论文标题
曲线网格上弹性动力模拟的高阶增量潜在接触
High-Order Incremental Potential Contact for Elastodynamic Simulation on Curved Meshes
论文作者
论文摘要
高阶基础在效率方面提供了比线性的主要优势，因为它们（对于相同的物理模型）在相同的运行时间和可靠性方面提供了更高的精度，因为它们受到锁定工件和网状质量的影响较小。因此，我们基于最近提出的增量势触点（IPC）模型，在高阶（弯曲）网格上引入了高阶元素（Fe）公式（高阶碱基），用于高阶（弯曲）网格上的弹性动力学模拟。 我们的方法基于这样的观察，即每个IPC优化步骤都用于最小化弹性，接触和摩擦电位，即使在存在非线性网格或非线性FE碱基的情况下，也会导致线性轨迹。因此，可以保留强大的非渗透保证和原始配方的巨大时间步骤，同时受益于高阶碱基和高阶几何形状。我们通过绘制位移和线性碰撞代理与基础高阶表示之间的接触力来实现这一目标。 我们证明了方法在从图形，计算制造和科学计算的各种问题中选择的有效性。
High-order bases provide major advantages over linear ones in terms of efficiency, as they provide (for the same physical model) higher accuracy for the same running time, and reliability, as they are less affected by locking artifacts and mesh quality. Thus, we introduce a high-order finite element (FE) formulation (high-order bases) for elastodynamic simulation on high-order (curved) meshes with contact handling based on the recently proposed Incremental Potential Contact (IPC) model. Our approach is based on the observation that each IPC optimization step used to minimize the elasticity, contact, and friction potentials leads to linear trajectories even in the presence of nonlinear meshes or nonlinear FE bases. It is thus possible to retain the strong non-penetration guarantees and large time steps of the original formulation while benefiting from the high-order bases and high-order geometry. We accomplish this by mapping displacements and resulting contact forces between a linear collision proxy and the underlying high-order representation. We demonstrate the effectiveness of our approach in a selection of problems from graphics, computational fabrication, and scientific computing.
