D parabolic interface models. Commun. Math. Sci. 15(4), 985\u20131019 (2017). https:\/\/doi.org\/10.4310\/CMS.2017.v15.n4.a4","journal-title":"Commun. Math. Sci."},{"key":"637_CR7","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1007\/s10915-014-9830-4","volume":"61","author":"M Almquist","year":"2014","unstructured":"Almquist, M., Karasalo, I., Mattsson, K.: Atmospheric sound propagation over large-scale irregular terrain. J. Sci. Comput. 61, 369\u2013397 (2014). https:\/\/doi.org\/10.1007\/s10915-014-9830-4","journal-title":"J. Sci. Comput."},{"issue":"1","key":"637_CR8","first-page":"84","volume":"5","author":"D Appel\u00f6","year":"2009","unstructured":"Appel\u00f6, D., Petersson, N.A.: A stable finite difference method for the elastic wave equation on complex geometries with free surfaces. Commun. Comput. Phys. 5(1), 84\u2013107 (2009)","journal-title":"Commun. Comput. Phys."},{"issue":"18","key":"637_CR9","doi-asserted-by":"publisher","first-page":"6405","DOI":"10.1016\/j.jcp.2010.05.002","volume":"229","author":"J Bedrossian","year":"2010","unstructured":"Bedrossian, J., Von Brecht, J.H., Zhu, S., Sifakis, E., Teran, J.M.: A second order virtual node method for elliptic problems with interfaces and irregular domains. J. Comput. Phys. 229(18), 6405\u20136426 (2010). https:\/\/doi.org\/10.1016\/j.jcp.2010.05.002","journal-title":"J. Comput. Phys."},{"key":"637_CR10","doi-asserted-by":"publisher","first-page":"1620","DOI":"10.1016\/j.apnum.2012.05.002","volume":"62","author":"J Berg","year":"2012","unstructured":"Berg, J., Nordstr\u00f6m, J.: Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains. Appl. Numer. Math. 62, 1620\u20131638 (2012). https:\/\/doi.org\/10.1016\/j.apnum.2012.05.002","journal-title":"Appl. Numer. Math."},{"issue":"9","key":"637_CR11","doi-asserted-by":"publisher","first-page":"1134","DOI":"10.1190\/1.1442748","volume":"54","author":"M Bouchon","year":"1989","unstructured":"Bouchon, M., Campillo, M., Gaffet, S.: A boundary integral equation-discrete wavenumber representation method to study wave propagation in multilayered media having irregular interfaces. Geophysics 54(9), 1134\u20131140 (1989). https:\/\/doi.org\/10.1190\/1.1442748","journal-title":"Geophysics"},{"key":"637_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2017.10.049","author":"S Britt","year":"2017","unstructured":"Britt, S., Tsynkov, S., Turkel, E.: Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials. J. Comput. Phys. (2017). https:\/\/doi.org\/10.1016\/j.jcp.2017.10.049","journal-title":"J. Comput. Phys."},{"issue":"7","key":"637_CR13","doi-asserted-by":"publisher","first-page":"472","DOI":"10.1002\/nme.4823","volume":"104","author":"E Burman","year":"2015","unstructured":"Burman, E., Claus, S., Hansbo, P., Larson, M.G., Massing, A.: CutFEM: Discretizing geometry and partial differential equations. Int. J. Numer. Methods Eng. 104(7), 472\u2013501 (2015). https:\/\/doi.org\/10.1002\/nme.4823","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"4","key":"637_CR14","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1016\/j.apnum.2011.01.008","volume":"62","author":"E Burman","year":"2012","unstructured":"Burman, E., Hansbo, P.: Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl. Numer. Math. 62(4), 328\u2013341 (2012). https:\/\/doi.org\/10.1016\/j.apnum.2011.01.008","journal-title":"Appl. Numer. Math."},{"issue":"2","key":"637_CR15","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/s00211-015-0744-3","volume":"133","author":"E Burman","year":"2016","unstructured":"Burman, E., Hansbo, P., Larson, M.G., Zahedi, S.: Cut finite element methods for coupled bulksurface problems. Numer. Math. 133(2), 203\u2013231 (2016). https:\/\/doi.org\/10.1007\/s00211-015-0744-3","journal-title":"Numer. Math."},{"key":"637_CR16","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1006\/jcph.1994.1057","volume":"111","author":"MH Carpenter","year":"1994","unstructured":"Carpenter, M.H., Gottlieb, D., Abarbanel, S.: Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes. J. Comput. Phys. 111, 220\u2013236 (1994). https:\/\/doi.org\/10.1006\/jcph.1994.1057","journal-title":"J. Comput. Phys."