相关论文: Preconditioners and Tensor Product Solvers for Opt…
In this paper, we propose a new finite element approach to simulate the time-dependent Ginzburg-Landau equations under the temporal gauge, and design an efficient preconditioner for the Newton iteration of the resulting discrete system. The…
We investigate the numerical discretization of a two-stream kinetic system with an internal state, such system has been introduced to model the motion of cells by chemotaxis. This internal state models the intracellular methylation level.…
We investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the…
Chemotaxis in bacteria such as \textit{E.\ coli} is controlled by the slow methylation of chemoreceptors. As a consequence, intrinsic time and length scales of tens of seconds and hundreds of micrometers emerge, making the Keller--Segel…
Engineering biology requires precise control of biomolecular circuits, and Cybergenetics is the field dedicated to achieving this goal. A significant challenge in developing controllers for cellular functions is designing systems that can…
The Keller--Segel PDE is a model for chemotaxis known to exhibit possible finite-time blow-up. Following a seminal work by Tello and Winkler, a logistic damping term is added in this PDE and local well-posedness of mild solutions is proven.…
Model predictive control (MPC) for linear dynamical systems requires solving an optimal control structured quadratic program (QP) at each sampling instant. This paper proposes a primal active-set strategy (PRESAS) for the efficient solution…
Gaussian process hyperparameter optimization requires linear solves with, and log-determinants of, large kernel matrices. Iterative numerical techniques are becoming popular to scale to larger datasets, relying on the conjugate gradient…
We consider a bilinear optimal control problem associated to the following chemotaxis-consumption model in a bounded domain $\Omega \subset \mathbb{R}^3$ during a time interval $(0,T)$: $$\partial_t u - \Delta u = - \nabla \cdot (u \nabla…
We study a Keller-Segel type chemotaxis model with a modified sensitivity function in a bounded domain $\Omega\subset \mathbb{R}^N$, $N\geq2$. The global existence of classical solutions to the fully parabolic system is established provided…
The purpose of this work is the study of \textit{chemotaxis} and how to model it through the equations of Keller-Segel. \textit{Chemotaxis} is a natural process which induces the organisms to direct their movement according to certain…
In this paper we deal with diffusive relaxation limits of nonlinear systems of Euler type modeling chemotactic movement of cells toward Keller--Segel type systems. The approximating systems are either hyperbolic--parabolic or…
Model predictive control (MPC) anticipates future events to take appropriate control actions. Nonlinear MPC (NMPC) describes systems with nonlinear models and/or constraints. A Continuation/GMRES Method for NMPC, suggested by T. Ohtsuka in…
A Keller-Segel model describes macroscopic dynamics of bacterial colonies and biological cells. Bacteria secret chemical which attracts other bacteria so that they move towards chemical gradient creating nonlocal attraction between…
Many techniques for real-time trajectory optimization and control require the solution of optimization problems at high frequencies. However, ill-conditioning in the optimization problem can significantly reduce the speed of first-order…
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization…
The Keller-Segel model is a system of partial differential equations that describes the movement of cells or organisms in response to chemical signals, a phenomenon known as chemotaxis. In this study, we analyze a doubly parabolic…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
A chemotaxis system possibly containing rotational components of the cross-diffusive flux is studied under no-flux boundary conditions in a bounded domain $\Omega\subset R^n$, $n\ge 1$, with smooth boundary, where the evolution of the…