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 127 articles )

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  1. Chen, Long; Hu, Xiaozhe; Wise, Steven M.: Convergence analysis of the fast subspace descent method for convex optimization problems (2020)
  2. Chen, Yaoyao; Huang, Yunqing; Yi, Nianyu: Recovery type a posteriori error estimation of adaptive finite element method for Allen-Cahn equation (2020)
  3. Hafemeyer, Dominik; Kahle, Christian; Pfefferer, Johannes: Finite element error estimates in (L^2) for regularized discrete approximations to the obstacle problem (2020)
  4. Han, Jiayu: Shifted inverse iteration based multigrid methods for the quad-curl eigenvalue problem (2020)
  5. 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)
  6. Li, Hao; Bi, Hai; Yang, Yidu: The two-grid and multigrid discretizations of the (C^0)IPG method for biharmonic eigenvalue problem (2020)
  7. Li, Rui; Gao, Yali; Chen, Jie; Zhang, Li; He, Xiaoming; Chen, Zhangxin: Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model (2020)
  8. Xu, Fei: A cascadic adaptive finite element method for nonlinear eigenvalue problems in quantum physics (2020)
  9. Zhang, Yongchao; Mei, Liquan: A hybrid high-order method for a class of quasi-Newtonian Stokes equations on general meshes (2020)
  10. Zhang, Yu; Bi, Hai; Yang, Yidu: The adaptive finite element method for the Steklov eigenvalue problem in inverse scattering (2020)
  11. Adler, James H.; Hu, Xiaozhe; Mu, Lin; Ye, Xiu: An a posteriori error estimator for the weak Galerkin least-squares finite-element method (2019)
  12. Bank, Randolph E.; Li, Yuwen: Superconvergent recovery of Raviart-Thomas mixed finite elements on triangular grids (2019)
  13. Bi, Hai; Han, Jiayu; Yang, Yidu: Local and parallel finite element algorithms for the transmission eigenvalue problem (2019)
  14. Chen, Long; Wang, Feng: A divergence free weak virtual element method for the Stokes problem on polytopal meshes (2019)
  15. Chen, Zixuan; Song, Xiaoliang; Zhang, Xuping; Yu, Bo: A FE-ADMM algorithm for Lavrentiev-regularized state-constrained elliptic control problem (2019)
  16. Funken, Stefan A.; Schmidt, Anja: Ameshref: a Matlab-toolbox for adaptive mesh refinement in two dimensions (2019)
  17. Gong, Shihua; Wu, Shuonan; Xu, Jinchao: New hybridized mixed methods for linear elasticity and optimal multilevel solvers (2019)
  18. Loisel, Sébastien; Nguyen, Hieu: On the convergence of an optimal additive Schwarz method for parallel adaptive finite elements (2019)
  19. Lu, Peipei; Wu, Haijun; Xu, Xuejun: Continuous interior penalty finite element methods for the time-harmonic Maxwell equation with high wave number (2019)
  20. Lu, Peipei; Xu, Xuejun: A robust multilevel preconditioner based on a domain decomposition method for the Helmholtz equation (2019)

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