},{"issue":"1\u20133","key":"637_CR17","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1007\/s10915-009-9301-5","volume":"45","author":"MH Carpenter","year":"2009","unstructured":"Carpenter, M.H., Nordstr\u00f6m, J., Gottlieb, D.: Revisiting and extending interface penalties for multi-domain summation-by-parts operators. J. Sci. Comput. 45(1\u20133), 118\u2013150 (2009). https:\/\/doi.org\/10.1007\/s10915-009-9301-5","journal-title":"J. Sci. Comput."},{"issue":"01","key":"637_CR18","doi-asserted-by":"publisher","first-page":"19","DOI":"10.4208\/nmtma.2011.m12si02","volume":"5","author":"A Coco","year":"2012","unstructured":"Coco, A., Russo, G.: Second order multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface, I: one dimensional problems. Numer. Math. Theory Methods Appl. 5(01), 19\u201342 (2012). https:\/\/doi.org\/10.4208\/nmtma.2011.m12si02","journal-title":"Numer. Math. Theory Methods Appl."},{"issue":"7","key":"637_CR19","doi-asserted-by":"publisher","first-page":"2451","DOI":"10.1016\/j.jcp.2010.12.017","volume":"230","author":"R Crockett","year":"2011","unstructured":"Crockett, R., Colella, P., Graves, D.T.: A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions. J. Comput. Phys. 230(7), 2451\u20132469 (2011). https:\/\/doi.org\/10.1016\/j.jcp.2010.12.017","journal-title":"J. Comput. Phys."},{"key":"637_CR20","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/j.jcp.2014.01.038","volume":"266","author":"DC Rey Fern\u00e1ndez Del","year":"2014","unstructured":"Del Rey Fern\u00e1ndez, D.C., Boom, P.D., Zingg, D.W.: A generalized framework for nodal first derivative summation-by-parts operators. J. Comput. Phys. 266, 214\u2013239 (2014). https:\/\/doi.org\/10.1016\/j.jcp.2014.01.038","journal-title":"J. Comput. Phys."},{"key":"637_CR21","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.compfluid.2014.02.016","volume":"95","author":"DC Rey Fern\u00e1ndez Del","year":"2014","unstructured":"Del Rey Fern\u00e1ndez, D.C., Hicken, J.E., Zingg, D.W.: Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations. Comput. Fluids 95, 171\u2013196 (2014). https:\/\/doi.org\/10.1016\/j.compfluid.2014.02.016","journal-title":"Comput. Fluids"},{"issue":"21","key":"637_CR22","doi-asserted-by":"publisher","first-page":"3751","DOI":"10.1002\/nme.1620372110","volume":"37","author":"I Demirdz\u0306i\u0107","year":"1994","unstructured":"Demirdz\u0306i\u0107, I., Muzaferija, S.: Finite volume method for stress analysis in complex domains. Int. J. Numer. Methods. Eng. 37(21), 3751\u20133766 (1994). https:\/\/doi.org\/10.1002\/nme.1620372110","journal-title":"Int. J. Numer. Methods. Eng."},{"key":"637_CR23","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1007\/s10915-009-9277-1","volume":"39","author":"A Ditkowski","year":"2009","unstructured":"Ditkowski, A., Harness, Y.: High-order embedded finite difference schemes for initial boundary value problems on time dependent irregular domains. J. Sci. Comput. 39, 394\u2013440 (2009). https:\/\/doi.org\/10.1007\/s10915-009-9277-1","journal-title":"J. Sci. Comput."},{"key":"637_CR24","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.jcp.2014.08.046","volume":"279","author":"K Duru","year":"2014","unstructured":"Duru, K., Virta, K.: Stable and high order accurate difference methods for the elastic wave equation in discontinuous media. J. Comput. Phys. 279, 37\u201362 (2014). https:\/\/doi.org\/10.1016\/j.jcp.2014.08.046","journal-title":"J. Comput. Phys."},{"issue":"3","key":"637_CR25","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1007\/s10915-012-9599-2","volume":"53","author":"Y Epshteyn","year":"2012","unstructured":"Epshteyn, Y.: Upwind-difference potentials method for Patlak\u2013Keller\u2013Segel chemotaxis model. J. Sci. Comput. 53(3), 689\u2013713 (2012). https:\/\/doi.org\/10.1007\/s10915-012-9599-2","journal-title":"J. Sci. Comput."