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Numerical method for constrained opt...
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Kurochkin, Dmitry V.
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Numerical method for constrained optimization problems governed by nonlinear hyperbolic systems of PDEs.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Numerical method for constrained optimization problems governed by nonlinear hyperbolic systems of PDEs./
作者:
Kurochkin, Dmitry V.
面頁冊數:
103 p.
附註:
Source: Dissertation Abstracts International, Volume: 76-09(E), Section: B.
Contained By:
Dissertation Abstracts International76-09B(E).
標題:
Mathematics. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3703406
ISBN:
9781321752120
Numerical method for constrained optimization problems governed by nonlinear hyperbolic systems of PDEs.
Kurochkin, Dmitry V.
Numerical method for constrained optimization problems governed by nonlinear hyperbolic systems of PDEs.
- 103 p.
Source: Dissertation Abstracts International, Volume: 76-09(E), Section: B.
Thesis (Ph.D.)--Tulane University School of Science and Engineering, 2015.
This item must not be sold to any third party vendors.
We develop novel numerical methods for optimization problems subject to constraints given by nonlinear hyperbolic systems of conservation and balance laws in one space dimension. These types of control problems arise in a variety of applications, in which inverse problems for the corresponding initial value problems are to be solved. The optimization method can be seen as a block Gauss-Seidel iteration. The optimization requires one to numerically solve the hyperbolic system forward in time and the corresponding linear adjoint system backward in time. We test the optimization method on a number of control problems constrained by nonlinear hyperbolic systems of PDEs with both smooth and discontinuous prescribed terminal states. The theoretical foundation of the introduced scheme is provided in the case of scalar hyperbolic conservation laws on an unbounded domain with a strictly convex flux. In addition, we empirically demonstrate that using a higher-order temporal discretization helps to substantially improve both the efficiency and accuracy of the overall numerical method.
ISBN: 9781321752120Subjects--Topical Terms:
515831
Mathematics.
Numerical method for constrained optimization problems governed by nonlinear hyperbolic systems of PDEs.
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We develop novel numerical methods for optimization problems subject to constraints given by nonlinear hyperbolic systems of conservation and balance laws in one space dimension. These types of control problems arise in a variety of applications, in which inverse problems for the corresponding initial value problems are to be solved. The optimization method can be seen as a block Gauss-Seidel iteration. The optimization requires one to numerically solve the hyperbolic system forward in time and the corresponding linear adjoint system backward in time. We test the optimization method on a number of control problems constrained by nonlinear hyperbolic systems of PDEs with both smooth and discontinuous prescribed terminal states. The theoretical foundation of the introduced scheme is provided in the case of scalar hyperbolic conservation laws on an unbounded domain with a strictly convex flux. In addition, we empirically demonstrate that using a higher-order temporal discretization helps to substantially improve both the efficiency and accuracy of the overall numerical method.
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