Topology-changing events such as pinch-off, self-intersection,or mesh degeneration are a recurring challenge in numerical simulationsbased on Lagrangian discretizations. While the governing partial differentialequations often remain formally well-defined, the discrete representationmay lose numerical resolvability, preventing stable and reproduciblecontinuation. In practice, such events are typically addressed either byintrinsically regularized models, such as phase-field methods 6, or by adhoc,solver-specific heuristics embedded directly into numerical codes 5.Both approaches hinder modularity, transparency, and systematic comparisonof alternative handling strategies 4.In this work, we propose the Algorithmic Surgery Protocol (ASP), anevent-driven architectural pattern for managing topology-changing eventsin Lagrangian simulations. ASP models the simulation as a hybrid automatonin which continuous PDE evolution is supervised by an externalmonitoring layer. When a resolvability criterion is violated, a structuredfive-stage protocol is triggered, comprising detection, solver halt, surgeryselection, validation, and resume. By formalizing topological interventionsas explicit algorithmic events and separating them from numericalintegration logic, ASP provides a solver-agnostic framework thatimproves modularity, maintainability, and reproducibility. The proposedapproach is intended as a software infrastructure layer that complementsexisting physical models and numerical methods rather than replacingthem.
Sergey Petrov (Fri,) studied this question.