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Robust Model Predictive Control (MPC) for nonlinear systems is a problem that poses significant challenges as highlighted by the diversity of approaches proposed in the last decades. Often compromises with respect to computational load,…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…
This paper presents a study of the inherent structural properties of Krylov subspaces, in particular for the self-adjoint class of operators, and how they relate with the important phenomenon of `Krylov solvability' of linear inverse…
The computation of sparse solutions of large-scale linear discrete ill-posed problems remains a computationally demanding task. A powerful framework in this context is the use of iteratively reweighted schemes, which are based on…
Stability, reachability, and safety are crucial properties of dynamical systems. While verification and control synthesis of reach-avoid-stay objectives can be effectively handled by abstraction-based formal methods, such approaches can be…
We consider the iterative solution of symmetric saddle-point matrices with a singular leading block. We develop a new ideal positive definite block diagonal preconditioner that yields a preconditioned operator with four distinct…
In this paper, a novel dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations is introduced. The discretization satisfies pointwise conservation of mass, magnetic Gauss's law, and…
Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners for solving symmetric positive definite (SPD) systems. In…
Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…
Designing efficient and high-accuracy numerical methods for complex dynamic incompressible magnetohydrodynamics (MHD) equations remains a challenging problem in various analysis and design tasks. This is mainly due to the nonlinear coupling…
Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data,…
Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block…
In this paper we develop adaptive numerical schemes for certain nonlinear variational problems. The discretization of the variational problems is done by representing the solution as a suitable frame decomposition, i.e., a complete, stable,…
Solving the indefinite Helmholtz equation is not only crucial for the understanding of many physical phenomena but also represents an outstandingly-difficult benchmark problem for the successful application of numerical methods. Here we…
This paper proposes a new preconditioning scheme for a linear system with a saddle-point structure arising from a hybrid approximation scheme on the sphere, an approximation scheme that combines (local) spherical radial basis functions and…
The problem of robust hedging requires to solve the problem of superhedging under a nondominated family of singular measures. Recent progress was achieved by [9,11]. We show that the dual formulation of this problem is valid in a context…
We consider a mixed hybrid finite element formulation for coupled poromechanics. A stabilization strategy based on a macro-element approach is advanced to eliminate the spurious pressure modes appearing in undrained/incompressible…
Despite extraordinary progress, current machine learning systems have been shown to be brittle against adversarial examples: seemingly innocuous but carefully crafted perturbations of test examples that cause machine learning predictors to…
We propose a rigorous, conservative invariant-domain preserving (IDP) projection technique for hierarchical discretizations that enforces membership in physics-implied convex sets when mapping between solution spaces. When coupled with…