Year: 2025
Type: article
Abstract: This paper investigates a path-following method inspired by the semismooth ∗ approach for solving algebraic inclusions, with a primary emphasis on the role of strong subregularity and its crucial role in ensuring the robustness and stability of the path-following method, as it provides a framework to uniformly control the distance between the input and the solution set across a continuous path. We explore the problem of finding a mapping $x: [0, T] \longrightarrow \mathbb{R}^{n} $ x : [ 0 , T ] ⟶ R n that satisfies $0 \in F(t, x(t)) $ 0 ∈ F ( t , x ( t ) ) for each $t \in [0, T] $ t ∈ [ 0 , T ] , where $F $ F is a set-valued mapping from $\mathbb{R} \times \mathbb{R}^{n} $ R × R n to $\mathbb{R}^{n} $ R n . We consider an approach based on mappings exhibiting uniform semismooth ∗ properties along continuous trajectories, thereby maintaining a uniform grid error throughout the interval. Error estimates demonstrate an $o(h)$ o ( h ) grid error with respect to the discretization parameter under natural regularity assumptions. Numerical experiments applied to electric circuit and elastoplastic models confirm the efficiency and robustness of the method.
Authors: Tomáš Roubal, Jan Valdman
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W4417233082