A High-Order Lower-Triangular Pseudo-Mass Matrix for Explicit Time Advancement of hp Triangular Finite Element Methods

Explicit time advancement for continuous finite elements requires the inversion of a global mass matrix. For spectral element simulations on quadrilaterals and hexahedra, there is an accurate approximate matrix which diagonal, making it computationally efficient explicit simulations. In this article shown that standard space polynomials used with triangular elements, denoted $\mathcal{T}(p)$, where $p$ degree space, no diagonal permits solutions accuracy defined as giving exact projection functions in ${\cal T} (p - 1)$. light this, lower-triangular pseudo-mass method introduced only local operations, method's demonstrated $\mathcal{T}(3)$. The accompanying high-order basis allow time-stepping techniques without sacrificing spatial approximation unstructured meshes.