{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:39:50Z","timestamp":1740123590689,"version":"3.37.3"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T00:00:00Z","timestamp":1620000000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T00:00:00Z","timestamp":1620000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["EAR-1547596","EAR-1547603"],"award-info":[{"award-number":["EAR-1547596","EAR-1547603"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["EAR-1916992"],"award-info":[{"award-number":["EAR-1916992"]}],"id":[{"id":"10.13039\/100000001","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":[[2021,6]]},"DOI":"10.1007\/s10915-021-01448-5","type":"journal-article","created":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T21:18:31Z","timestamp":1620076711000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Hybridized Summation-by-Parts Finite Difference Methods"],"prefix":"10.1007","volume":"87","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2493-4292","authenticated-orcid":false,"given":"Jeremy E.","family":"Kozdon","sequence":"first","affiliation":[]},{"given":"Brittany A.","family":"Erickson","sequence":"additional","affiliation":[]},{"given":"Lucas C.","family":"Wilcox","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,3]]},"reference":[{"issue":"1","key":"1448_CR1","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1137\/141000671","volume":"59","author":"J Bezanson","year":"2017","unstructured":"Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65\u201398 (2017). https:\/\/doi.org\/10.1137\/141000671","journal-title":"SIAM Rev."},{"issue":"2","key":"1448_CR2","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(2), 220\u2013236 (1994). https:\/\/doi.org\/10.1006\/jcph.1994.1057","journal-title":"J. Comput. Phys."},{"issue":"2","key":"1448_CR3","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1006\/jcph.1998.6114","volume":"148","author":"MH Carpenter","year":"1999","unstructured":"Carpenter, M.H., Nordstr\u00f6m, J., Gottlieb, D.: A stable and conservative interface treatment of arbitrary spatial accuracy. J. Comput. Phys. 148(2), 341\u2013365 (1999). https:\/\/doi.org\/10.1006\/jcph.1998.6114","journal-title":"J. Comput. Phys."},{"issue":"3","key":"1448_CR4","doi-asserted-by":"publisher","first-page":"22:1","DOI":"10.1145\/1391989.1391995","volume":"3","author":"Y Chen","year":"2008","unstructured":"Chen, Y., Davis, T.A., Hager, W.W., Rajamanickam, S.: Algorithm 887: Cholmod, supernodal sparse Cholesky factorization and update\/downdate. ACM Trans. Math. Softw. 3(3), 22:1-22:14 (2008). https:\/\/doi.org\/10.1145\/1391989.1391995","journal-title":"ACM Trans. Math. Softw."},{"key":"1448_CR5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719208","volume-title":"The Finite Element Method for Elliptic Problems","author":"PG Ciarlet","year":"2002","unstructured":"Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. Society for Industrial and Applied Mathematics, Philadelphia (2002). https:\/\/doi.org\/10.1137\/1.9780898719208"},{"issue":"2","key":"1448_CR6","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1137\/070706616","volume":"47","author":"B Cockburn","year":"2009","unstructured":"Cockburn, B., Gopalakrishnan, J., Lazarov, R.: Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems. SIAM J. Numer. Anal. 47(2), 1319\u20131365 (2009). https:\/\/doi.org\/10.1137\/070706616","journal-title":"SIAM J. Numer. Anal."},{"key":"1448_CR7","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718881","volume-title":"Direct methods for sparse linear systems","author":"TA Davis","year":"2006","unstructured":"Davis, T.A.: Direct methods for sparse linear systems. Society for Industrial and Applied Mathematics, Philadelphia (2006). https:\/\/doi.org\/10.1137\/1.9780898718881"},{"key":"1448_CR8","doi-asserted-by":"publisher","first-page":"2480","DOI":"10.1002\/2015JB012470","volume":"121","author":"BA Erickson","year":"2016","unstructured":"Erickson, B.A., Day, S.M.: Bimaterial effects in an earthquake cycle model using rate-and-state friction. J. Geophys. Res. Solid Earth 121, 2480\u20132506 (2016). https:\/\/doi.org\/10.1002\/2015JB012470","journal-title":"J. Geophys. Res. Solid Earth"},{"issue":"4","key":"1448_CR9","doi-asserted-by":"publisher","first-page":"3290","DOI":"10.1002\/2013JB010614","volume":"119","author":"BA