دانلود رایگان مقاله تحلیل مودال کوپلینگ متغیر با زمان و FEM برای شبیه سازی برش زمان واقعی اشیا

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.

7. Conclusion and discussion

In this paper, we have systematically presented a novel and versatile method to address a suite of research challenges encountered in modal reduction based real-time deformation and arbitrary cutting simulation of heterogeneous objects (with multiple sub-domains and large variations of material distribution). The most critical idea of our novel approach is to conduct a dynamic interchange between adaptively integrating material-aware and/or geometry-structure-aware simulation with full-physics capability and performing deformation reconstruction based on sub-domain-specific local modal’ reuse, and all of the above numerical procedures have been implemented in a CUDA-centric parallel computation framework. The novel technical components within our new framework include: the space–time-varying local modal generation from previous-cycles’ fully-physical simulation, the adaptive alternation scheme between sub-domain physical simulation and modal reuse, the cross-domain coupling of spatially-varying numerous deformations (i.e., some sub-domains’ deformation is from physical simulation, and others are from modal-subspace reconstruction), and the sub-domain-level parallel implicit integration solvers supporting CUDA-enabled numerical computation, which collectively equip our method with remarkable advantages in terms of realtime efficiency, high-accuracy simulation, unconditional stableness, and practical versatility. Currently, our prototype system is still a proof-of-concept only at the experimental stage, hence, it is not yet of practical use due to certain limitations. For example, we should introduce some collision detection function (Li et al., 2014b) into our current system to make it possible to support more complex interactions far beyond the simple cutting operations. And we should also incorporate certain mature techniques (Barbicˇ and James, 2010; Teng et al., 2014) to accommodate self-collision caused by elastic deformation. In addition, our ongoing research efforts are concentrated on seeking an efficient optimization method to guarantee the physical accuracy in an absolute sense. Meanwhile, it also deserves our efforts to extend our method to handle more sophisticated fluid-elasticity coupling phenomena. In terms of limitations, it should be noted that, our domain coupling method’s requirement for construction consistency of sub-domain interface may not be appropriate in practical applications and our current method is lack of flexibility in supporting more comprehensive adaptivity when handling much more complex boundary interfaces.