顶点映射金字塔的正交基底
Orthogonal bases for vertex-mapped pyramids
AI总结：
本文提出一种基于半节点高阶基底的显式DG方法，该基底在参考金字塔的特定变换下正交，验证了DG方法在该基底下的收敛性及效率。
摘要：
本文提出了一种基于半节点高阶基底的显式DG方法，该基底在参考金字塔的特定变换下正交，验证了DG方法在该基底下的收敛性及效率。
英文摘要：
Discontinuous Galerkin (DG) methods discretized under the method of lines must handle the inverse of a block diagonal mass matrix at each time step. Efficient implementations of the DG method hinge upon inexpensive and low-memory techniques for the inversion of each dense mass matrix block. We propose an efficient time-explicit DG method on meshes of pyramidal elements based on the construction of a semi-nodal high order basis, which is orthogonal for a class of transformations of the reference pyramid, despite the non-affine nature of the mapping. We give numerical results confirming both expected convergence rates and discuss efficiency of DG methods under such a basis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
