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Different types of evolutionary algorithms have been developed for constrained continuous optimization. We carry out a feature-based analysis of evolved constrained continuous optimization instances to understand the characteristics of…
Internal microscopic symmetry of a many body system leads to global constraints. We obtain explicit forms of the global macroscopic condition assuring that at the microscopic level the evolution respects the overall symmetry.
We consider solutions of two-dimensional $m \times m$ systems hyperbolic conservation laws that are constant in time and along rays starting at the origin. The solutions are assumed to be small $L^\infty$ perturbations of a constant state…
In this paper we study the general relationship between the evolutionary conditions for discontinuous solutions of hyperbolic conservation laws with a concave entropy function and the existence and uniqueness of steady dissipative shock…
This paper studies set-invariance and stabilization of hyperbolic sets over rate-limited channels for discrete-time control systems. We first investigate structural and control-theoretic properties of hyperbolic sets, in particular such…
This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially)…
We shall deal with both the barotropic and the full compressible Euler system in multiple space dimensions. Both systems are particular examples of hyperbolic conservation laws. Whereas for scalar conservation laws there exists a well-known…
We investigate the initial-boundary value problem for linearized gravitational theory in harmonic coordinates. Rigorous techniques for hyperbolic systems are applied to establish well-posedness for various reductions of the system into a…
We review some recent advances in the field of element-based algebraic stabilization for continuous finite element discretizations of nonlinear hyperbolic problems. The main focus is on multidimensional convex limiting techniques designed…
Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of…
We study the robust output regulation of linear boundary control systems by constructing extended systems. The extended systems are established based on solving static differential equations under two new conditions. We first consider the…
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution…
We present our numerical comparisons between the BSSN formulation widely used in numerical relativity today and its adjusted versions using constraints. We performed three testbeds: gauge-wave, linear wave, and Gowdy-wave tests, proposed by…
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…
This work focuses on the numerical solution of hyperbolic conservations laws (possibly endowed with a source term) using the Active Flux method. This method is an extension of the finite volume method. Instead of solving a Riemann Problem,…
The augmented Lagrange method is employed to address the optimal control problem involving pointwise state constraints in parabolic equations. The strong convergence of the primal variables and the weak convergence of the dual variables are…
We are interested in supporting software evolution caused by changing requirements and/or environmental settings. For example, users of a system may require new functionality (changing requirements), or performance enhancements to cope with…
The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on "asymptotically constrained" systems, we here…
We study the boundary control of solutions of the Helmholtz and Maxwell equations to enforce local non-zero constraints. These constraints may represent the local absence of nodal or critical points, or that certain functionals depending on…
This work is devoted to the design of boundary controls of physical systems that are described by semilinear hyperbolic balance laws. A computational framework is presented that yields sufficient conditions for a boundary control to steer…