HYHuidong Yang
Huidong Yang
*This is an algorithmically generated author record based on publicly available information.
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Huidong Yang has a total of 13 co-authors. Here are the top co-authors by number of shared publications:
- Olaf Steinbach
Institut für Angewandte Mathematik, TU Graz, Graz, Austria
10 shared publications - Richard Löscher
Institut für Angewandte Mathematik Technische Universität Graz Steyrergasse 30 8010 Graz Austria
10 shared publications - Ulrich Langer
Institute of Numerical Mathematics JKU Linz Austria
10 shared publications - Aleksei Kalinov
Institute of Science and Technology Austria, Klosterneuburg, Austria
1 shared publication - Arian Etemadi
ISTA (Institute of Science and Technology Austria), Klosterneuburg, Austria
1 shared publication - Chris Wojtan
Institute of Science and Technology Austria, Klosterneuburg, Austria
1 shared publication
Latest Publications
- 21 November 2025
- Published by Institute of Mathematics, Czech Academy of Sciences
- Vol. 70 (6) , 797-824
State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
Institute of Mathematics of the Czech Academy of Sciences
- 21 November 2025
- Published by Institute of Mathematics, Czech Academy of Sciences
- Vol. 70 (6) , 797-824
State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
Institute of Mathematics of the Czech Academy of Sciences
- Open Access
State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
We investigate the Dirichlet boundary control of the Laplace equation, considering the control in $H^{1/2}(\partial Ω)$, which is the natural space for Dirichlet data when the state belongs to $H^1(Ω)$. The cost of the control is measured in the $H^{1/2}(\partial Ω)$ norm that also plays the role of the regularization term. We discuss regularization and finite element error estimates enabling us to derive an optimal relation between the finite element mesh size $h$ and the regularization parameter $\varrho$, balancing the energy cost for the control and the accuracy of the approximation of the desired state. This relationship is also crucial in designing efficient solvers. We also discuss additional box constraints imposed on the control and the state. Our theoretical findings are complemented by numerical examples, including one example with box constraints.Open AccessState-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
We investigate the Dirichlet boundary control of the Laplace equation, considering the control in $H^{1/2}(\partial Ω)$, which is the natural space for Dirichlet data when the state belongs to $H^1(Ω)$. The cost of the control is measured in the $H^{1/2}(\partial Ω)$ norm that also plays the role of the regularization term. We discuss regularization and finite element error estimates enabling us to derive an optimal relation between the finite element mesh size $h$ and the regularization parameter $\varrho$, balancing the energy cost for the control and the accuracy of the approximation of the desired state. This relationship is also crucial in designing efficient solvers. We also discuss additional box constraints imposed on the control and the state. Our theoretical findings are complemented by numerical examples, including one example with box constraints. - Open Access
State-based nested iteration solution of optimal control problems with PDE constraints
We consider an abstract framework for the numerical solution of optimal control problems (OCPs) subject to partial differential equations (PDEs). Examples include not only the distributed control of elliptic PDEs such as the Poisson equation discussed in this paper in detail but also parabolic and hyperbolic equations. The approach covers the standard $L^2$ setting as well as the more recent energy regularization, also including state and control constraints. We discretize OCPs subject to parabolic or hyperbolic PDEs by means of space-time finite elements similar as in the elliptic case. We discuss regularization and finite element error estimates, and derive an optimal relation between the regularization parameter and the finite element mesh size in order to balance the accuracy, and the energy costs for the corresponding control. Finally, we also discuss the efficient solution of the resulting systems of algebraic equations, and their use in a state-based nested iteration procedure that allows us to compute finite element approximations to the state and the control in asymptotically optimal complexity. The numerical results illustrate the theoretical findings quantitatively.Open AccessState-based nested iteration solution of optimal control problems with PDE constraints