},{"issue":"4","key":"637_CR26","doi-asserted-by":"publisher","first-page":"723","DOI":"10.4310\/cms.2014.v12.n4.a7","volume":"12","author":"Y Epshteyn","year":"2014","unstructured":"Epshteyn, Y.: Algorithms composition approach based on difference potentials method for parabolic problems. Commun. Math. Sci. 12(4), 723\u2013755 (2014). https:\/\/doi.org\/10.4310\/cms.2014.v12.n4.a7","journal-title":"Commun. Math. Sci."},{"key":"637_CR27","doi-asserted-by":"publisher","unstructured":"Epshteyn, Y., Medvinsky, M.: On the solution of the elliptic interface problems by difference potentials method. In: Kirby, R.M., Berzins, M., Hesthaven, J.S. (eds.) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014, pp. 197\u2013205. Springer (2015). https:\/\/doi.org\/10.1007\/978-3-319-19800-2_16","DOI":"10.1007\/978-3-319-19800-2_16"},{"key":"637_CR28","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.apnum.2014.02.005","volume":"93","author":"Y Epshteyn","year":"2015","unstructured":"Epshteyn, Y., Phippen, S.: High-order difference potentials methods for 1D elliptic type models. Appl. Numer. Math. 93, 69\u201386 (2015). https:\/\/doi.org\/10.1016\/j.apnum.2014.02.005","journal-title":"Appl. Numer. Math."},{"issue":"Supplement C","key":"637_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.apnum.2015.02.001","volume":"93","author":"Y Epshteyn","year":"2015","unstructured":"Epshteyn, Y., Sofronov, I., Tsynkov, S.: Professor V. S. Ryaben\u2019kii. On the occasion of the 90-th birthday. Appl. Numer. Math. 93(Supplement C), 1\u20132 (2015). https:\/\/doi.org\/10.1016\/j.apnum.2015.02.001","journal-title":"Appl. Numer. Math."},{"issue":"1","key":"637_CR30","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1006\/jcph.2000.6484","volume":"161","author":"E Fadlun","year":"2000","unstructured":"Fadlun, E., Verzicco, R., Orlandi, P., Mohd-Yusof, J.: Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161(1), 35\u201360 (2000). https:\/\/doi.org\/10.1006\/jcph.2000.6484","journal-title":"J. Comput. Phys."},{"issue":"2","key":"637_CR31","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1006\/jcph.1999.6236","volume":"152","author":"RP Fedkiw","year":"1999","unstructured":"Fedkiw, R.P., Aslam, T., Merriman, B., Osher, S.: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152(2), 457\u2013492 (1999). https:\/\/doi.org\/10.1006\/jcph.1999.6236","journal-title":"J. Comput. Phys."},{"issue":"2","key":"637_CR32","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1016\/j.jcp.2004.07.018","volume":"202","author":"F Gibou","year":"2005","unstructured":"Gibou, F., Fedkiw, R.: A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem. J. Comput. Phys. 202(2), 577\u2013601 (2005). https:\/\/doi.org\/10.1016\/j.jcp.2004.07.018","journal-title":"J. Comput. Phys."},{"issue":"6","key":"637_CR33","doi-asserted-by":"publisher","first-page":"1183","DOI":"10.1070\/RM2015v070n06ABEH004981","volume":"70","author":"SK Godunov","year":"2015","unstructured":"Godunov, S.K., Zhukov, V.T., Lazarev, M.I., Sofronov, I.L., Turchaninov, V.I., Kholodov, A.S., Tsynkov, S.V., Chetverushkin, B.N., Epshteyn, Y.Y.: Viktor Solomonovich Ryaben\u2019kii and his school (on his 90th birthday). Russ. Math. Surv. 70(6), 1183 (2015). https:\/\/doi.org\/10.1070\/RM2015v070n06ABEH004981","journal-title":"Russ. Math. Surv."},{"issue":"3","key":"637_CR34","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1080\/10407790.2013.751251","volume":"63","author":"J Gong","year":"2013","unstructured":"Gong, J., Xuan, L., Ming, P., Zhang, W.: An unstructured finite-volume method for transient heat conduction analysis of multilayer functionally graded materials with mixed grids. Numer. Heat Transfer, Part B 63(3), 222\u2013247 (2013). https:\/\/doi.org\/10.1080\/10407790.2013.751251","journal-title":"Numer. Heat Transfer, Part B"},{"key":"637_CR35","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1016\/j.jcp.2015.06.026","volume":"298","author":"A Guittet","year":"2015","unstructured":"Guittet, A., Lepilliez, M., Tanguy, S., Gibou, F.: Solving elliptic problems with discontinuities on irregular domains\u2014the Voronoi interface method. J. Comput. Phys. 298, 747\u2013765 (2015). https:\/\/doi.org\/10.1016\/j.jcp.2015.06.026","journal-title":"J. Comput. Phys."