{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T10:57:15Z","timestamp":1760266635276},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1996,3,1]],"date-time":"1996-03-01T00:00:00Z","timestamp":825638400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computing"],"published-print":{"date-parts":[[1996,3]]},"DOI":"10.1007\/bf02238289","type":"journal-article","created":{"date-parts":[[2005,11,14]],"date-time":"2005-11-14T17:39:14Z","timestamp":1131989954000},"page":"1-27","source":"Crossref","is-referenced-by-count":14,"title":["Massively parallel methods for semiconductor device modelling"],"prefix":"10.1007","volume":"56","author":[{"given":"R. K.","family":"Coomer","sequence":"first","affiliation":[]},{"given":"I. G.","family":"Graham","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"BF02238289_CR1","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1137\/0720034","volume":"20","author":"I. Babuska","year":"1983","unstructured":"Babuska, I., Osborne, J. E.: Generalised finite element methods: their performance and their relation to mixed methods. SIAM. J. Numer. Anal.20, 510\u2013536 (1983).","journal-title":"SIAM. J. Numer. Anal."},{"key":"BF02238289_CR2","volume-title":"PLTMG: A software package for solving elliptic partial differential equations","author":"R. E. Bank","year":"1990","unstructured":"Bank, R. E.: PLTMG: A software package for solving elliptic partial differential equations. Philadelphia: SIAM 1990."},{"key":"BF02238289_CR3","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0010-4655(89)90160-4","volume":"53","author":"R. E. Bank","year":"1989","unstructured":"Bank, R. E., Coughran, W. M., Driscoll, M. A., Smith, R. K., Fichtner, W.: Iterative methods in semiconductor device simulation. Comput. Phys. Commun.53, 201\u2013212 (1989).","journal-title":"Comput. Phys. Commun."},{"key":"BF02238289_CR4","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1137\/0904032","volume":"4","author":"R. E. Bank","year":"1983","unstructured":"Bank, R. E., Rose, D. J., Fichtner, W. F.: Numerical methods for semiconductor device simulation. SIAM J. Sci. Stat. Comp.4, 416\u2013435 (1983).","journal-title":"SIAM J. Sci. Stat. Comp."},{"key":"BF02238289_CR5","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1137\/0723075","volume":"23","author":"P. E. Bj\u00f8rstad","year":"1986","unstructured":"Bj\u00f8rstad, P. E., Widlund, O. B.: Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal.23, 1097\u20131120 (1986).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02238289_CR6","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1090\/S0025-5718-1986-0842125-3","volume":"47","author":"J. H. Bramble","year":"1986","unstructured":"Bramble, J. H., Pasciak, J. E., Schatz, A. H.: The construction of preconditioners for elliptic problems by substructuring. Math Comp.47, 103\u2013134 (1986).","journal-title":"Math Comp."},{"key":"BF02238289_CR7","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1016\/0045-7825(89)90044-3","volume":"75","author":"F. Brezzi","year":"1989","unstructured":"Brezzi, F., Marini, L. D., Pietra. P.: Numerical simulation of semiconductor devices. Comp. Meth. Appl. Mech. Eng.75, 493\u2013514 (1989).","journal-title":"Comp. Meth. Appl. Mech. Eng."},{"key":"BF02238289_CR8","volume-title":"The finite element method for elliptic problems","author":"P. G. Ciarlet","year":"1978","unstructured":"Ciarlet, P. G.: The finite element method for elliptic problems. Amsterdam: North-Holland 1978."},{"key":"BF02238289_CR9","unstructured":"Coomer., R. K.: Parallel iterative methods in semiconductor device modelling. PhD thesis, School of Mathematical Sciences, University of Bath, 1994."},{"key":"BF02238289_CR10","volume-title":"Domain decomposition techniques in science and engineering","author":"R. K. Coomer","year":"1994","unstructured":"Coomer, R. K., Graham, I. G.: Domain decomposition methods for device modelling. In: Keyes, D. E., Xu, J. (eds.) Domain decomposition techniques in science and engineering. Providence American Mathematical Society, 1994."},{"key":"BF02238289_CR11","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1137\/0913028","volume":"13","author":"P. M. Zeeuw De","year":"1992","unstructured":"De Zeeuw, P. M.: Nonlinear multigrid applied to a 1D stationary semiconductor model. SIAM J. Sci. Stat. Comp.13, 512\u2013530 (1992).","journal-title":"SIAM J. Sci. Stat. Comp."