第110回 金沢解析セミナー（ハイブリッド開催）
The 110th Kanazawa Analysis Seminar (Hybrid)
日時: 2023年10月6日(金) 16時30分〜18時00分
Date&time: October 6, 2023 (Fri.) 16:30--18:00
場所: 自然科学５号館数学棟４階コロキウム３ (471室)
＋ Zoomによるオンライン配信(参加登録: TBA)
Place: Natural Science and Technology Hall 5, 4th floor, Colloquium 3 (room 471)
講演者(Speaker): Steffen Plunder (京都大学・ASHBi ヒト生物学高等研究拠点)
題目(Title): Analyzing non-smooth dynamics without convexity: Theory, numerics, and convergence of position based dynamics
概要(abstract):
The simulation of contact problems (such as physical objects with collisions) usually leads to non-smooth dynamical systems, which can be treated analytically with the theory of differential inclusions (set-valued ODEs). In this talk, we will introduce to the general theory of differential inclusions on uniformly prox-regular sets, which is in particular applicable to overdamped particle systems with volume exclusion. We will outline the classical existence and uniqueness theory which relies on concepts from variational analysis such as scalarly upper semicontinuity, metric calmness and hypomonotonicity.
The theoretical foundation allows us to motivate a new approach for the numerical analysis of time-stepping methods for differential inclusions. Our main result is the first convergence proof of NVIDIA's position based dynamics method (PBD), which is used in numerous movies, computer games and industrial applications. Unlike most other time-stepping methods for differential inclusions, PBD is an explicit method but with excellent numerical stability. These properties make PBD an attractive choice for the simulation of large-scale particle systems like those arising in mathematical biology.
The first part is roughly based on "Adly, S., Nacry, F., Thibault, L.: Discontinuous sweeping process with prox-regular sets" and the second part presents our new results in collaboration with Sara Merino Aceituno (University Vienna).
