偏微分方程高分辨数值方法,科学计算,自适应方法
1. 国家自然科学基金数学天元青年基金项目,11126287,基于移动网格的局部间断Galerkin
有限元方法研究,2012.01-2012.12,3万元,已结题,主持
2. 国家自然科学基金青年科学基金项目,11201242,Runge-Kutta间断Galerkin方法的各项异性自适应方法及其应用,2013.01-2015.12,22万元,已结题,主持
3. 江苏省高等学校自然科学研究面上项目,17KJB110013,求解高阶偏微分方程的h自适应LDG方法,2017.09-2019.08,3万元,结题中,主持
1. 江苏省自然科学青年基金项目,BK20130860,时间分数阶偏微分方程的高精度差分算法设计及理论分析,2013.07-2016.06,20万元,已结题,参加
2. 国家自然科学基金数学天元青年基金项目,11426137,基于对偶两步模型的图像放大问题,2015.01-2015.12,3万元,已结题,参加
3. 国家自然科学基金青年科学基金项目,11401319,数值求解分数阶偏微分方程的高精度快速算法研究,2015.01-2017.12,22万元,已结题,参加
4. 国家自然科学基金面上项目,11871443,不确定性下的三维气体爆炸波的数值方法研究,2019.01-2022.12,50万元,在研,参加
1. Hongqiang
Zhu, Jianxian Qiu*.
Adaptive Runge-Kutta discontinuous Galerkin methods using different indicators:
One-dimensional case. Journal of Computational Physics, 228: 6957-6976, 2009.
2. Hongqiang
Zhu, Yue Cheng, Jianxian
Qiu*. A Comparison of the performance of limiters for Runge-Kutta discontinuous
Galerkin methods. Advances in Applied Mathematics and Mechanics, 5: 365-390,
2013.
3. Hongqiang
Zhu, Jianxian Qiu*. An h-adaptive
Runge-Kutta discontinuous Galerkin method for Hamilton-Jacobi equations. Numerical
Mathematics: Theory, Methods and Applications, 6: 617-636, 2013.
4. Hongqiang
Zhu, Jianxian Qiu*. An
h-adaptive RKDG method with troubled-cell indicator for two-dimensional
hyperbolic conservation laws. Advances in Computational Mathematics, 39: 445-463,
2013.
5. Hongqiang
Zhu, Zhen Gao*. An
h-adaptive RKDG method with troubled-cell indicator for one-dimensional detonation
wave simulations. Advances in Computational Mathematics, 42: 1081-1102, 2016.
6. Hongqiang
Zhu, Jianxian Qiu, Jing-Mei
Qiu*. An h-adaptive RKDG method for the Vlasov-Poisson system, Journal of
Scientific Computing, 69:
1346-1365, 2016.
7. Hongqiang
Zhu, Jianxian Qiu,
Jing-Mei Qiu*. An h-adaptive RKDG method for the two-dimensional incompressible
Euler equations and the guiding center Vlasov model, Journal of Scientific
Computing, 73: 1316-1337, 2017.
8. Hongqiang
Zhu, Zhen Gao*. An
h-Adaptive RKDG Method for Two-Dimensional Detonation Wave Simulations. East
Asian Journal on Applied Mathematics, 9: 165-184, 2019.
9. Hongqiang
Zhu, Jianxian Qiu, Jun
Zhu*. A simple, high-order and compact WENO limiter for RKDG method. Computers
and Mathematics with Applications, 79: 317–336, 2020.
10. 朱洪强,求解Hamilton-Jacobi方程的局部移动网格方法,数学的实践与认识,2013,43:179-187.
11. 朱洪强,简化的WENO重构在h自适应RKDG方法中的应用,科学技术与工程,2013,13:6365-6369.
12. 朱洪强*,邱建贤,交错网格上高斯型格式的逐点收敛阶估计,南京邮电大学学报,2014,34:127-132.
13. 袁安安,朱洪强*,刘蕊,基于坏单元指示子的p自适应RKDG算法,数学的实践与认识,2020,50:165-172.