},{"key":"637_CR36","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.jcp.2016.11.048","volume":"332","author":"A Guittet","year":"2017","unstructured":"Guittet, A., Poignard, C., Gibou, F.: A Voronoi interface approach to cell aggregate electropermeabilization. J. Comput. Phys. 332, 143\u2013159 (2017). https:\/\/doi.org\/10.1016\/j.jcp.2016.11.048","journal-title":"J. Comput. Phys."},{"issue":"47","key":"637_CR37","doi-asserted-by":"publisher","first-page":"5537","DOI":"10.1016\/S0045-7825(02)00524-8","volume":"191","author":"A Hansbo","year":"2002","unstructured":"Hansbo, A., Hansbo, P.: An unfitted finite element method, based on Nitsche\u2019s method, for elliptic interface problems. Comput. Methods Appl. Mech. Eng. 191(47), 5537\u20135552 (2002). https:\/\/doi.org\/10.1016\/S0045-7825(02)00524-8","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"637_CR38","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.apnum.2014.06.009","volume":"85","author":"P Hansbo","year":"2014","unstructured":"Hansbo, P., Larson, M.G., Zahedi, S.: A cut finite element method for a Stokes interface problem. Appl. Numer. Math. 85, 90\u2013114 (2014). https:\/\/doi.org\/10.1016\/j.apnum.2014.06.009","journal-title":"Appl. Numer. Math."},{"issue":"4","key":"637_CR39","doi-asserted-by":"publisher","first-page":"2015","DOI":"10.1016\/j.jcp.2011.11.023","volume":"231","author":"JL Hellrung","year":"2012","unstructured":"Hellrung, J.L., Wang, L., Sifakis, E., Teran, J.M.: A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions. J. Comput. Phys. 231(4), 2015\u20132048 (2012). https:\/\/doi.org\/10.1016\/j.jcp.2011.11.023","journal-title":"J. Comput. Phys."},{"key":"637_CR40","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-72067-8","volume-title":"Nodal Discontinuous Galerkin Methods","author":"JS Hesthaven","year":"2008","unstructured":"Hesthaven, J.S., Warburton, T.: Nodal Discontinuous Galerkin Methods. Springer, Berlin (2008). https:\/\/doi.org\/10.1007\/978-0-387-72067-8"},{"issue":"1","key":"637_CR41","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1006\/jcph.1998.5965","volume":"147","author":"H Johansen","year":"1998","unstructured":"Johansen, H., Colella, P.: A Cartesian grid embedded boundary method for Poisson\u2019s equation on irregular domains. J. Comput. Phys. 147(1), 60\u201385 (1998). https:\/\/doi.org\/10.1006\/jcph.1998.5965","journal-title":"J. Comput. Phys."},{"issue":"1","key":"637_CR42","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1006\/jcph.2001.6778","volume":"171","author":"J Kim","year":"2001","unstructured":"Kim, J., Kim, D., Choi, H.: An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171(1), 132\u2013150 (2001). https:\/\/doi.org\/10.1006\/jcph.2001.6778","journal-title":"J. Comput. Phys."},{"key":"637_CR43","volume-title":"Fundamentals of Grid Generation","author":"P Knupp","year":"1993","unstructured":"Knupp, P., Steinberg, S.: Fundamentals of Grid Generation. CRC Press, Boca Raton (1993)"},{"key":"637_CR44","doi-asserted-by":"publisher","first-page":"A923","DOI":"10.1137\/15M1022823","volume":"38","author":"JE Kozdon","year":"2016","unstructured":"Kozdon, J.E., Wilcox, L.C.: Stable coupling of nonconforming, high-order finite difference methods. SIAM J. Sci. Comput. 38, A923\u2013A952 (2016). https:\/\/doi.org\/10.1137\/15M1022823","journal-title":"SIAM J. Sci. Comput."},{"key":"637_CR45","doi-asserted-by":"publisher","unstructured":"Kreiss, H.O., Scherer, G.: Finite element and finite difference methods for hyperbolic partial differential equations. In: Mathematical Aspects of Finite Elements in Partial Differential Equations, Symposium Proceedings pp. 195\u2013212 (1974). https:\/\/doi.org\/10.1016\/B978-0-12-208350-1.50012-1","DOI":"10.1016\/B978-0-12-208350-1.50012-1"},{"issue":"4","key":"637_CR46","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1137\/0731054","volume":"31","author":"RJ Leveque","year":"1994","unstructured":"Leveque, R.J., Li, Z.: The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31(4), 1019\u20131044 (1994). https:\/\/doi.org\/10.1137\/0731054","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"637_CR47","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1137\/S1064827595282532","volume":"18","author":"RJ LeVeque","year":"1997","unstructured":"LeVeque, R.J., Li, Z.: Immersed interface methods for Stokes flow with elastic boundaries or surface tension. SIAM J. Sci. Comput. 