Adaptive Virtual Element Method for Optimal Control Problem Governed by General Elliptic Equation

2021 ◽  
Vol 88 (1) ◽  
Author(s):  
Qiming Wang ◽  
Zhaojie Zhou
Keyword(s):  
Optimal Control ◽  
Elliptic Equation ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Virtual Element Method ◽  
General Elliptic ◽  
Virtual Element ◽  
Element Method

scholarly journals SUPG-Stabilized Virtual Element Method for Optimal Control Problem Governed by a Convection Dominated Diffusion Equation

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 723
Author(s):  
Qiming Wang ◽  
Zhaojie Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Diffusion Equation ◽  
Control Problem ◽  
State Equation ◽  
The State ◽  
Virtual Element Method ◽  
Adjoint State ◽  
Virtual Element ◽  
Convection Dominated

In this paper, the streamline upwind/Petrov Galerkin (SUPG) stabilized virtual element method (VEM) for optimal control problem governed by a convection dominated diffusion equation is investigated. The virtual element discrete scheme is constructed based on the first-optimize-then-discretize strategy and SUPG stabilized virtual element approximation of the state equation and adjoint state equation. An a priori error estimate is derived for both the state, adjoint state, and the control. Numerical experiments are carried out to illustrate the theoretical findings.

scholarly journals A numerical method of optimizing the stretch forming process for the production of panels

2019 ◽  
pp. 386-395
Author(s):  
К.С. Бормотин ◽  
А. Вин
Keyword(s):  
Finite Element Method ◽  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Program ◽  
The Finite Element Method ◽  
Forming Process ◽  
Residual Deformations ◽  
Element Method

Рассматривается моделирование технологий обтяжки на прессе для изготовления обшивок двойной кривизны. Автоматизированное формообразование деталей требует разработки управляющей программы и электронной модели пуансона. Качество полученной детали будет зависеть от точности вычисленной и изготовленной формы оснастки, задающей упреждающую форму панели, и траектории деформирования листовой заготовки. При условии заданной оснастки ставится задача оптимального управления для поиска наилучшей траектории движения зажимов в оборудовании. Вводятся критерии оптимизации процессов деформирования, которые обеспечивают минимальную поврежденность и максимальные остаточные деформации. Вычисление критериев выполняется с помощью моделирования и анализа нелинейного деформирования панели с контактными ограничениями методом конечных элементов. Формулируется дискретная задача оптимального управления, которая решается методом динамического программирования. Алгоритмы численного метода, реализованные в пакете программ MSC.Marc, позволяют вычислить оптимальные параметры работы обтяжного пресса. Программная реализация алгоритма выполнена в последовательном и параллельном режимах. На основе вычислительных экспериментов показана эффективность параллельного расчета на кластере вычислительных машин. We analyze the stretchforming technology using a press to manufacture the doublecurvature shells. The automated shaping of parts requires the development of a control program and an electronic model of a punch. The quality of the part obtained depends on the accuracy of the calculated and manufactured tools that specify the anticipated shape of the panel and on the deformation path of the sheet. Under the condition of a given tooling, an optimal control problem is formulated to find the best trajectory of movement of the clamps in the equipment. Some criteria for deformation optimization processes are introduced to ensure a minimum damage and maximum residual deformations. The calculation of the criteria is performed with the aid of modeling and analyzing the panel nonlinear deformation with contact constraints by the finite element method. The problems of inelastic deformation are solved by the finite element method. A discrete optimal control problem is formulated and solved by the methods of dynamic programming. The algorithms are implemented using the MSC.Marc package and allow us to calculate the optimal parameters of the stretchforming press in serial and parallel modes. The obtained numerical results show the efficiency of parallel implementations on a cluster of computers.

A morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraints

2018 ◽  
Vol 24 (3) ◽  
pp. 1181-1206 ◽  
Author(s):  
Susanne C. Brenner ◽  
Thirupathi Gudi ◽  
Kamana Porwal ◽  
Li-yeng Sung
Keyword(s):  
Finite Element Method ◽  
Optimal Control ◽  
Finite Element ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Constraints ◽  
Distributed Optimal Control ◽  
And Control ◽  
State And Control Constraints ◽  
Element Method

We design and analyze a Morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraints on convex polygonal domains. It is based on the formulation of the optimal control problem as a fourth order variational inequality. Numerical results that illustrate the performance of the method are also presented.

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