Erickson","year":"2014","unstructured":"Erickson, B.A., Dunham, E.M.: An efficient numerical method for earthquake cycles in heterogeneous media: alternating subbasin and surface-rupturing events on faults crossing a sedimentary basin. J. Geophys. Res. Solid Earth 119(4), 3290\u20133316 (2014). https:\/\/doi.org\/10.1002\/2013JB010614","journal-title":"J. Geophys. Res. Solid Earth"},{"issue":"3","key":"1448_CR10","doi-asserted-by":"publisher","first-page":"A1233","DOI":"10.1137\/120890144","volume":"35","author":"G Gassner","year":"2013","unstructured":"Gassner, G.: A skew-symmetric discontinuous Galerkin spectral element discretization and its relation to SBP-SAT finite difference methods. SIAM J. Sci. Comput. 35(3), A1233\u2013A1253 (2013). https:\/\/doi.org\/10.1137\/120890144","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"1448_CR11","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1137\/0710032","volume":"10","author":"A George","year":"1973","unstructured":"George, A.: Nested dissection of a regular finite element mesh. SIAM J. Numer. Anal. 10(2), 345\u2013363 (1973). https:\/\/doi.org\/10.1137\/0710032","journal-title":"SIAM J. Numer. Anal."},{"issue":"2","key":"1448_CR12","doi-asserted-by":"publisher","first-page":"380","DOI":"10.2514\/3.2874","volume":"3","author":"RJ Guyan","year":"1965","unstructured":"Guyan, R.J.: Reduction of stiffness and mass matrices. AIAA J. 3(2), 380 (1965). https:\/\/doi.org\/10.2514\/3.2874","journal-title":"AIAA J."},{"key":"1448_CR13","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1017\/jfm.2016.257","volume":"797","author":"L Karlstrom","year":"2016","unstructured":"Karlstrom, L., Dunham, E.M.: Excitation and resonance of acoustic-gravity waves in a column of stratified, bubbly magma. J. Fluid Mech. 797, 431\u2013470 (2016). https:\/\/doi.org\/10.1017\/jfm.2016.257","journal-title":"J. Fluid Mech."},{"key":"1448_CR14","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/s10915-011-9485-3","volume":"50","author":"JE Kozdon","year":"2012","unstructured":"Kozdon, J.E., Dunham, M., Nordstr\u00f6m, J.: Interaction of waves with frictional interfaces using summation-by-parts difference operators: weak enforcement of nonlinear boundary conditions. J. Sci. Comput. 50, 341\u2013367 (2012). https:\/\/doi.org\/10.1007\/s10915-011-9485-3","journal-title":"J. Sci. Comput."},{"issue":"2","key":"1448_CR15","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(2), A923\u2013A952 (2016). https:\/\/doi.org\/10.1137\/15M1022823","journal-title":"SIAM J. Sci. Comput."},{"key":"1448_CR16","doi-asserted-by":"publisher","unstructured":"Kreiss, H., Scherer, G.: Finite element and finite difference methods for hyperbolic partial differential equations. In: Mathematical Aspects of Finite Elements in Partial Differential Equations; Proceedings of the Symposium, Madison, WI, 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"},{"key":"1448_CR17","unstructured":"Kreiss, H., Scherer, G.: On the Existence of Energy Estimates for Difference Approximations for Hyperbolic Systems. Technical report, Department of Scientific Computing, Uppsala University (1977)"},{"issue":"2","key":"1448_CR18","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1007\/s10596-015-9472-0","volume":"19","author":"GC Lotto","year":"2015","unstructured":"Lotto, G.C., Dunham, E.M.: High-order finite difference modeling of tsunami generation in a compressible ocean from offshore earthquakes. Comput. Geosci. 19(2), 327\u2013340 (2015). https:\/\/doi.org\/10.1007\/s10596-015-9472-0","journal-title":"Comput. Geosci."},{"issue":"3","key":"1448_CR19","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 coefficients. J. Sci. Comput. 51(3), 650\u2013682 (2012). https:\/\/doi.org\/10.1007\/s10915-011-9525-z","journal-title":"J. Sci. Comput."},{"issue":"4","key":"1448_CR20","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(4), 2298\u20132320 (2010). https:\/\/doi.org\/10.1137\/090750068","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"1448_CR21","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1007\/s10915-009-9305-1","volume":"41","author":"K Mattsson","year":"2009","unstructured":"Mattsson, K., Ham, F., Iaccarino, G.: Stable boundary treatment for the wave equation on second-order form. J. Sci. Comput. 