18(3), 709\u2013735 (1997). https:\/\/doi.org\/10.1137\/S1064827595282532","journal-title":"SIAM J. Sci. Comput."},{"key":"637_CR48","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717464","author":"Z Li","year":"2006","unstructured":"Li, Z., Ito, K.: The immersed interface method: numerical solutions of PDEs involving interfaces and irregular domains. Front. Appl. Math. Soc. Ind. Appl. Math. (2006). https:\/\/doi.org\/10.1137\/1.9780898717464","journal-title":"Front. Appl. Math. Soc. Ind. Appl. Math."},{"issue":"1","key":"637_CR49","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.jcp.2004.09.017","volume":"204","author":"MN Linnick","year":"2005","unstructured":"Linnick, M.N., Fasel, H.F.: A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains. J. Comput. Phys. 204(1), 157\u2013192 (2005). https:\/\/doi.org\/10.1016\/j.jcp.2004.09.017","journal-title":"J. Comput. Phys."},{"issue":"2","key":"637_CR50","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1016\/S0021-9991(03)00301-2","volume":"190","author":"T Liu","year":"2003","unstructured":"Liu, T., Khoo, B., Yeo, K.: Ghost fluid method for strong shock impacting on material interface. J. Comput. Phys. 190(2), 651\u2013681 (2003). https:\/\/doi.org\/10.1016\/S0021-9991(03)00301-2","journal-title":"J. Comput. Phys."},{"issue":"244","key":"637_CR51","doi-asserted-by":"publisher","first-page":"1731","DOI":"10.1090\/S0025-5718-03-01525-4","volume":"72","author":"XD Liu","year":"2003","unstructured":"Liu, X.D., Sideris, T.: Convergence of the ghost fluid method for elliptic equations with interfaces. Math. Comput. 72(244), 1731\u20131746 (2003). https:\/\/doi.org\/10.1090\/S0025-5718-03-01525-4","journal-title":"Math. Comput."},{"key":"637_CR52","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.apnum.2017.02.013","volume":"118","author":"S Magura","year":"2017","unstructured":"Magura, S., Petropavlovsky, S., Tsynkov, S., Turkel, E.: High-order numerical solution of the Helmholtz equation for domains with reentrant corners. Appl. Numer. Math. 118, 87\u2013116 (2017). https:\/\/doi.org\/10.1016\/j.apnum.2017.02.013","journal-title":"Appl. Numer. Math."},{"issue":"3","key":"637_CR53","doi-asserted-by":"publisher","first-page":"604","DOI":"10.1007\/s10915-014-9838-9","volume":"61","author":"A Massing","year":"2014","unstructured":"Massing, A., Larson, M.G., Logg, A., Rognes, M.E.: A stabilized Nitsche fictitious domain method for the Stokes problem. J. Sci. Comput. 61(3), 604\u2013628 (2014). https:\/\/doi.org\/10.1007\/s10915-014-9838-9","journal-title":"J. Sci. Comput."},{"key":"637_CR54","doi-asserted-by":"publisher","first-page":"650","DOI":"10.1007\/s10915-011-9525-z","volume":"51","author":"K Mattsson","year":"2012","unstructured":"Mattsson, K.: Summation by parts operators for finite difference approximations of second-derivatives with variable coefficient. J. Sci. Comput. 51, 650\u2013682 (2012). https:\/\/doi.org\/10.1007\/s10915-011-9525-z","journal-title":"J. Sci. Comput."},{"key":"637_CR55","doi-asserted-by":"publisher","first-page":"2298","DOI":"10.1137\/090750068","volume":"32","author":"K Mattsson","year":"2010","unstructured":"Mattsson, K., Carpenter, M.H.: Stable and accurate interpolation operators for high-order multiblock finite difference methods. SIAM J. Sci. Comput. 32, 2298\u20132320 (2010). https:\/\/doi.org\/10.1137\/090750068","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"637_CR56","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1137\/0721021","volume":"21","author":"A Mayo","year":"1984","unstructured":"Mayo, A.: The fast solution of Poisson\u2019s and the biharmonic equations on irregular regions. SIAM J. Sci. Comput. 