A Reduced Order Explicit Dynamic Finite Element Algorithm for Surgical Simulation
A Reduced Order Explicit Dynamic Finite Element Algorithm for Surgical Simulation
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DOI：
10.1109/tmi.2011.2143723
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发表时间：
2011-09-01
影响因子：
10.6
通讯作者：
Ourselin, Sebastien
中科院分区：
文献类型：
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作者：
Taylor, Zeike A.;Crozier, Stuart;Ourselin, Sebastien
降阶建模将完整的系统响应投影到较低维度的子空间上，之前已用于通过减小所涉及的线性系统的大小来加速有限元求解方案。在目前的工作中，我们利用这种减少显式分析的二次效应，即稳定的积分时间步长增加远远超过了整个系统。与隐式格式相比，这种现象说明了显式方法的一个主要缺点。我们提出了一个显式有限元方案，其中时间积分是在一个减少的基础上进行。此外，我们提出了一个简单的程序施加非齐次本质边界条件，从而克服了这种方法的主要缺陷之一。在一个基于GPU的执行框架内的程序的计算效益进行检查，并评估引入的错误。结果表明，加速接近一个数量级是可行的，而不引入禁止错误，没有硬件修改。该过程可能有应用程序在交互式仿真和医学图像引导问题，其中速度和精度都是至关重要的。
Reduced order modelling, in which a full system response is projected onto a subspace of lower dimensionality, has been used previously to accelerate finite element solution schemes by reducing the size of the involved linear systems. In the present work we take advantage of a secondary effect of such reduction for explicit analyses, namely that the stable integration time step is increased far beyond that of the full system. This phenomenon alleviates one of the principal drawbacks of explicit methods, compared with implicit schemes. We present an explicit finite element scheme in which time integration is performed in a reduced basis. Futhermore, we present a simple procedure for imposing inhomogeneous essential boundary conditions, thus overcoming one of the principal deficiencies of such approaches. The computational benefits of the procedure within a GPU-based execution framework are examined, and an assessment of the errors introduced is given. It is shown that speedups approaching an order of magnitude are feasible, without introduction of prohibitive errors, and without hardware modifications. The procedure may have applications in interactive simulation and medical image-guidance problems, in which both speed and accuracy are vital.