基于IMEX的织物动态仿真的近似解法

An Approximate Scheme Based on IMEX for Cloth Simulation

织物在空间运动的刚性特征始终是困扰织物动态仿真的难题 显式方法简单灵活 ,易于实现 ,但受稳定因素影响 ,无法实现具有刚性特征的织物动态模拟 ;隐式方法稳定性好 ,却忽略了非线性因素 ,而且计算复杂 ,直接影响到仿真的最终结果和实际效率 .针对这一问题 ,提出了基于隐式 -显式的近似解法 ,该方案从系统受力形变的非线性特征出发 ,将质点受力分为线性和非线性两部分 ,线性部分采用隐式解法 ,非线性部分利用显式解法 ,线性方程组的求解则运用近似解法 实验结果表明 ,该方法兼具两种方法的优点 ,既保留了隐式方法的稳定性 ,又充分利用了显式方法的简易性处理非线性特征 。

One of the difficulties in cloth simulation is how to solve the motion differential equations with high stiff characteristics. The explicit schemes are simple and require considerably less work per step,but too unstable to satisfy the real-time effects for cloth simulation with stiff characteristics. The implicit method is of great stability,but it does not integrate the nonlinear term and is too complex that the results and the real-time efficiency are unsatisfied. An approximate scheme based on implicit-explicit method is presented to solve the raised differential equations. Considering the nonlinear characteristics of the deformation about a particle system,the forces acting on a particle are split into a linear part and a non-linear part and the linear part is treated implicitly,while the non-linear part is treated,explicitly. The linear system is solved efficiently by an approximate scheme. By joining the merits of both the implicit and explicit methods,the good stability of the implicit method is kept and the explicit method is used to deal with the nonlinear term. So,the stiff problem in cloth simulation is solved effectively.