We consider an abstract framework for the numerical solution of optimal control problems (OCPs) subject to partial differential equations (PDEs). Examples include not only the distributed control of elliptic PDEs such as the Poisson equation discussed in this paper in detail but also parabolic and hyperbolic equations. The approach covers the standard $L^2$ setting as well as the more recent energy regularization, also including state and control constraints. We discretize OCPs subject to parabolic or hyperbolic PDEs by means of space-time finite elements similar as in the elliptic case. We discuss regularization and finite element error estimates, and derive an optimal relation between the regularization parameter and the finite element mesh size in order to balance the accuracy, and the energy costs for the corresponding control. Finally, we also discuss the efficient solution of the resulting systems of algebraic equations, and their use in a state-based nested iteration procedure that allows us to compute finite element approximations to the state and the control in asymptotically optimal complexity. The numerical results illustrate the theoretical findings quantitatively. - 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Control and Related Fields
- Vol. 15 (4) , 1496-1537
State-based nested iteration solution of a class of optimal control problems with PDE constraints
We consider an abstract framework for the numerical solution of optimal control problems (OCPs) subject to partial differential equations (PDEs). Examples include not only the distributed control of elliptic PDEs such as the Poisson equation discussed in this paper in detail but also parabolic and hyperbolic equations. The approach covers the standard $ L^2 $ setting as well as the more recent energy regularization, also including state and control constraints. We discretize OCPs subject to parabolic or hyperbolic PDEs by means of space-time finite elements, similar as in the elliptic case. We discuss regularization and finite element error estimates, and derive an optimal relation between the regularization parameter and the finite element mesh size in order to balance the accuracy, and the energy costs for the corresponding control. Finally, we also discuss the efficient solution of the resulting systems of algebraic equations, and their use in a state-based nested iteration procedure that allows us to compute finite element approximations to the state and the control in asymptotically optimal complexity. The numerical results illustrate the theoretical findings quantitatively.- 1 January 2025
- Published by American Institute of Mathematical Sciences (AIMS) in Mathematical Control and Related Fields
- Vol. 15 (4) , 1496-1537
State-based nested iteration solution of a class of optimal control problems with PDE constraints
We consider an abstract framework for the numerical solution of optimal control problems (OCPs) subject to partial differential equations (PDEs). Examples include not only the distributed control of elliptic PDEs such as the Poisson equation discussed in this paper in detail but also parabolic and hyperbolic equations. The approach covers the standard $ L^2 $ setting as well as the more recent energy regularization, also including state and control constraints. We discretize OCPs subject to parabolic or hyperbolic PDEs by means of space-time finite elements, similar as in the elliptic case. We discuss regularization and finite element error estimates, and derive an optimal relation between the regularization parameter and the finite element mesh size in order to balance the accuracy, and the energy costs for the corresponding control. Finally, we also discuss the efficient solution of the resulting systems of algebraic equations, and their use in a state-based nested iteration procedure that allows us to compute finite element approximations to the state and the control in asymptotically optimal complexity. The numerical results illustrate the theoretical findings quantitatively.- Open Access
- 4 October 2024
- Published by IOP Publishing in Inverse Problems
- Vol. 40 (11) , 115007
Diffraction tomography for incident Herglotz waves
Diffraction tomography (DT) is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the scattered waves induced from different incident field angles are recorded. In conventional DT, the incident wave is assumed to be a monochromatic plane wave, an unrealistic simplification in practical imaging scenarios. In this article, we extend conventional DT by introducing the concept of customized illumination scenarios, with a pronounced emphasis on imaging with focused beams. More specifically, we consider incident Herglotz waves and extend the classical Fourier diffraction theorem to this setting. This yields a new two-step reconstruction process which we comprehensively evaluate through numerical experiments.
- 4 October 2024
- Published by IOP Publishing in Inverse Problems
- Vol. 40 (11) , 115007
Open AccessDiffraction tomography for incident Herglotz waves
Diffraction tomography (DT) is an inverse scattering technique used to reconstruct the spatial distribution of the material properties of a weakly scattering object. The object is exposed to radiation, typically light or ultrasound, and the scattered waves induced from different incident field angles are recorded. In conventional DT, the incident wave is assumed to be a monochromatic plane wave, an unrealistic simplification in practical imaging scenarios. In this article, we extend conventional DT by introducing the concept of customized illumination scenarios, with a pronounced emphasis on imaging with focused beams. More specifically, we consider incident Herglotz waves and extend the classical Fourier diffraction theorem to this setting. This yields a new two-step reconstruction process which we comprehensively evaluate through numerical experiments.
