{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T09:20:09Z","timestamp":1787390409363,"version":"build-2736575974"},"reference-count":43,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>Computational analysis of systems governed by partial differential equations (PDEs) requires not only the calculation of a solution but the extraction of additional information such as the sensitivity of that solution with respect to input parameters or the inversion of the system in an optimization or design loop. Moving beyond the automation of discretization of PDEs by finite element methods, we present a mathematical framework that unifies the discretization of PDEs with these additional analysis requirements. In particular, Fr\u00e9chet differentiation on a class of functionals together with a high-performance finite element framework has led to a code, called Sundance, that provides high-level programming abstractions for the automatic, efficient evaluation of finite variational forms together with the derived operators required by engineering analysis.<\/jats:p>","DOI":"10.1137\/09076920x","type":"journal-article","created":{"date-parts":[[2010,11,17]],"date-time":"2010-11-17T18:05:33Z","timestamp":1290017133000},"page":"3323-3351","source":"Crossref","is-referenced-by-count":31,"title":["Unified Embedded Parallel Finite Element Computations via Software-Based Fr\u00e9chet Differentiation"],"prefix":"10.1137","volume":"32","author":[{"given":"Kevin","family":"Long","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert","family":"Kirby","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bart","family":"van Bloemen Waanders","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,11,17]]},"reference":[{"key":"R1","unstructured":"M. S. Alnaes and A. Logg,\n                      UFL Specification and User Manual\n                      0.1, http:\/\/www.fenics.org\/ pub\/documents\/ufl\/ufl-user-manual\/ufl-user-manual.pdf (April 2009)."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1504\/IJCSE.2009.029160"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"V. I. Arnold,\n                      Mathematical Methods of Classical Mechanics\n                      , Springer-Verlag, New York, 1989.","DOI":"10.1007\/978-1-4757-2063-1"},{"key":"R4","unstructured":"B. Bagheri and L. Ridgway Scott,\n                      About Analysa\n                      , Technical report TR-2004-09, Department of Computer Science, University of Chicago, Chicago, IL, 2004."},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1145\/1268776.1268779"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1145\/1055531.1055533"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"J. J. Binney, N. J. Dowrick, A. J. Fisher, and M. E. J. Newman,\n                      The Theory of Critical Phenomena: An Introduction to the Renormalization Group\n                      , Oxford University Press, New York, 1992.","DOI":"10.1093\/oso\/9780198513940.001.0001"},{"key":"R8","doi-asserted-by":"crossref","unstructured":"P. M. Chaikin and T. C. Lubensky,\n                      Principles of Condensed-Matter Physics\n                      , Cambridge University Press, Cambridge, UK, 1995.","DOI":"10.1017\/CBO9780511813467"},{"key":"R9","unstructured":"S. Chandrasekhar,\n                      Hydrodynamic and Hydromagnetic Stability\n                      , Dover, New York, 1981."},{"key":"R10","doi-asserted-by":"crossref","unstructured":"E. W. Cheney,\n                      Analysis for Applied Mathematics\n                      , Springer-Verlag, New York, 2001.","DOI":"10.1007\/978-1-4757-3559-8"},{"key":"R11","unstructured":"S. S. Collis and M. Heinkenschloss,\n                      Analysis of the Streamline Upwind\/Petrov Galerkin Method Applied to the Solution of Optimal Control Problems\n                      , Technical report TR02-01, Department of Computational and Applied Mathematics, Rice University, Houston, TX, 2002."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1109\/78.942628"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2002.06.005"},{"key":"R14","unstructured":"H. Elman, D. Silvester, and A. Wathen,\n                      Finite Elements and Fast Linear Solvers\n                      , Oxford University Press, New York, 2005."},{"key":"R15","unstructured":"E. Gamma, R. Helm, R. Johnson, and J. Vlissides,\n                      Design Patterns: Elements of Reusable Object-Oriented Software\n                      , Addison-Wesley, Reading, MA, 1995."},{"key":"R16","unstructured":"A. Griewank,\n                      Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation\n                      , SIAM, Philadelphia, 2000."},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1145\/504210.504213"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"E. Guyon, J.P. Hulin, L. Petit, and C. D. Mitescu,\n                      Physical Hydrodynamics\n                      , Oxford University Press, Oxford, UK, 2001.","DOI":"10.1093\/oso\/9780198517467.001.0001"},{"key":"R19","unstructured":"F. Hecht, O. Pironneau, A. L. Hyaric, and K. Ohtsuka,\n                      FreeFEM$++$ Manual\n                      , 2005; available online from http:\/\/www.freefem.org."},{"key":"R20","unstructured":"M. Heroux, R. Bartlett, V. Howle, R. Heokstra, J. Hu, T. Kolda, R. Lehoucq, K. Long, R. Pawlowski, E. Phipps, A. Salinger, H. Thornquist, R. Tuminaro, J. Willenbring, and A. Williams,\n                      An Overview of Trilinos\n                      , Technical report SAND2003-2927, Sandia National Laboratories, Albuquerque, NM, 2003."},{"key":"R21","unstructured":"M. A. Heroux et al.\n                      The Trilinos Project\n                      , http:\/\/trilinos.sandia.gov\/(2010)."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1145\/1039813.1039820"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/040607824"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1145\/1163641.1163644"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1145\/1268769.1268771"},{"key":"R26","first-page":"articl","volume":"35","author":"Kirby R. C.","year":"2009","journal-title":"ACM Trans. Math. Software","ISSN":"https:\/\/id.crossref.org\/issn\/0098-3500","issn-type":"print"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1137\/050635547"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1137\/060660722"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1145\/1731022.1731030"},{"key":"R30","unstructured":"K. Long,\n                      Efficient discretization and differentiation of partial differential equations through automatic functional differentiation\n                      , in AD 2004\u2014Fourth International Workshop on Automatic Differentiation, B. Norris and P. Hovland, eds., Atlas Conferences, Toronto, 2004."},{"key":"R31","unstructured":"K. Long,\n                      Sundance $2.0$ Tutorial\n                      , Technical report SAND2004-4793, Sandia National Laboratories, Albuquerque, NM, 2004."},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1007\/BF02995904"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1145\/1644001.1644009"},{"key":"R34","unstructured":"S. J. Owen,\n                      Cubit $10.2$ Documentation\n                      , Technical report SAND2006-7156P, Sandia National Laboratories, Albuquerque, NM, 2006."},{"key":"R35","first-page":"81","volume":"14","author":"Prud'homme C.","year":"2006","journal-title":"Sci. Program.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-8504","issn-type":"print"},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2002.0566"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2008.925261"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2004.840306"},{"key":"R39","unstructured":"S. N. Rasband,\n                      Dynamics\n                      , John Wiley & Sons, New York, 1989."},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.2514\/2.457"},{"key":"R41","doi-asserted-by":"publisher","DOI":"10.1115\/1.1436090"},{"key":"R42","unstructured":"H. Sagan,\n                      Introduction to the Calculus of Variations\n                      , Dover, New York, 1993."},{"key":"R43","doi-asserted-by":"crossref","unstructured":"B. van Bloemen Waanders, R. Bartlett, K. Long, P. Boggs, and A. Salinger,\n                      Large Scale Nonlinear Programming for PDE Constrained Optimization\n                      , Technical report SAND2002-3198, Sandia National Laboratories, Albuquerque, NM, 2002.","DOI":"10.2172\/805833"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/09076920X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:34:14Z","timestamp":1787330054000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/09076920X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":43,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/09076920X"],"URL":"https:\/\/doi.org\/10.1137\/09076920x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}