论文标题
相对论恒星模拟中极高的收敛性
Extremely High-Order Convergence in Simulations of Relativistic Stars
论文作者
论文摘要
我们提供了从灵感材料二进制文件中获得引力波形的道路，其精确度可适用于第三代重力波检测器，而无需推进计算硬件或大规模并行软件基础架构。我们展示了原理证明1+1维数值实现，该实现在弯曲时空中表现出高达7阶收敛的高度动态性压缩恒星，而数值误差则比标准方法高6个数量级。除了高阶插值错误（Runge的现象）外，还没有明显的基本障碍来获得甚至更高阶的收敛性。该实现使用了一种新型的表面跟踪方法，其中表面进化并在那里施加了高阶精确边界条件。在时空的真空区域中，计算存储器不需要分配给流体变量。我们预计将这种新方法应用于全额3美元\！ +\！ 1 $ - 二维的模拟紧凑型二进制系统具有至少一个物质主体。可变形表面的附加挑战必须在多个空间维度中解决，但这也是输入更精确的表面张力物理学的机会。
We provide a road towards obtaining gravitational waveforms from inspiraling material binaries with an accuracy viable for third-generation gravitational wave detectors, without necessarily advancing computational hardware or massively-parallel software infrastructure. We demonstrate a proof-of-principle 1+1-dimensional numerical implementation that exhibits up to 7th-order convergence for highly dynamic barotropic stars in curved spacetime, and numerical errors up to 6 orders of magnitude smaller than a standard method. Aside from high-order interpolation errors (Runge's phenomenon), there are no obvious fundamental obstacles to obtaining convergence of even higher order. The implementation uses a novel surface-tracking method, where the surface is evolved and high-order accurate boundary conditions are imposed there. Computational memory does not need to be allocated to fluid variables in the vacuum region of spacetime. We anticipate the application of this new method to full $3\! +\! 1$-dimensional simulations of the inspiral phase of compact binary systems with at least one material body. The additional challenge of a deformable surface must be addressed in multiple spatial dimensions, but it is also an opportunity to input more precise surface tension physics.
