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Structure-preserving scheme for 1D KWC system
Makoto Okumura, Shodai Kubota, Ken Shirakawa
https://arxiv.org/abs/2506.16963 https://a…

Structure-preserving scheme for 1D KWC system
In this paper, we consider a system of one-dimensional parabolic PDEs, known as the KWC system, as a phase-field model for grain boundary motion. A key feature of this system is that the equation for the crystalline orientation angle is described as a quasilinear diffusion equation with variable mobility. The goal of this paper is to establish a structure-preserving numerical scheme for the system, focusing on two main structural properties: $\sharp\,1)$ range preservation; and $\sharp\,2)$ ene…

Progressively Projected Newton's Method
Jos\'e Antonio Fern\'andez-Fern\'andez, Fabian L\"oschner, Jan Bender
https://arxiv.org/abs/2505.21013

Progressively Projected Newton's Method
Newton's Method is widely used to find the solution of complex non-linear simulation problems in Computer Graphics. To guarantee a descent direction, it is common practice to clamp the negative eigenvalues of each element Hessian prior to assembly - a strategy known as Projected Newton (PN) - but this perturbation often hinders convergence. In this work, we observe that projecting only a small subset of element Hessians is sufficient to secure a descent direction. Building on this insight, we…