报告题目：

（1）Iterative solvers for polyconvex variational problems

（2）Untangling for meshes with topological singularities

报告时间：2026年1月7日14:00-17:00

报告地点：信息楼302

报告人：Vladimir Anatolyevich Garanzha

报告内容（摘要）：

（1）Iterative solvers for polyconvex variational problems

Mesh optimization and untangling are based on continuation technique for parameter-dependent variational problems. Success of continuation technique relies on essential minimization property: the ability to attain fixed relative functional decrease for fixed continuation parameter. We consider solvers based on the polyconvexity property, enabling local convex minimizations. The goal is to develop a "scalar" preconditioner based on solving discrete Poisson-like equation for a single scalar function, even though the problem is 3D and vector-valued, resulting in an iterative technique roughly three times faster than the current version.

Applications: construction and optimization of thick prismatic layers, hybrid and mixed meshes

（2）Untangling for meshes with topological singularities

In Garanzha, Sokolov et al 2024 it was formulated an idea of adaptive untangling for meshes with topological singularities.

Currently, topological singularities, such as double or multiple covering, may provide parasitic local minima for untangling techniques, resulting in unrecoverable deadlocks of iterative processes. Such situations may appear in free boundary untangling and cut-and-paste manifold untangling. Previous work in the 2D case demonstrated that special adaptive untangling either forces singularities out of the boundary or forces them to attract each other and mutually annihilate. The 3D version of this algorithm should be implemented and analyzed.

报告人简介：

Vladimir Anatolyevich Garanzha

Professor, Russian Academy of Sciences (RAS). He earned his doctorate in 2011 at the Sobolev Institute of Mathematics (Novosibirsk) under the supervision of S.K. Godunov. Since 1991, he has been affiliated with the Federal Research Center for Computer Science and Control of the RAS. With over 30 years of research in mesh generation and mesh optimization, his work notably applies Chebyshev cartography to Inverse Lithography Technology (ILT) problems. His recent contributions include: A mesh untangling algorithm featured in two SIGGRAPH papers in 2021 and 2024. The 2017 IMR Best Technical Paper Award for pioneering work on prismatic boundary-layer mesh generation.