时间：2025年11月14日

地点：数学院南楼 N202 教室

10:00 卷积位势和线性响应问题的快速高精度算法及应用

报告人：张勇 （天津大学）

摘要：卷积位势和线性响应问题广泛存在于科学和工程领域，包括物理、化学、材料等学科，其高精度快速计算往往是数值模拟的关键。常见卷积包括库仑势、偶极势和 Yukawa势等，卷积的非局部性、核函数奇异性和密度函数的强各向异性给位势快速计算带来了精度和效率上的挑战。我们将报告非均匀快速傅里叶变换法、高斯和方法、核截断法、各向异性核截断法、远场近似法和矩匹配法等在内的一系列谱精度O(N log N)快速算法及其应用。线性响应问题是一类特殊的非对称特征值问题，在凝聚态物理、电子结构计算中有广泛应用，我们利用其特征空间的双正交结构设计开发了一套并行大规模求解器，在充分结合其零不变子空间结构的基础上，可实现高维 BdG问题的高精度高效求解。

11:00 An efficient and spectrally-accurate solver for computing the Bogoliubov-de Gennes excitations of rotating Bose-Einstein condensate

报告人：李瑜（天津财经大学）

摘要：In this talk, we introduce an efficient and robust numerical method to study the elementary excitations of rotating Bose-Einstein condensates (BEC), which is governed by the Bogoliubov-de Gennes (BdG) equations, around the mean-field ground state. The BdG is essentially a complex-valued constrained eigenvalue problem. We firstly derive analytical results of the BdG, especially some analytical eigenpairs and generalized nullspace which plays a key role in eigensolver’s performance in terms of convergence, accuracy and efficiency. Next, We present real representation of the complex BdG, which exactly corresponds to a double-sized real linear response eigenvalue problem (LREP). And then we integrate the standard Fourier spectral method for spatial discretization and a stable Gram-Schmidt bi-orthogonal algorithm to construct an eigensolver for computing the BdG with spectral accuracy and nearly optimal efficiency. Finally, ample numerical results are provided to illustrate the accuracy and efficiency, together with applications to Bogoliubov amplitudes around the ground state and the influence of physical parameters on the excitation spectrum.

13:30 玻色-爱因斯坦凝聚态中Bogoliubov集体激发的数值计算

报告人：谢满庭（天津大学）

摘要：Bogoliubov集体激发是玻色-爱因斯坦凝聚态中一种特殊的物质状态，数学上对应于一类线性响应特征值问题，即Bogoliubov-de Gennes方程（BdGEs）。本报告将介绍若干高效、稳健且高精度的数值方法，用于求解这类BdGEs。内容涵盖相关数学理论基础与数值分析框架，并通过数值实验验证所提方法在精度与计算效率方面的优越性。结果表明，所采用的算法能够准确刻画低能激发谱，为研究超冷量子气体的宏观量子现象提供可靠的数值支撑。

14:30 On the convergence of the discontinuous Galerkin scheme for Einstein-scalar equations

报告人：陈跃文（清华大学）

摘要：We prove the stability and convergence of the high order discontinuoud Galerkin scheme to spherically symmetric Einstein-scalar equations for a class of large initial data that ensures the formation of black hole. Having chosen the Bondi coordinate system, we achieve $L^2$ stability and obtain the optimal error estimates.

16:00 Hyperboloidal framework in black hole dynamics

报告人：何振涛 （国科大）

摘要：Hyperboloidal framework is an elegent method to study radiative phenomena in black hole spacetime, in which boundary conditions and physical quantities at null infinity are easily addressable. In this talk, I will discuss its application in black hole perturbation theory and numerical relativity.

16:30 Following the null rays Bondi-Saches formulism in numerical relativity

报告人：杜佳（国科大）

摘要：Numerical relativity is usually formulated on space-like hypersurface, but an alternative and elegent approach evolves the geometry along null directions-following the path of light itself. In this talk, I will introduce the main ideas of this approach, discuss its numerical realization and highlight its applications in asymptotically AdS space-time.

17:00 Holographic dynamics of vortex pair in shell-shaped superfluid

报告人：严昌旭（北师大）

摘要：在本报告中，我将介绍在球面上超流涡旋对的动力学线性稳定性及其非线性演化。所用框架为是全息引力，而所用方法为空间拟谱方法与时间龙格库塔方法。