21(2), 285\u2013299 (1984). https:\/\/doi.org\/10.1137\/0721021","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"637_CR57","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1006\/jcph.2001.6900","volume":"173","author":"P McCorquodale","year":"2001","unstructured":"McCorquodale, P., Colella, P., Johansen, H.: A Cartesian grid embedded boundary method for the heat equation on irregular domains. J. Comput. Phys. 173(2), 620\u2013635 (2001). https:\/\/doi.org\/10.1006\/jcph.2001.6900","journal-title":"J. Comput. Phys."},{"issue":"1","key":"637_CR58","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/s10915-012-9602-y","volume":"53","author":"M Medvinsky","year":"2012","unstructured":"Medvinsky, M., Tsynkov, S., Turkel, E.: The method of difference potentials for the Helmholtz equation using compact high order schemes. J. Sci. Comput. 53(1), 150\u2013193 (2012). https:\/\/doi.org\/10.1007\/s10915-012-9602-y","journal-title":"J. Sci. Comput."},{"key":"637_CR59","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/j.wavemoti.2015.12.004","volume":"62","author":"M Medvinsky","year":"2016","unstructured":"Medvinsky, M., Tsynkov, S., Turkel, E.: Solving the Helmholtz equation for general smooth geometry using simple grids. Wave Motion 62, 75\u201397 (2016). https:\/\/doi.org\/10.1016\/j.wavemoti.2015.12.004","journal-title":"Wave Motion"},{"issue":"9","key":"637_CR60","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/BF02995904","volume":"36","author":"J Nitsche","year":"1971","unstructured":"Nitsche, J.: \u00dcber ein variationsprinzip zur l\u00f6sung von Dirichlet-problemen bei verwendung von teilr\u00e4men, die keinen randbedingungen unterworfen sind. Abhandlungen aus dem mathematischen Seminar der Universit\u00e4t Hamburg 36(9), 9\u201315 (1971). https:\/\/doi.org\/10.1007\/BF02995904","journal-title":"Abhandlungen aus dem mathematischen Seminar der Universit\u00e4t Hamburg"},{"key":"637_CR61","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1017\/S0962492902000077","volume":"11","author":"CS Peskin","year":"2002","unstructured":"Peskin, C.S.: The immersed boundary method. Acta Numer. 11, 479\u2013517 (2002). https:\/\/doi.org\/10.1017\/S0962492902000077","journal-title":"Acta Numer."},{"key":"637_CR62","first-page":"1318","volume":"263","author":"AA Reznik","year":"1982","unstructured":"Reznik, A.A.: Approximation of surface potentials of elliptic operators by difference potentials. Dokl. Akad. Nauk SSSR 263, 1318\u20131321 (1982)","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"637_CR63","unstructured":"Reznik, A.A.: Approximation of the Surface Potentials of Elliptic Operators by Difference Potentials and the Solution of Boundary Value Problems. Ph.D. thesis, Moscow Institute for Physics and Technology (1983)"},{"issue":"2(242)","key":"637_CR64","first-page":"121","volume":"40","author":"VS Ryaben\u2019ki\u012d","year":"1985","unstructured":"Ryaben\u2019ki\u012d, V.S.: Boundary equations with projectors. Uspekhi Mat. Nauk 40(2(242)), 121\u2013149 (1985)","journal-title":"Uspekhi Mat. Nauk"},{"key":"637_CR65","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56344-7","volume-title":"Method of Difference Potentials and Its Applications","author":"VS Ryaben\u2019kii","year":"2002","unstructured":"Ryaben\u2019kii, V.S.: Method of Difference Potentials and Its Applications. Springer, Berlin (2002). https:\/\/doi.org\/10.1007\/978-3-642-56344-7"},{"issue":"3(405)","key":"637_CR66","doi-asserted-by":"crossref","first-page":"147","DOI":"10.4213\/rm9483","volume":"67","author":"VS Ryaben\u2019ki\u012d","year":"2012","unstructured":"Ryaben\u2019ki\u012d, V.S.: Difference potentials analogous to Cauchy integrals. Uspekhi Mat. Nauk 67(3(405)), 147\u2013172 (2012)","journal-title":"Uspekhi Mat. Nauk"},{"issue":"10","key":"637_CR67","doi-asserted-by":"publisher","first-page":"1768","DOI":"10.1134\/s0965542506100137","volume":"46","author":"VS Ryaben\u2019kii","year":"2006","unstructured":"Ryaben\u2019kii, V.S., Turchaninov, V.I., Epshteyn, Y.Y.: Algorithm composition scheme for problems in composite domains based on the difference potential method. Comp. Math. Math. Phys. 46(10), 1768\u20131784 (2006). https:\/\/doi.org\/10.1134\/s0965542506100137","journal-title":"Comp. Math. Math. Phys."