Homotopy continuation methods for computer-aided process design |
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| Affiliation: | 1. Department of Mathematics, Harvard University, Cambridge, MA 02138, USA;2. Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;3. Mathematical Institute, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany;4. Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland;5. Franklin W. Olin College of Engineering, Needham, MA 02492, USA;1. The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark;2. Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands;3. Institute of Physics, Jagiellonian University, Reymonta 4, PL 30-059 Krakow, Poland;1. MTA Lendület Holographic QFT Group, Wigner Research Centre for Physics, H-1525 Budapest 114, P.O.B. 49, Hungary;2. Department of Mathematics, King''s College London, Strand, London WC2R 2LS, UK;1. Key Laboratory for Enhanced Oil & Gas Recovery of the Ministry of Education, Northeast Petroleum University, Daqing, 163318, China;2. School of Petroleum Engineering, Guangdong University of Petrochemical Technology, Maoming, 525000, China;3. Gas Recovery Plant No.3, PetroChina Changqing Oilfield Company, Xian, Shaanxi, 710000, China |
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| Abstract: | Homotopy continuation methods have been used by the authors and others to solve difficult chemical engineering flowsheeting and design problems involving the solution of simultaneous nonlinear equations. Such methods can fail when: (1) the homotopy path, which one follows from the solution of a simple problem to the solution of the original (difficult) problem, returns to a second solution of the simple problem; (2) the homotopy path strikes an interior boundary of the domain of definition of the original (vector-valued) function; and (3) the homotopy path goes off to infinity. For the first two modes of failure, the use of an affine homotopy is discussed here as a possible remedy. Failure due to an unbounded homotopy path is the subject of current research. |
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