- Open Access
- 19 July 2024
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Graphics
- Vol. 43 (4) , 1-14
Multi-Material Mesh-Based Surface Tracking with Implicit Topology Changes
We introduce a multi-material non-manifold mesh-based surface tracking algorithm that converts self-intersections into topological changes. Our algorithm generalizes prior work on manifold surface tracking with topological changes: it preserves surface features like mesh-based methods, and it robustly handles topological changes like level set methods. Our method also offers improved efficiency and robustness over the state of the art. We demonstrate the effectiveness of the approach on a range of examples, including complex soap film simulations with thousands of interacting bubbles, and boolean unions of non-manifold meshes consisting of millions of triangles.
- 19 July 2024
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Graphics
- Vol. 43 (4) , 1-14
Open AccessMulti-Material Mesh-Based Surface Tracking with Implicit Topology Changes
We introduce a multi-material non-manifold mesh-based surface tracking algorithm that converts self-intersections into topological changes. Our algorithm generalizes prior work on manifold surface tracking with topological changes: it preserves surface features like mesh-based methods, and it robustly handles topological changes like level set methods. Our method also offers improved efficiency and robustness over the state of the art. We demonstrate the effectiveness of the approach on a range of examples, including complex soap film simulations with thousands of interacting bubbles, and boolean unions of non-manifold meshes consisting of millions of triangles.
- 24 May 2024
- Published by Springer Nature
- p. 35-43
Robust Iterative Solvers for Algebraic Systems Arising from Elliptic Optimal Control Problems
- 24 May 2024
- Published by Springer Nature
- p. 35-43
Robust Iterative Solvers for Algebraic Systems Arising from Elliptic Optimal Control Problems
- Open Access
- 10 April 2024
- Published by Springer Nature in Advances in Computational Mathematics
- Vol. 50 (2) , 1-30
Robust space-time finite element methods for parabolic distributed optimal control problems with energy regularization
As in our previous work (SINUM59(2):660–674, 2021) we consider space-time tracking optimal control problems for linear parabolic initial boundary value problems that are given in the space-time cylinder $$Q = \Omega \times (0,T)$$ , and that are controlled by the right-hand side $$z_\varrho $$ from the Bochner space $$L^2(0,T;H^{-1}(\Omega ))$$ . So it is natural to replace the usual $$L^2(Q)$$ norm regularization by the energy regularization in the $$L^2(0,T;H^{-1}(\Omega ))$$ norm. We derive new a priori estimates for the error $$\Vert \widetilde{u}_{\varrho h} - \overline{u}\Vert _{L^2(Q)}$$ between the computed state $$\widetilde{u}_{\varrho h}$$ and the desired state $$\overline{u}$$ in terms of the regularization parameter $$\varrho $$ and the space-time finite element mesh sizeh, and depending on the regularity of the desired state $$\overline{u}$$ . These new estimates lead to the optimal choice $$\varrho = h^2$$ . The approximate state $$\widetilde{u}_{\varrho h}$$ is computed by means of a space-time finite element method using piecewise linear and continuous basis functions on completely unstructured simplicial meshes forQ. The theoretical results are quantitatively illustrated by a series of numerical examples in two and three space dimensions. We also provide performance studies for different solvers.- 10 April 2024
- Published by Springer Nature in Advances in Computational Mathematics
- Vol. 50 (2) , 1-30
Open AccessRobust space-time finite element methods for parabolic distributed optimal control problems with energy regularization
As in our previous work (SINUM59(2):660–674, 2021) we consider space-time tracking optimal control problems for linear parabolic initial boundary value problems that are given in the space-time cylinder $$Q = \Omega \times (0,T)$$ , and that are controlled by the right-hand side $$z_\varrho $$ from the Bochner space $$L^2(0,T;H^{-1}(\Omega ))$$ . So it is natural to replace the usual $$L^2(Q)$$ norm regularization by the energy regularization in the $$L^2(0,T;H^{-1}(\Omega ))$$ norm. We derive new a priori estimates for the error $$\Vert \widetilde{u}_{\varrho h} - \overline{u}\Vert _{L^2(Q)}$$ between the computed state $$\widetilde{u}_{\varrho h}$$ and the desired state $$\overline{u}$$ in terms of the regularization parameter $$\varrho $$ and the space-time finite element mesh sizeh, and depending on the regularity of the desired state $$\overline{u}$$ . These new estimates lead to the optimal choice $$\varrho = h^2$$ . The approximate state $$\widetilde{u}_{\varrho h}$$ is computed by means of a space-time finite element method using piecewise linear and continuous basis functions on completely unstructured simplicial meshes forQ. The theoretical results are quantitatively illustrated by a series of numerical examples in two and three space dimensions. We also provide performance studies for different solvers. - Open Access
