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 148 articles )

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  1. Antil, Harbir; Kouri, Drew P.; Pfefferer, Johannes: Risk-averse control of fractional diffusion with uncertain exponent (2021)
  2. 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)
  3. Xie, Yingying; Zhong, Liuqiang: Convergence of adaptive weak Galerkin finite element methods for second order elliptic problems (2021)
  4. Xu, Shipeng: A posteriori error estimates for weak Galerkin methods for second order elliptic problems on polygonal meshes (2021)
  5. Zhang, Guoyu; Huang, Chengming; Fei, Mingfa; Wang, Nan: A linearized high-order Galerkin finite element approach for two-dimensional nonlinear time fractional Klein-Gordon equations (2021)
  6. Zhang, Xiaohua; Hu, Zhicheng; Wang, Min: An adaptive interpolation element free Galerkin method based on a posteriori error estimation of FEM for Poisson equation (2021)
  7. Zhang, Yu; Bi, Hai; Yang, Yidu: Asymptotic lower bounds for eigenvalues of the Steklov eigenvalue problem with variable coefficients. (2021)
  8. Bi, Hai; Zhang, Yu; Yang, Yidu: Two-grid discretizations and a local finite element scheme for a non-selfadjoint Stekloff eigenvalue problem (2020)
  9. Bonito, Andrea; Demlow, Alan; Licht, Martin: A divergence-conforming finite element method for the surface Stokes equation (2020)
  10. Chen, Long; Hu, Xiaozhe; Wise, Steven M.: Convergence analysis of the fast subspace descent method for convex optimization problems (2020)
  11. Chen, Xiaotong; Song, Xiaoliang; Chen, Zixuan; Yu, Bo: A multi-level ADMM algorithm for elliptic PDE-constrained optimization problems (2020)
  12. Chen, Yaoyao; Huang, Yunqing; Yi, Nianyu: Recovery type a posteriori error estimation of adaptive finite element method for Allen-Cahn equation (2020)
  13. Chen, Yuan; Hou, Songming; Zhang, Xu: A bilinear partially penalized immersed finite element method for elliptic interface problems with multi-domain and triple-junction points (2020)
  14. Dong, Guozhi; Guo, Hailong: Parametric polynomial preserving recovery on manifolds (2020)
  15. Funken, Stefan A.; Schmidt, Anja: Adaptive mesh refinement in 2D -- an efficient implementation in \textscMatlab (2020)
  16. Gao, Huadong; Ju, Lili; Li, Xiao; Duddu, Ravindra: A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion (2020)
  17. Hafemeyer, Dominik; Kahle, Christian; Pfefferer, Johannes: Finite element error estimates in (L^2) for regularized discrete approximations to the obstacle problem (2020)
  18. Han, Jiayu: Shifted inverse iteration based multigrid methods for the quad-curl eigenvalue problem (2020)
  19. Hou, Tianliang; Chen, Luoping; Yang, Yueting; Yang, Yin: Two-grid Raviart-Thomas mixed finite element methods combined with Crank-Nicolson scheme for a class of nonlinear parabolic equations (2020)
  20. Li, Hao; Bi, Hai; Yang, Yidu: The two-grid and multigrid discretizations of the (C^0)IPG method for biharmonic eigenvalue problem (2020)

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