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报告题目: A Bi-Orthogonal Structure-Preserving eigensolverfor large-scale linear response eigenvalue problem
报告人：张勇 教授 天津大学 应用数学中心
报告时间：2025年5月28日15:00
报告地点：红瓦楼726
报告内容简介：The linear response eigenvalue problem, which arises from many scientific and engineering fields, is quite challenging to solve numerically, especially when it has zero eigenvalues and the sparse/dense system is large-scale. Based on a direct sum decomposition of biorthogonal invariant subspaces, using the structure of generalized nullspace, we propose a Bi-Orthogonal Structure-Preserving subspace iterative solver, which is stable, efficient, and of excellent parallel scalability. The biorthogonality is of essential importance and create by a modified Gram-Schmidt biorthogonalization (MGS-Biorth) algorithm. We naturally deflate out the already converged eigenvectors by searching the next eigenpairs in the biorthogonal complementary subspace without introducing artificial parameters. When the number of requested eigenpairs is very large, we propose a moving mechanism to compute the eigenpairs batch by batch so that the projection matrix size is small and independent of the number of requested eigenpairs. For large-scale problems, one only needs to provide the matrix-vector product implementation, thus waiving any explicit matrix storage. The performance is further improved when the matrix-vector product is implemented using parallel computing. Ample numerical examples are provided to demonstrate the stability, efficiency, and parallel scalability.
报告人简介：张勇教授目前担任天津应用数学中心副主任，天津大学数学学院院长助理。 2007年本科毕业于天津大学，2012年在清华大学获得博士学位。他先后在奥地利维也纳大学的Wolfgang Pauli 研究所，法国雷恩一大和美国纽约大学克朗所从事博士后研究工作。2015年7月获得奥地利自然科学基金委支持的薛定谔基金，2018年入选国家海外高层次人才计划。研究兴趣主要是偏微分方程的数值计算和分析工作，尤其是快速算法的设计和应用。迄今发表论文30余篇，主要发表在包括Mathematical Models and Methods in Applied Sciences, SIAM Journal on Scientific Computing, SIAM Journal on Applied Mathematics, SIAM Multiscale Modeling and Simulation, Journal of Computational Physics, Mathematics of Computation, Computer Physics Communication 等计算数学顶尖杂志。
报告邀请人：盛长滔
