代表性成果与荣誉
1. F. Xu, H. Xie and N. Zhang, A parallel augmented subspace method for eigenvalue problems, SIAM Journal on Scientific Computing, 42(5), A2655–A2677, 2020.
2. F. Xu, Q. Huang, H. Ma, A novel domain decomposition framework for the ground state solution of Bose-Einstein condensates, Computers and Mathematics with Applications,80,1287–1300,2020..
3. F. Xu, A cascadic adaptive finite element method for nonlinear eigenvalue problems in quantum physics, SIAM Multiscale Modeling and Simulation. 18(1), 198-220, 2020.
4. F. Xu, Q. Huang, Cascadic adaptive finite element method for nonlinear eigenvalue problem based on complementary approach, Journal of Computational and Applied Mathematics, 372, 2020, 112720.
5. F. Xu, Q. Huang, Local and parallel multigrid method for nonlinear eigenvalue problems, Journal of Scientific Computing, (2020) 82:20.
6. F. Xu, M. Yue, Q. Huang, H. Ma, An asymptotically exact a posteriori error estimator for non-selfadjoint Steklov eigenvalue problem,Applied Numerical Mathematics, 156, 210-227,2020.
7. F. Xu, Q. Huang, M. Wang, H. Ma, A novel adaptive finite element method for the ground state solution of Bose-Einstein Condensates, Applied Mathematics and Computation, 125404, 2020.
8. F. Xu and Q. Huang, A type of cascadic multigrid method for coupled semilinear elliptic equations, Numerical Algorithms, 83(2), 485–510, 2020.
9. F. Xu and Q. Huang, An accurate a posteriori error estimator for the Steklov eigenvalue problem and its applications, Science China Mathematics, 64, pages623–638(2021). .
10. F. Luo, H. Xie, M. Xie and F. Xu, Adaptive time-stepping algorithms for molecular beam epitaxy: Based on energy or roughness, Applied Mathematics Letters, 2020, 99, 105991.
11. F. Xu, Q. Huang, S. Chen and H. Ma, A type of cascadic adaptive finite element method for eigenvalue problem, Advances in Applied Mathematics and Mechanics, 12(3) (2020), 774-796.
12. F. Xu and F. Luo, A cascadic multigrid method for semilinear elliptic equations, Journal of Computational Mathematics, 2019, 31(7), 1-18.
13. F. Xu and H. Ma, Multigrid method for coupled semilinear elliptic equation, Mathematical Methods in Applied Sciences, 2019, 42(8), 2707-2720.
14. H. Xie, F. Xu and N. Zhang, An efficient multigrid method for ground state solution of Bose-Einstein condensates，International Journal of Numerical Analysis and Modeling, 2019, 16(5), 789-803.
15.F. Xu, Q. Huang, S. Chen and T. Bing, An adaptive multigrid method for semilinear elliptic equation, East Asian Journal on Applied Mathematics, 9(4), 683-702, 2019.
16. F.Xu, A full multigrid method for the Steklov eigenvalue problem, International Journal of Computer Mathematics, 96(12), 2371-2386, 2019.
17. F. Xu, Q. Huang, An accurate a posteriori error estimator for semilinear Neumann problem and its applications, Applied Mathematics and Computation, 2019, 9, 683-702.
18. C. Wang, P. Sun, R. Lan, H. Shi and F. Xu, Effects of numerical integration on DLM/FD method for solving interface problems with body-unfitted meshes, Springer Lecture Notes in Computer Science, 2019, 11539, 551-567.
19. Q. Huang, S, Jia, F. Xu, Z. Xu and C. Yao, Solvability of wave propagation with Debye polarization in nonlinear dielectric materials and its finite element methods approximation, Applied Numerical Mathematics. 146,145-164, 2019
20. Q.Hong, H. Xie and F. Xu, A multilevel correction type of adaptive finite element method for eigenvalue problem, Siam Journal on Scientific Computing,2018, 40(6), A4208-A4235.
