[图书][B] Optimal control of partial differential equations
This is a book on Optimal Control Problems (OCPs): how to formulate them, how to set up a
suitable mathematical framework for their analysis, how to approximate them numerically …
suitable mathematical framework for their analysis, how to approximate them numerically …
Topology optimization of unsteady incompressible Navier–Stokes flows
Y Deng, Z Liu, P Zhang, Y Liu, Y Wu - Journal of Computational Physics, 2011 - Elsevier
This paper discusses the topology optimization of unsteady incompressible Navier–Stokes
flows. An optimization problem is formulated by adding the artificial Darcy frictional force into …
flows. An optimization problem is formulated by adding the artificial Darcy frictional force into …
A novel W1,∞ approach to shape optimisation with Lipschitz domains
K Deckelnick, PJ Herbert, M Hinze - ESAIM: Control, Optimisation …, 2022 - esaim-cocv.org
This article introduces a novel method for the implementation of shape optimisation with
Lipschitz domains. We propose to use the shape derivative to determine deformation fields …
Lipschitz domains. We propose to use the shape derivative to determine deformation fields …
A continuous perspective on shape optimization via domain transformations
In this article we consider shape optimization problems as optimal control problems via the
method of mappings. Instead of optimizing over a set of admissible shapes, a reference …
method of mappings. Instead of optimizing over a set of admissible shapes, a reference …
Improved discrete boundary type shape gradients for PDE-constrained shape optimization
We propose in this paper two kinds of continuity preserving discrete shape gradients of
boundary type for PDE-constrained shape optimizations. First, a modified boundary shape …
boundary type for PDE-constrained shape optimizations. First, a modified boundary shape …
Numerical approximation of phase field based shape and topology optimization for fluids
We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the
Navier--Stokes equations. Inside a holdall container we use a phase field approach using …
Navier--Stokes equations. Inside a holdall container we use a phase field approach using …
[HTML][HTML] Mesh quality preserving shape optimization using nonlinear extension operators
S Onyshkevych, M Siebenborn - Journal of Optimization Theory and …, 2021 - Springer
In this article, we propose a shape optimization algorithm which is able to handle large
deformations while maintaining a high level of mesh quality. Based on the method of …
deformations while maintaining a high level of mesh quality. Based on the method of …
PDE-constrained models with neural network terms: Optimization and global convergence
Recent research has used deep learning to develop partial differential equation (PDE)
models in science and engineering. The functional form of the PDE is determined by a …
models in science and engineering. The functional form of the PDE is determined by a …
On discrete shape gradients of boundary type for PDE-constrained shape optimization
Shape gradients have been widely used in numerical shape gradient descent algorithms for
shape optimization. The two types of shape gradients, ie, the distributed one and the …
shape optimization. The two types of shape gradients, ie, the distributed one and the …
[HTML][HTML] Adjoint method for a tumor growth PDE-constrained optimization problem
DA Knopoff, DR Fernández, GA Torres… - Computers & Mathematics …, 2013 - Elsevier
In this paper we present a method for estimating unknown parameters that appear on an
avascular, spheric tumor growth model. The model for the tumor is based on nutrient driven …
avascular, spheric tumor growth model. The model for the tumor is based on nutrient driven …