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 168 articles )

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  1. Cao, Pei; Chen, Jinru; Wang, Feng: An extended mixed finite element method for elliptic interface problems (2022)
  2. Cao, Xiaoting; Zhang, Xiaohua; Shi, Xiaotao: An adaptive variational multiscale element free Galerkin method based on the residual-based a posteriori error estimators for convection-diffusion-reaction problems (2022)
  3. Li, Songxin; Wu, Yongke: Energy-preserving mixed finite element methods for the elastic wave equation (2022)
  4. Liu, Ying; Wang, Gang; Wu, Mengyao; Nie, Yufeng: A recovery-based a posteriori error estimator of the weak Galerkin finite element method for elliptic problems (2022)
  5. Li, Yanjun; Bi, Hai; Yang, Yidu: The a priori and a posteriori error estimates of DG method for the Steklov eigenvalue problem in inverse scattering (2022)
  6. Sun, Lingling; Yang, Yidu: The a posteriori error estimates and adaptive computation of nonconforming mixed finite elements for the Stokes eigenvalue problem (2022)
  7. Yang, Wei; Wang, Tiancheng: Isotropic cloak materials design based on the numerical optimization method of the inverse medium problem (2022)
  8. Yue Yu: mVEM: A MATLAB Software Package for the Virtual Element Methods (2022) arXiv
  9. Antil, Harbir; Kouri, Drew P.; Pfefferer, Johannes: Risk-averse control of fractional diffusion with uncertain exponent (2021)
  10. Bi, Hai; Han, Jiayu; Yang, Yidu: Local and parallel finite element schemes for the elastic transmission eigenvalue problem (2021)
  11. Cao, Shuhao: A simple virtual element-based flux recovery on quadtree (2021)
  12. Chen, Yaoyao; Huang, Yunqing; Yi, Nianyu: A decoupled energy stable adaptive finite element method for Cahn-Hilliard-Navier-Stokes equations (2021)
  13. Li, Bowen; Zou, Jun: An adaptive edge element method and its convergence for an electromagnetic constrained optimal control problem (2021)
  14. Liu, Ying; Nie, Yufeng: A priori and a posteriori error estimates of the weak Galerkin finite element method for parabolic problems (2021)
  15. Li, Yuwen: Quasi-optimal adaptive hybridized mixed finite element methods for linear elasticity (2021)
  16. Tian, Wenyi; Yuan, Xiaoming; Yue, Hangrui: An ADMM-Newton-CNN numerical approach to a TV model for identifying discontinuous diffusion coefficients in elliptic equations: convex case with gradient observations (2021)
  17. Wu, Shu-Lin; Zhou, Tao: Parallel implementation for the two-stage SDIRK methods via diagonalization (2021)
  18. Xie, Hui; Xu, Xuejun; Zhai, Chuanlei; Yong, Heng: A positivity-preserving finite volume scheme with least square interpolation for 3D anisotropic diffusion equation (2021)
  19. Xie, Yingying; Zhong, Liuqiang: Convergence of adaptive weak Galerkin finite element methods for second order elliptic problems (2021)
  20. Xu, Shipeng: A posteriori error estimates for weak Galerkin methods for second order elliptic problems on polygonal meshes (2021)

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