My work involves the multilevel simulation of deformable structures with applications to modeling the flow of blood cell membranes in the human blood stream. I have written computer code to simulate the way in which thin, smooth objects change shape when subjected to forces and pressures.
The goals of my work are twofold: to make these simulations efficient and accurate.
Seth Green, and George Turkiyyah
Doctoral Dissertation
Abstract: This work focuses on efficient hierarchical, numerical simulation of the deformation of thin walled structures. We address the need to characterize and improve the performance of the subdivision thin shell finite element for practical applications in engineering design and analysis. The contribution of this document is to provide a thorough investigation of thin shell simulation using the subdivision shell element, focusing on novel element design and implementation, accurate boundary conditions, efficient multilevel solution strategies, and applications to the current engineering problem of blood cell membrane simulation.
We describe a unified framework for the simulation of thin bodies via hierarchical, rotation-free thin shell finite elements. Our examples show that the run time of the algorithm presented scales nearly linearly with problem size. We present a new method for enforcing boundary conditions within subdivision finite element simulations of thin shells which is demonstrated to be second order accurate. We demonstrate the application of these techniques for the numerical simulation of red blood cell models. Two specific simulations are demonstrated for constant-volume deformation of a red blood cell: micropipette aspiration and point load application.
Animations:Subdivision-Based Multilevel Methods for Large Scale Engineering Simulation of Thin Shells
Seth Green, George Turkiyyah and Duane Storti
Proceedings of ACM Solid Modeling 2002
This paper presents a multilevel algorithm to accelerate the numerical solution of thin shell finite element problems described by subdivision surfaces. Specifically the subdivision matrix is used as the intergrid information transfer operator in a multilevel preconditioner. The method described in the paper allows the practical simulation or a broad range of problems. Included examples show that the run time of the algorithm presented scales nearly linearly in time with problem size.
Interactive Skeleton Driven Deformations
Steve Capell, Seth Green, Brian Curless, Zoran Popovic, Tom Duchamp
Proceedings of ACM Siggraph 2002
In this paper, we present a framework for physically-based, skeleton driven animation. We employ a hierarchical, volumetric, finite element mesh to simulate elastic body dynamics. By embedding an object within the mesh, we can simulate physics over the object. The simulation adapts the level of detail as needed during deforma-tions. To simulate skeletal controls, we introduce line constraints along bones of simple skeletons. To accelerate computation, we associate regions of the volumetric mesh with particular bones and perform locally linearized simulations, which are blended at each time step. We demonstrate the ability to animate complex models using simple skeletons and coarse volumetric meshes in a manner that simulates secondary motions at interactive rates.
A Multiresolution Framework for Dynamic Deformations
Steve Capell, Seth Green, Brian Curless, Zoran Popovic, Tom Duchamp
ACM Siggraph Symposium on Computer Animation
We present a novel framework for dynamic simulation of elastically deformable solids. Our approach combines classical finite element methodology with subdivision wavelets to meet the needs of computer graphics applications. We represent deformations using a wavelet basis constructed from volumetric Catmull-Clark subdivision. Catmull-Clark subdivision solids allow the domain of deformation to be taylored to objects of arbitrary topology. The domain of deformation can correspond to the interior of a subdivision surface or can enclose an arbitrary surface mesh. Within the wavelet framework we develop the equations of motion for elastic deformations in the presence of external forces and constraints. We solve the resulting differential equations using an implicit method, which lends stability. Our framework allows trade-off between speed and accuracy. For interactive applications, we accelerate the simulation by adaptively refining the wavelet basis while avoiding visual popping artifacts. Offline simulations can employ a fine basis for higher accuracy at the cost of more computation time. By exploiting the properties of smooth subdivision we can compute less expensive solutions using a trilinear basis yet produce a smooth result that meets the constraints.