},{"issue":"2","key":"637_CR68","doi-asserted-by":"publisher","first-page":"A993","DOI":"10.1137\/140966290","volume":"37","author":"RI Saye","year":"2015","unstructured":"Saye, R.I.: High-order quadrature methods for implicitly defined surfaces and volumes in hyperrectangles. SIAM J. Sci. Comput. 37(2), A993\u2013A1019 (2015). https:\/\/doi.org\/10.1137\/140966290","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"637_CR69","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1006\/jcph.2000.6581","volume":"163","author":"JA Sethian","year":"2000","unstructured":"Sethian, J.A., Wiegmann, A.: Structural boundary design via level set and immersed interface methods. J. Comput. Phys. 163(2), 489\u2013528 (2000). https:\/\/doi.org\/10.1006\/jcph.2000.6581","journal-title":"J. Comput. Phys."},{"key":"637_CR70","unstructured":"Sticko, S.: Towards Higher Order Immersed Finite Elements for the Wave Equation. Licentiate thesis, Uppsala University, Division of Scientific Computing (2016)"},{"key":"637_CR71","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1016\/j.cma.2016.06.001","volume":"309","author":"S Sticko","year":"2016","unstructured":"Sticko, S., Kreiss, G.: A stabilized Nitsche cut element method for the wave equation. Comput. Methods Appl. Mech. Eng. 309, 364\u2013387 (2016). https:\/\/doi.org\/10.1016\/j.cma.2016.06.001","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"637_CR72","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1006\/jcph.1994.1005","volume":"110","author":"B Strand","year":"1994","unstructured":"Strand, B.: Summation by parts for finite difference approximations for d\/dx. J. Comput. Phys. 110, 47\u201367 (1994). https:\/\/doi.org\/10.1006\/jcph.1994.1005","journal-title":"J. Comput. Phys."},{"key":"637_CR73","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.jcp.2014.02.031","volume":"268","author":"M Sv\u00e4rd","year":"2014","unstructured":"Sv\u00e4rd, M., Nordstr\u00f6m, J.: Review of summation-by-parts schemes for initial-boundary-value problems. J. Comput. Phys. 268, 17\u201338 (2014). https:\/\/doi.org\/10.1016\/j.jcp.2014.02.031","journal-title":"J. Comput. Phys."},{"issue":"2","key":"637_CR74","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1016\/j.jcp.2003.07.024","volume":"192","author":"YH Tseng","year":"2003","unstructured":"Tseng, Y.H., Ferziger, J.H.: A ghost-cell immersed boundary method for flow in complex geometry. J. Comput. Phys. 192(2), 593\u2013623 (2003). https:\/\/doi.org\/10.1016\/j.jcp.2003.07.024","journal-title":"J. Comput. Phys."},{"key":"637_CR75","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1007\/s10915-014-9817-1","volume":"61","author":"K Virta","year":"2014","unstructured":"Virta, K., Mattsson, K.: Acoustic wave propagation in complicated geometries and heterogeneous media. J. Sci. Comput. 61, 90\u2013118 (2014). https:\/\/doi.org\/10.1007\/s10915-014-9817-1","journal-title":"J. Sci. Comput."},{"issue":"3","key":"637_CR76","doi-asserted-by":"publisher","first-page":"791","DOI":"10.1007\/s10543-012-0417-x","volume":"53","author":"E Wadbro","year":"2013","unstructured":"Wadbro, E., Zahedi, S., Kreiss, G., Berggren, M.: A uniformly well-conditioned, unfitted Nitsche method for interface problems. BIT Numer. Math. 53(3), 791\u2013820 (2013). https:\/\/doi.org\/10.1007\/s10543-012-0417-x","journal-title":"BIT Numer. Math."},{"issue":"1","key":"637_CR77","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s10915-016-0297-3","volume":"71","author":"S Wang","year":"2017","unstructured":"Wang, S., Kreiss, G.: Convergence of summation-by-parts finite difference methods for the wave equation. J. Sci. Comput. 71(1), 219\u2013245 (2017). https:\/\/doi.org\/10.1007\/s10915-016-0297-3","journal-title":"J. Sci. Comput."