کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6422470 1632010 2015 40 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
An equation-based algorithmic differentiation technique for differential algebraic equations
ترجمه فارسی عنوان
معادله مبتنی بر الگوریتم روش تمایز برای معادلات جبری دیفرانسیل
کلمات کلیدی
تمایز الگوریتمی، معادلات جبری دیفرانسیل، تجزیه و تحلیل میزان حساسیت، الگوریتم درخت، زبان های مبتنی بر معادله، مدلیکا،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی
This work presents a novel Algorithmic Differentiation (AD) approach for sensitivity analysis of Differential Algebraic Equation systems (DAEs). For the first time, the algorithmic specification of a computationally memory-efficient equation-based AD technique is presented. This approach is mainly targeting equation-based modeling and simulation tools capable of constructing high-level models using state of the art object-oriented modeling principles. The approach is based on fundamental tree algorithms that are (even manually) applicable on implicit equation systems of long formulas, the main building blocks of model components. By applying the presented forward differentiation scheme on a given DAE, efficient representation of Sensitivity Equation Systems (SESs) is computed. Parameter sensitivities are evaluated by direct integration of the derived SESs. To overcome the runtime performance drawback of direct numerical integration, a system decomposition approach is recommended. It is shown that the runtime performance using modern variable-step integration methods tends to achieve the expected theoretical complexity of the forward differentiation scheme under few realistic assumptions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 281, June 2015, Pages 135-151
نویسندگان
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