Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors
Yuyang Guo and Jun Hu and Ting Lin
爱因斯坦-比安奇系统使用对称和无痕的张量来重新计算爱因斯坦的原始场方程。 然而,同时保留这些代数约束仍然是数值方法的挑战。 本文提出了一种新的公式,将线性化的爱因斯坦 - 比安奇系统(靠近琐碎的闵可夫斯基度量)视为与构象赫生复合物相关的霍奇波方程。 为了离散这个方程,一个符合的有限元素构象Hessian复合物,同时保持对称性和无痕性,在一般的三维四面体网格上构建,并且其精确性得到证实。
The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper proposes a new formulation that treats the linearized Einstein-Bianchi system (near the trivial Minkowski metric) as the Hodge wave equation associated with the conformal Hessian complex. To discretize this equation, a conforming finite element conformal Hessian com...