论文标题
骨折的网格
Fractured Meshes
论文作者
论文摘要
这项工作介绍了``通用的网格''，这是一种针对非规范几何形状中部分微分方程离散的网格。广义网格通过允许重叠的元素和更灵活的邻接关系来扩展常规的简单网格，它们可以具有几个不同的``广义上的''vertices（或edente fertices fertices nore fertices cooters，forders），以弥补（或edge cane forders），以下效率（或者）。这些普遍的方面是在有限和边界元素应用中出现的离散差分形式的经典构象空间的自然自由度。特别注意破裂域及其边界的表示。提出了一种算法来构造所谓的{\ em上虚拟上的网状}，该{\ em上膨胀的网状}对应于骨折的``双面''网格。离散的$ d $ d $ d $ d $ - 差异的网格上的形式的特征是在周围卷中的离散$ d $ d $ d $ d $ d $ d $ d $的痕迹。
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements and more flexible adjacency relations. They can have several distinct ``generalized" vertices (or edges, faces) that occupy the same geometric position. These generalized facets are the natural degrees of freedom for classical conforming spaces of discrete differential forms appearing in finite and boundary element applications. Special attention is devoted to the representation of fractured domains and their boundaries. An algorithm is proposed to construct the so-called {\em virtually inflated mesh}, which correspond to a ``two-sided" mesh of a fracture. Discrete $d$-differential forms on the virtually inflated mesh are characterized as the trace space of discrete $d$-differential forms in the surrounding volume.