21. G. Hu, H. Xie and F. Xu, A multilevel correction adaptive finite element method for Kohn-Sham equation, Journal of Computational Physics, 2018, 355, 436–449.
22. F. Xu and H. Xie, A full multigrid method for semilinear elliptic equation, Applications of Mathematics, 2017, 60(3), 225-241.
23. X. Han, H. Xie and F. Xu, A cascadic multigrid method for eigenvalue problem, Journal of Computational Mathematics, 2014.
24. S. Jia, H. Xie, M. Xie and F. Xu, A full multigrid method for nonlinear eigenvalue problems, Science China Mathematics, 2016，59(10), 2037-2048.
25. H. Chen, H. Xie and F. Xu, A full multigrid method for eigenvalue problems, Journal of Computational Physics, 2016, 322, 747-759.
26. Q Lin, H. Xie and F. Xu, Multilevel correction adaptive finite element method for semilinear elliptic equation, Applications of Mathematics, 2015, 60(5), 527-550.
27. Fei Xu, Qiumei Huang, Hongkun Ma, A new type of full multigrid method for the elasticity eigenvalue problem, Numerical Methods for Partial Differential Equations,37,(1), 2021, 444-461
28. Fei Xu, Hehu Xie, Mnaitng Xie and Meiling Yue, A multigrid method for the ground state solution of Bose–Einstein condensates based on Newton iteration, BIT Numerical Mathematics, 61, 2021, 645-663.
29. F. Xu, Q. Huang, K. Jiang, H. Ma, Local and parallel multigrid method for semilinear elliptic equations. Applied Numerical Mathematics, 162, 2021, 20-34.
30. F. Xu, M. Yue, B. Zheng, Multilevel correction adaptive finite element method for solving nonsymmetric eigenvalue problems, Advances in Computational Mathematics, 47, 27 (2021).
31. M. Yue, F. Xu and H. Ma, A novel domain decomposition method for coupled semilinear elliptic equation, Mathematical Methods in Applied Sciences, 44(13)2021, 10387–10402.
32. M.Xie, F. Xu and M. Yue, A type of full multigrid method for non-selfadjoint Steklov eigenvalue problems in inverse scattering.ESAIM Math. Model. Numer. Anal.55(5),2021,1779–1802.
33. F. Xu, Q. Huang, H. Yang and H. Ma, Multilevel correction goal-oriented adaptive finite element method for semilinear elliptic equations, Applied Numerical Mathematics 172 (2022) 224–241.
34. Shuangshuang Chen, Qiumei Huang, Fei Xu, A Two-Grid Decoupled Algorithm for a Multi-Dimensional Darcy–Brinkman Fracture Model, Journal of Scientific Computing (2022) 90:88
35. Xu Fei, Chen Liu, Huang Qiumei, Local defect-correction method based on multilevel discretization for Steklov eigenvalue problem, ESAIM: Mathematical Modeling and Numerical Analysis, 2021, 55(6): 2899-2920
36.F. Xu, Q. Huang, S. Chen and H. Ma, Adaptive multigrid method for eigenvalue problem, International Journal of Numerical Analysis and Modeling, 2022, 19(1), 1-18.
37.G. Hu, H. Xie and F. Xu, On accelerating a multilevel correction adaptive finite element method for Kohn-Sham equation, Journal of Computational Physics, 2023, 472, 111674.
38. F. Xu, M. Xie, Q. Huang, M. Yue and H. Ma, Convergence and optimality of adaptive multigrid method for multiple eigenvalue problems, Journal of Computational and Applied Mathematics, 415 (2022) 114450
39. Fei Xu Qiumei Huang Manting Xie, An efficient adaptive multigrid method for the elasticity eigenvalue problem, BIT Numerical Mathematics,https://doi.org/10.1007/s10543-022-00939-7, 2022.
40. Xu, F., Huang, Q., Dai, H. et al. Multilevel local defect-correction method for nonsymmetric eigenvalue problems, Journal of Scientifc Computing, 92, 85 (2022).