41(3), 366\u2013383 (2009). https:\/\/doi.org\/10.1007\/s10915-009-9305-1","journal-title":"J. Sci. Comput."},{"issue":"2","key":"1448_CR22","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1016\/j.jcp.2004.03.001","volume":"199","author":"K Mattsson","year":"2004","unstructured":"Mattsson, K., Nordstr\u00f6m, J.: Summation by parts operators for finite difference approximations of second derivatives. J. Comput. Phys. 199(2), 503\u2013540 (2004). https:\/\/doi.org\/10.1016\/j.jcp.2004.03.001","journal-title":"J. Comput. Phys."},{"issue":"1","key":"1448_CR23","doi-asserted-by":"publisher","first-page":"103","DOI":"10.4208\/cicp.2009.08.135","volume":"7","author":"K Mattsson","year":"2010","unstructured":"Mattsson, K., Parisi, F.: Stable and accurate second-order formulation of the shifted wave equation. Commun. Comput. Phys. 7(1), 103 (2010). https:\/\/doi.org\/10.4208\/cicp.2009.08.135","journal-title":"Commun. Comput. Phys."},{"issue":"1","key":"1448_CR24","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/s10915-012-9628-1","volume":"55","author":"A Nissen","year":"2013","unstructured":"Nissen, A., Kreiss, G., Gerritsen, M.: High order stable finite difference methods for the Schr\u00f6dinger equation. J. Sci. Comput. 55(1), 173\u2013199 (2013). https:\/\/doi.org\/10.1007\/s10915-012-9628-1","journal-title":"J. Sci. Comput."},{"issue":"1","key":"1448_CR25","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1006\/jcph.2001.6864","volume":"173","author":"J Nordstr\u00f6m","year":"2001","unstructured":"Nordstr\u00f6m, J., Carpenter, M.H.: High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates. J. Comput. Phys. 173(1), 149\u2013174 (2001). https:\/\/doi.org\/10.1006\/jcph.2001.6864","journal-title":"J. Comput. Phys."},{"key":"1448_CR26","volume-title":"Verification and Validation in Computational Science and Engineering","author":"P Roache","year":"1998","unstructured":"Roache, P.: Verification and Validation in Computational Science and Engineering, 1st edn. Hermosa Publishers, Albuquerque (1998)","edition":"1"},{"key":"1448_CR27","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.jcp.2018.01.011","volume":"359","author":"AA Ruggiu","year":"2018","unstructured":"Ruggiu, A.A., Weinerfelt, P., Nordstr\u00f6m, J.: A new multigrid formulation for high order finite difference methods on summation-by-parts form. J. Comput. Phys. 359, 216\u2013238 (2018). https:\/\/doi.org\/10.1016\/j.jcp.2018.01.011","journal-title":"J. Comput. Phys."},{"issue":"1","key":"1448_CR28","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(1), 47\u201367 (1994). https:\/\/doi.org\/10.1006\/jcph.1994.1005","journal-title":"J. Comput. Phys."},{"key":"1448_CR29","doi-asserted-by":"publisher","unstructured":"Thom\u00e9e, V.: From finite differences to finite elements: a short history of numerical analysis of partial differential equations. In: Numerical Analysis: Historical Developments in the 20th Century, pp. 361\u2013414. Elsevier, Amsterdam (2001). https:\/\/doi.org\/10.1016\/S0377-0427(00)00507-0","DOI":"10.1016\/S0377-0427(00)00507-0"},{"issue":"1","key":"1448_CR30","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(1), 90\u2013118 (2014). https:\/\/doi.org\/10.1007\/s10915-014-9817-1","journal-title":"J. Sci. Comput."},{"issue":"3","key":"1448_CR31","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."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01448-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-021-01448-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01448-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T18:29:55Z","timestamp":1621880995000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-021-01448-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,3]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["1448"],"URL":"https:\/\/doi.org\/10.1007\/s10915-021-01448-5","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2021,5,3]]},"assertion":[{"value":"31 January 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 February 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 February 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 May 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The Julia based computer codes used that support the findings of this study are available in the github repository .","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}}],"article-number":"85"}}