},{"key":"BF02238289_CR12","volume-title":"Iterative methods for large linear systems","author":"M. Dryja","year":"1989","unstructured":"Dryja, M., Widlund, O. B.: Some domain decomposition algorithms for elliptic problems. In: Hayes, L., Kincaid, D. (eds.) Iterative methods for large linear systems. Orlando: Academic Press 1989."},{"key":"BF02238289_CR13","volume-title":"Parallel algorithms for PDEs","author":"M. Dryja","year":"1991","unstructured":"Dryja, M., Widlund, O. B.: Multilevel additive methods for elliptic finite element problems. In: Hackbusch, W. (ed.) Parallel algorithms for PDEs. Braunschweig: Vieweg 1991."},{"key":"BF02238289_CR14","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1109\/T-ED.1964.15364","volume":"11","author":"H. K. Gummel","year":"1964","unstructured":"Gummel, H. K.: A self-consistent iterative scheme for one-dimensional steady state transistor calculations. IEEE Trans. Electronic Dev.ED-11, 455\u2013465 (1964).","journal-title":"IEEE Trans. Electronic Dev."},{"key":"BF02238289_CR15","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1137\/0145034","volume":"45","author":"J. W. Jerome","year":"1985","unstructured":"Jerome, J. W.: Consistency of semiconductor modeling: an existence\/stability analysis for the stationary Van Roosbroeck system. SIAM. J. Appl. Math.45, 565\u2013590 (1985).","journal-title":"SIAM. J. Appl. Math."},{"key":"BF02238289_CR16","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1137\/0728023","volume":"28","author":"J. W. Jerome","year":"1991","unstructured":"Jerome, J. W., Kerkhoven, T.: A finite element approximation theory for the drift diffusion semiconductor model. SIAM J. Numer. Anal.28, 403\u2013422 (1991).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02238289_CR17","volume-title":"Numerical solutions of partial differential equations by the finite element method","author":"C. Johnson","year":"1987","unstructured":"Johnson, C.: Numerical solutions of partial differential equations by the finite element method. Cambridge: Cambridge University Press 1987."},{"key":"BF02238289_CR18","unstructured":"Kerkhoven, T.: Coupled and decoupled algorithms for semiconductor simulation. PhD thesis, Department of Computer Science, Yale University, 1985 (Yale Research Report YALEU\/DCS\/RR-429)."},{"key":"BF02238289_CR19","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1137\/0723076","volume":"23","author":"T. Kerkhoven","year":"1986","unstructured":"Kerkhoven, T.: A proof of convergence of Gummel's algorithm for realistic device geometries. SIAM J. Numer. Anal.23, 1121\u20131136 (1986).","journal-title":"SIAM J. Numer. Anal."},{"key":"BF02238289_CR20","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1137\/0909005","volume":"9","author":"T. Kerkhoven","year":"1988","unstructured":"Kerkhoven, T.: On the effectiveness of Gummel's method. SIAM J. Sci. Stat. Comput.9, 48\u201360 (1988).","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"BF02238289_CR21","doi-asserted-by":"crossref","unstructured":"Mandel, J.: Hybrid domain decomposition with unstructured subdomains. Preprint, 1993.","DOI":"10.1090\/conm\/157\/01411"},{"key":"BF02238289_CR22","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7091-3678-2","volume-title":"The stationary semiconductor device equations","author":"P. A. Markowich","year":"1986","unstructured":"Markowich, P. A.: The stationary semiconductor device equations. Wien-New York: Springer 1986."},{"key":"BF02238289_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7091-6961-2","volume-title":"Semiconductor equations","author":"P. A. Markowich","year":"1990","unstructured":"Markowich, P. A., Ringhofer, C. A., Schmeiser, C.: Semiconductor equations. Wien-New York: Springer 1990."},{"key":"BF02238289_CR24","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1090\/S0025-5718-1988-0930223-7","volume":"51","author":"P. A. Markowich","year":"1988","unstructured":"Markowich, P. A., Zl\u00e1mal, M. A.: Inverse-average-type finite element discretizations of selfadjoint second-order elliptic problems. Math. Comput.51, 431\u2013449 (1988).","journal-title":"Math. Comput."