iFEM: an innovative finite element methods package in MATLAB. Sparse matrixlization, an innovative programming style for MATLAB, is introduced and used to develop an efficient software package, iFEM, on adaptive finite element methods. In this novel coding style, the sparse matrix and its operation is used extensively in the data structure and algorithms. Our main algorithms are written in one page long with compact data structure following the style “Ten digit, five seconds, and one page” proposed by Trefethen. The resulting code is simple, readable, and efficient. A unique strength of iFEM is the ability to perform three dimensional local mesh refinement and two dimensional mesh coarsening which are not available in existing MATLAB packages. Numerical examples indicate thatiFEM can solve problems with size 105 unknowns in few seconds in a standard laptop. iFEM can let researchers considerably reduce development time than traditional programming method

References in zbMATH (referenced in 97 articles )

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  1. Bi, Hai; Han, Jiayu; Yang, Yidu: Local and parallel finite element algorithms for the transmission eigenvalue problem (2019)
  2. Gong, Shihua; Wu, Shuonan; Xu, Jinchao: New hybridized mixed methods for linear elasticity and optimal multilevel solvers (2019)
  3. Antil, Harbir; Otárola, Enrique; Salgado, Abner J.: Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects (2018)
  4. Broersen, D.; Dahmen, W.; Stevenson, R. P.: On the stability of DPG formulations of transport equations (2018)
  5. Chen, Long; Hu, Jun; Huang, Xuehai: Multigrid methods for Hellan-Herrmann-Johnson mixed method of Kirchhoff plate bending problems (2018)
  6. Chen, Long; Wu, Yongke; Zhong, Lin; Zhou, Jie: Multigrid preconditioners for mixed finite element methods of the vector Laplacian (2018)
  7. Froyland, Gary; Junge, Oliver: Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories (2018)
  8. Han, Jiayu: Nonconforming elements of class (L^2) for Helmholtz transmission eigenvalue problems (2018)
  9. Hofherr, Florian; Karrasch, Daniel: Lagrangian transport through surfaces in compressible flows (2018)
  10. Hou, Tianliang; Chen, Luoping; Yang, Yin: Two-grid methods for expanded mixed finite element approximations of semi-linear parabolic integro-differential equations (2018)
  11. Huang, Jian; Chen, Long; Rui, Hongxing: Multigrid methods for a mixed finite element method of the Darcy-Forchheimer model (2018)
  12. Joshi, Vaibhav; Jaiman, Rajeev K.: An adaptive variational procedure for the conservative and positivity preserving Allen-Cahn phase-field model (2018)
  13. Li, Hao; Yang, Yidu: An adaptive (C^0)IPG method for the Helmholtz transmission eigenvalue problem (2018)
  14. Li, Hao; Yang, Yidu: (C^0\mathrmIPG) adaptive algorithms for the biharmonic eigenvalue problem (2018)
  15. Li, Qi; Mei, Liquan; You, Bo: A second-order, uniquely solvable, energy stable BDF numerical scheme for the phase field crystal model (2018)
  16. Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran: The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes (2018)
  17. Song, Xiaoliang; Chen, Bo; Yu, Bo: An efficient duality-based approach for PDE-constrained sparse optimization (2018)
  18. Song, Xiaoliang; Yu, Bo; Wang, Yiyang; Zhang, Xuping: An FE-inexact heterogeneous ADMM for elliptic optimal control problems with (L^1)-control cost (2018)
  19. Wang, Fei; Wei, Huayi: Virtual element method for simplified friction problem (2018)
  20. Wang, Gang; He, Yinnian; Yang, Jinjin: Weak Galerkin finite element methods for the simulation of single-phase flow in fractured porous media (2018)

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Further publications can be found at: http://www.math.uci.edu/~chenlong/publication.html