Robust finite element solvers for distributed hyperbolic optimal control problems
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic distributed, tracking-type optimal control problems with both the standard $L^2$ and the more general energy regularizations. In contrast to the usual time-stepping approach, we discretize the optimality system by space-time continuous piecewise-linear finite element basis functions which are defined on fully unstructured simplicial meshes. If we aim at the asymptotically best approximation of the given desired state $y_d$ by the computed finite element state $y_{\varrho h}$, then the optimal choice of the regularization parameter $\varrho$ is linked to the space-time finite element mesh-size $h$ by the relations $\varrho=h^4$ and $\varrho=h^2$ for the $L^2$ and the energy regularization, respectively. For this setting, we can construct robust (parallel) iterative solvers for the reduced finite element optimality systems. These results can be generalized to variable regularization parameters adapted to the local behavior of the mesh-size that can heavily change in the case of adaptive mesh refinements. The numerical results illustrate the theoretical findings firmly.Open AccessRobust finite element solvers for distributed hyperbolic optimal control problems
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic distributed, tracking-type optimal control problems with both the standard $L^2$ and the more general energy regularizations. In contrast to the usual time-stepping approach, we discretize the optimality system by space-time continuous piecewise-linear finite element basis functions which are defined on fully unstructured simplicial meshes. If we aim at the asymptotically best approximation of the given desired state $y_d$ by the computed finite element state $y_{\varrho h}$, then the optimal choice of the regularization parameter $\varrho$ is linked to the space-time finite element mesh-size $h$ by the relations $\varrho=h^4$ and $\varrho=h^2$ for the $L^2$ and the energy regularization, respectively. For this setting, we can construct robust (parallel) iterative solvers for the reduced finite element optimality systems. These results can be generalized to variable regularization parameters adapted to the local behavior of the mesh-size that can heavily change in the case of adaptive mesh refinements. The numerical results illustrate the theoretical findings firmly. - Open Access
Parallel iterative solvers for discretized reduced optimality systems
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the solution of elliptic tracking-type distributed optimal control problems with both the standard $L_2$ and the more general energy regularizations. If we aim at an approximation of the given desired state $y_d$ by the computed finite element state $y_h$ that asymptotically differs from $y_d$ in the order of the best $L_2$ approximation under acceptable costs for the control, then the optimal choice of the regularization parameter $\varrho$ is linked to the mesh-size $h$ by the relations $\varrho=h^4$ and $\varrho=h^2$ for the $L_2$ and the energy regularization, respectively. For this setting, we can construct efficient parallel iterative solvers for the reduced finite element optimality systems. These results can be generalized to variable regularization parameters adapted to the local behavior of the mesh-size that can heavily change in case of adaptive mesh refinement. Similar results can be obtained for the space-time finite element discretization of the corresponding parabolic and hyperbolic optimal control problems.Open AccessParallel iterative solvers for discretized reduced optimality systems
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the solution of elliptic tracking-type distributed optimal control problems with both the standard $L_2$ and the more general energy regularizations. If we aim at an approximation of the given desired state $y_d$ by the computed finite element state $y_h$ that asymptotically differs from $y_d$ in the order of the best $L_2$ approximation under acceptable costs for the control, then the optimal choice of the regularization parameter $\varrho$ is linked to the mesh-size $h$ by the relations $\varrho=h^4$ and $\varrho=h^2$ for the $L_2$ and the energy regularization, respectively. For this setting, we can construct efficient parallel iterative solvers for the reduced finite element optimality systems. These results can be generalized to variable regularization parameters adapted to the local behavior of the mesh-size that can heavily change in case of adaptive mesh refinement. Similar results can be obtained for the space-time finite element discretization of the corresponding parabolic and hyperbolic optimal control problems.