},{"key":"BF02238289_CR25","unstructured":"MasPar Computer corporation, Sunnyvale, California, 1990. MasPar system overview."},{"key":"BF02238289_CR26","volume-title":"Iterative solution of nonlinear equations in several variables","author":"J. M. Ortega","year":"1970","unstructured":"Ortega, J. M., Rheinboldt, W. C.: Iterative solution of nonlinear equations in several variables. New York: Academic Press 1970."},{"key":"BF02238289_CR27","volume-title":"Numerical heat transfer and fluid flow","author":"S. V. Patankar","year":"1980","unstructured":"Patankar, S. V.: Numerical heat transfer and fluid flow. New York: McGraw-Hill 1980."},{"key":"BF02238289_CR28","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1002\/nme.1620240408","volume":"24","author":"S. J. Polak","year":"1987","unstructured":"Polak, S. J., Den Heijer, C., Schilders, W. H. A., Markowich, P.: Semiconductor device modelling from the numerical point of view. Int. J. Numer. Meth. Eng.24, 763\u2013838 (1987).","journal-title":"Int. J. Numer. Meth. Eng."},{"key":"BF02238289_CR29","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1016\/0362-546X(87)90037-X","volume":"11","author":"F. A. Potra","year":"1987","unstructured":"Potra, F. A.: Newton-like methods with monotone convergence for solving nonlinear operator equations. Nonlinear Anal. Theory Meth. Appl.11, 697\u2013717 (1987).","journal-title":"Nonlinear Anal. Theory Meth. Appl."},{"key":"BF02238289_CR30","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/T-ED.1969.16566","volume":"16","author":"D. L. Scharfetter","year":"1991","unstructured":"Scharfetter, D. L., Gummel, H. K.: Large-signal analysis of a silicon Read diode oscillator. IEEE Trans. Electron Dev.ED-16, 64\u201377 (1991).","journal-title":"IEEE Trans. Electron Dev."},{"key":"BF02238289_CR31","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF01385722","volume":"60","author":"B. F. Smith","year":"1991","unstructured":"Smith, B. F.: A domain decomposition algorithm for elliptic problems in three dimensions. Numer. Math.60, 219\u2013234 (1991).","journal-title":"Numer. Math."},{"key":"BF02238289_CR32","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1137\/0913019","volume":"13","author":"B. F. Smith","year":"1992","unstructured":"Smith, B. F.: An optimal domain decomposition preconditioner for the finite element solution of linear elasticity problems. SIAM. J. Sci. Stat. Comput.13, 364\u2013378 (1992).","journal-title":"SIAM. J. Sci. Stat. Comput."},{"key":"BF02238289_CR33","doi-asserted-by":"crossref","first-page":"1212","DOI":"10.1137\/0911069","volume":"11","author":"B. F. Smith","year":"1990","unstructured":"Smith, B. F., Widlund, O. B.: A domain decomposition algorithm using a hierarchical basis. SIAM J. Sci. Stat. Comp.11, 1212\u20131220 (1990).","journal-title":"SIAM J. Sci. Stat. Comp."},{"key":"BF02238289_CR34","doi-asserted-by":"crossref","first-page":"1334","DOI":"10.1109\/43.177397","volume":"11","author":"Z.-Y. Wang","year":"1992","unstructured":"Wang, Z.-Y., Wu, K.-C., Dutton, R. W.: An approach to construct pre conditioning matrices for block iteration of linear equations. IEEE Trans. CAD11, 1334\u20131343 (1992).","journal-title":"IEEE Trans. CAD"},{"key":"BF02238289_CR35","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1109\/43.24881","volume":"8","author":"K.-C. Wu","year":"1989","unstructured":"Wu, K.-C., Lucas, Z.-Y., Dutton, R. W.: New approaches in a 3D one-carrier device solver. IEEE Trans. CAD8, 528\u2013537 (1989).","journal-title":"IEEE Trans. CAD"}],"container-title":["Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02238289.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02238289\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02238289","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,10]],"date-time":"2020-04-10T21:29:47Z","timestamp":1586554187000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02238289"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,3]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,3]]}},"alternative-id":["BF02238289"],"URL":"https:\/\/doi.org\/10.1007\/bf02238289","relation":{},"ISSN":["0010-485X","1436-5057"],"issn-type":[{"value":"0010-485X","type":"print"},{"value":"1436-5057","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,3]]}}}