论文标题
2d离散的hodge-dirac操作员
2D discrete Hodge-Dirac operator on the torus
论文作者
论文摘要
我们讨论了基于离散的外部演算框架的二维情况下，De Rham-Hodge理论的离散化。我们介绍了Hodge-Dirac和Laplace操作员的离散类似物，其中捕获了连续体的关键几何方面。我们提供并证明了Hodge分解定理的离散版本。已经特别注意组合曲线上的离散模型。在这种特殊情况下，我们还定义和计算了同种学组。
We discuss a discretisation of the de Rham-Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge-Dirac and Laplace operators in which key geometric aspects of the continuum counterpart are captured. We provide and prove a discrete version of the Hodge decomposition theorem. Special attention has been paid to discrete models on a combinatorial torus. In this particular case, we also define and calculate the cohomology groups.
