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 110 articles )

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  1. Chen, Yaoyao; Huang, Yunqing; Yi, Nianyu: Recovery type a posteriori error estimation of adaptive finite element method for Allen-Cahn equation (2020)
  2. Hafemeyer, Dominik; Kahle, Christian; Pfefferer, Johannes: Finite element error estimates in (L^2) for regularized discrete approximations to the obstacle problem (2020)
  3. Han, Jiayu: Shifted inverse iteration based multigrid methods for the quad-curl eigenvalue problem (2020)
  4. Zhang, Yongchao; Mei, Liquan: A hybrid high-order method for a class of quasi-Newtonian Stokes equations on general meshes (2020)
  5. Adler, James H.; Hu, Xiaozhe; Mu, Lin; Ye, Xiu: An a posteriori error estimator for the weak Galerkin least-squares finite-element method (2019)
  6. Bank, Randolph E.; Li, Yuwen: Superconvergent recovery of Raviart-Thomas mixed finite elements on triangular grids (2019)
  7. Bi, Hai; Han, Jiayu; Yang, Yidu: Local and parallel finite element algorithms for the transmission eigenvalue problem (2019)
  8. Gong, Shihua; Wu, Shuonan; Xu, Jinchao: New hybridized mixed methods for linear elasticity and optimal multilevel solvers (2019)
  9. Loisel, Sébastien; Nguyen, Hieu: On the convergence of an optimal additive Schwarz method for parallel adaptive finite elements (2019)
  10. Lu, Peipei; Wu, Haijun; Xu, Xuejun: Continuous interior penalty finite element methods for the time-harmonic Maxwell equation with high wave number (2019)
  11. Song, Yongcun; Yuan, Xiaoming; Yue, Hangrui: An inexact Uzawa algorithmic framework for nonlinear saddle point problems with applications to elliptic optimal control problem (2019)
  12. Antil, Harbir; Otárola, Enrique; Salgado, Abner J.: Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects (2018)
  13. Broersen, D.; Dahmen, W.; Stevenson, R. P.: On the stability of DPG formulations of transport equations (2018)
  14. Chen, Long; Hu, Jun; Huang, Xuehai: Multigrid methods for Hellan-Herrmann-Johnson mixed method of Kirchhoff plate bending problems (2018)
  15. Chen, Long; Wu, Yongke; Zhong, Lin; Zhou, Jie: Multigrid preconditioners for mixed finite element methods of the vector Laplacian (2018)
  16. Dudzinski, Michael; Rozgi\`{c}, Marco; Stiemer, Marcus: (o) FEM: an object oriented finite element package for Matlab (2018)
  17. Fang, Jun; Qian, Jianliang; Zepeda-Núñez, Leonardo; Zhao, Hongkai: A hybrid approach to solve the high-frequency Helmholtz equation with source singularity in smooth heterogeneous media (2018)
  18. Froyland, Gary; Junge, Oliver: Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories (2018)
  19. Han, Jiayu: Nonconforming elements of class (L^2) for Helmholtz transmission eigenvalue problems (2018)
  20. Hofherr, Florian; Karrasch, Daniel: Lagrangian transport through surfaces in compressible flows (2018)

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