Journal Title
Title of Journal: Comput Geosci
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Abbravation: Computational Geosciences
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Publisher
Springer International Publishing
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Authors: Xiang Li Dongxiao Zhang
Publish Date: 2014/09/17
Volume: 18, Issue: 6, Pages: 1009-1022
Abstract
In numerical reservoir simulations Newton’s method is a concise robust and perhaps the most commonly used method to solve nonlinear partial differential equations PDEs However as reservoir simulators incorporate more and more physical and chemical phenomena writing codes that compute gradients for reservoir simulation equations can become quite complicated This paper presents an automatic differentiation AD framework that is specially designed for simplifying coding and simultaneously maintaining computational efficiency First a parse tree for a mathematical expression is built and evaluated with the backward mode AD and then the derivatives with respect to the expression’s arguments are transformed to derivatives with respect to the PDE’s independent variables The first stage can be realized either by runtime polymorphism to gain higher flexibility or by compiletime polymorphism to gain faster execution speed the second stage is realized by linear combinations of sparse vectors which can be accelerated by recording the target column indices The AD framework has been implemented in an inhouse reservoir simulator Individual tests on some complex mathematical expressions were carried out to compare the speed of the manual implementation the runtime polymorphic implementation and the compiletime polymorphic implementation of the differentiation Then the performance of the three was analyzed in complete simulations These cases indicate that the proposed approach has good efficiency and is applicable to reservoir simulationsThis article is published under an open access license Please check the Copyright Information section for details of this license and what reuse is permitted If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and reuse information please contact the Rights and Permissions team
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