Coupling time-varying modal analysis and FEM for real-time cutting simulation of objects with multi-material sub-domains

Abstract

Powerful global modal reduction techniques have received growing recognition towards significant performance gain in physical simulation, yet such numerical methods generally will fail when handling deformation of heterogeneous materials across multiple sub-domains involving cutting simulation. This is because the corresponding topological changes (due to cutting across multiple sub-domains) and/or drastic local deformations tend to invalidate the global subspace techniques. To ameliorate, this paper systematically advocates a novel deformation and arbitrary cutting simulation approach by adaptively integrating FEM-based fully-physical simulation and local deformation's modal reuse into a CUDA-enabled parallel computation framework. This paper's originality hinges upon the maximal reuse of the space–time-varying local modes from prior fully-physical simulations and the adaptively coupling of sub-domain behaviors, which give rise to great improvement of computational complexity while guaranteeing high-fidelity simulation effects. Other key advantages include, being independent of underlying physical models (e.g., either FEM or meshless methods), being flexibly accommodating sub-domains' heterogeneous material distributions, and being accurately responding to local user interactions. During the initialization stage, we partition the object into multiple sub-domains according to its material distributions and/or geometric structures, and respectively employ FEM for physics-based representation/simulation. During the dynamic stage, for each sub-domain, we leverage its local modal reduction in order to project complex deformations onto a low-dimensional subspace. We dynamically determine the sub-domain-specific switch between deformation reconstruction based on modal reuse and FEM-based physical simulation according to the physically-consistent error estimates, and couple all the sub-domains' physical behaviors together by imposing adjacent sub-domains' geometric-continuity constraints. To validate our method, we conduct extensive and quantitative evaluations over comprehensive and well-designed experiments, and all the experimental results have confirmed the advantages of our method in terms of efficiency, accuracy, and unconditional stableness in practical graphics applications.