Multiresolution green’s function methods for interactive simulation of large-scale elastostatic objects

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Multiresolution green’s function methods for interactive simulation of large-scale elastostatic objects (2003)

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by Douglas Leonard James

Venue:	ACM Trans. Graph
Citations:	53 - 12 self

BibTeX

@ARTICLE{James03multiresolutiongreen’s,
    author = {Douglas Leonard James},
    title = {Multiresolution green’s function methods for interactive simulation of large-scale elastostatic objects},
    journal = {ACM Trans. Graph},
    year = {2003},
    pages = {47--82}
}

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Abstract

This thesis presents a framework for low-latency interactive simulation of linear elastostatic models and other systems associated with linear elliptic partial differention equations. This approach makes it feasible to interactively simulate large-scale physical models. Linearity is exploited by formulating the boundary value problem (BVP) solution in terms of Green’s functions (GFs) which may be precomputed to provide speed and cheap lookup operations. Runtime BVPs are solved using a collection of Capacitance Matrix Algorithms (CMAs) based on the Sherman-Morrison-Woodbury formula. Temporal coherence is exploited by caching and reusing, as well as sequentially updating, previous capacitance matrix inverses. Multiresolution enhancements make it practical to simulate and store very large models. Efficient compressed representations of precomputed GFs are obtained using secondgeneration wavelets defined on surfaces. Fast inverse wavelet transforms allow fast summation methods to be used to accelerate runtime BVP solution. Wavelet GF compression factors are directly related to interactive simulation speedup, and examples are provided with

Keyphrases

multiresolution green function method interactive simulation large-scale elastostatic object interactive simulation speedup capacitance matrix algorithm runtime bvp solution boundary value problem multiresolution enhancement linear elliptic partial differention equation runtime bvps low-latency interactive simulation secondgeneration wavelet fast summation method wavelet gf compression factor previous capacitance matrix inverse fast inverse wavelet transforms green function large model precomputed gfs large-scale physical model linear elastostatic model sherman-morrison-woodbury formula cheap lookup operation temporal coherence

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