},{"issue":"3","key":"637_CR78","doi-asserted-by":"publisher","first-page":"1002","DOI":"10.1007\/s10915-016-0165-1","volume":"68","author":"S Wang","year":"2016","unstructured":"Wang, S., Virta, K., Kreiss, G.: High order finite difference methods for the wave equation with non-conforming grid interfaces. J. Sci. Comput. 68(3), 1002\u20131028 (2016). https:\/\/doi.org\/10.1007\/s10915-016-0165-1","journal-title":"J. Sci. Comput."},{"key":"637_CR79","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1016\/j.jappgeo.2016.12.002","volume":"136","author":"Y Wang","year":"2017","unstructured":"Wang, Y., Zhou, H., Yuan, S., Ye, Y.: A fourth order accuracy summation-by-parts finite difference scheme for acoustic reverse time migration in boundary-conforming grids. J. Appl. Geophys. 136, 498\u2013512 (2017). https:\/\/doi.org\/10.1016\/j.jappgeo.2016.12.002","journal-title":"J. Appl. Geophys."},{"key":"637_CR80","doi-asserted-by":"crossref","unstructured":"Woodward, W.H.: On the Application of the Method of Difference Potentials to Linear Elastic Fracture Mechanics. Ph.D. thesis, The University of Manchester (2015)","DOI":"10.1002\/nme.4903"},{"issue":"10","key":"637_CR81","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1002\/nme.4903","volume":"103","author":"WH Woodward","year":"2015","unstructured":"Woodward, W.H., Utyuzhnikov, S., Massin, P.: On the application of the method of difference potentials to linear elastic fracture mechanics. Int. J. Numer. Methods Eng. 103(10), 703\u2013736 (2015). https:\/\/doi.org\/10.1002\/nme.4903","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"12","key":"637_CR82","doi-asserted-by":"publisher","first-page":"4588","DOI":"10.1016\/j.jcp.2011.02.037","volume":"230","author":"K Xia","year":"2011","unstructured":"Xia, K., Zhan, M., Wei, G.W.: MIB method for elliptic equations with multi-material interfaces. J. Comput. Phys. 230(12), 4588\u20134615 (2011). https:\/\/doi.org\/10.1016\/j.jcp.2011.02.037","journal-title":"J. Comput. Phys."},{"issue":"2","key":"637_CR83","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1006\/jcph.1999.6356","volume":"156","author":"T Ye","year":"1999","unstructured":"Ye, T., Mittal, R., Udaykumar, H., Shyy, W.: An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries. J. Comput. Phys. 156(2), 209\u2013240 (1999). https:\/\/doi.org\/10.1006\/jcph.1999.6356","journal-title":"J. Comput. Phys."},{"issue":"1","key":"637_CR84","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1016\/j.jcp.2007.08.003","volume":"227","author":"S Yu","year":"2007","unstructured":"Yu, S., Wei, G.: Three-dimensional matched interface and boundary (MIB) method for treating geometric singularities. J. Comput. Phys. 227(1), 602\u2013632 (2007). https:\/\/doi.org\/10.1016\/j.jcp.2007.08.003","journal-title":"J. Comput. Phys."},{"issue":"2","key":"637_CR85","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1016\/j.jcp.2006.10.030","volume":"224","author":"S Yu","year":"2007","unstructured":"Yu, S., Zhou, Y., Wei, G.W.: Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces. J. Comput. Phys. 224(2), 729\u2013756 (2007). https:\/\/doi.org\/10.1016\/j.jcp.2006.10.030","journal-title":"J. Comput. Phys."},{"issue":"1","key":"637_CR86","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jcp.2005.07.022","volume":"213","author":"Y Zhou","year":"2006","unstructured":"Zhou, Y., Zhao, S., Feig, M., Wei, G.W.: High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources. J. Comput. Phys. 213(1), 1\u201330 (2006). https:\/\/doi.org\/10.1016\/j.jcp.2005.07.022","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-017-0637-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0637-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-017-0637-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,30]],"date-time":"2024-06-30T11:57:54Z","timestamp":1719748674000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-017-0637-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,10]]},"references-count":86,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,8]]}},"alternative-id":["637"],"URL":"https:\/\/doi.org\/10.1007\/s10915-017-0637-y","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1,10]]}}}