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.

翻译：高阶基函数相较于线性基函数在效率上具有显著优势：在相同物理模型下，同等运行时间可实现更高精度；同时因其受锁定伪影和网格质量影响较小，可靠性更强。为此，我们提出一种基于高阶基函数的高阶有限元公式，用于在包含接触处理的曲线网格上开展弹性动力学模拟，该方法基于近期提出的增量势能接触模型。其核心思路在于：即便采用非线性网格或非线性有限元基函数，用于最小化弹性势能、接触势能和摩擦势能的每个IPC优化步骤都会生成线性轨迹。因此，该方法既保留了原始公式的强非穿透性保障与大时间步长特性，又充分受益于高阶基函数与高阶几何表示。我们通过将位移及由此产生的接触力在线性碰撞代理与底层高阶表示之间进行映射来实现这一目标。通过在图形学、计算制造及科学计算领域的一系列问题中验证了本方法的有效性。