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 51 articles )

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  1. Demlow, Alan: Convergence and quasi-optimality of adaptive finite element methods for harmonic forms (2017)
  2. Yang, Yidu; Bi, Hai; Li, Hao; Han, Jiayu: A $C^0 \mathrmIPG$ method and its error estimates for the Helmholtz transmission eigenvalue problem (2017)
  3. Zhang, Xuping; Zhang, Jintao; Yu, Bo: Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities (2017)
  4. Bi, Hai; Li, Hao; Yang, Yidu: An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem (2016)
  5. Chen, Long; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.: Multilevel methods for nonuniformly elliptic operators and fractional diffusion (2016)
  6. Cuvelier, François; Japhet, Caroline; Scarella, Gilles: An efficient way to assemble finite element matrices in vector languages (2016)
  7. Demlow, Alan; Kopteva, Natalia: Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems (2016)
  8. Garcke, Harald; Hinze, Michael; Kahle, Christian: A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow (2016)
  9. Han, Jiayu; Yang, Yidu: An adaptive finite element method for the transmission eigenvalue problem (2016)
  10. Jamei, Mehdi; Ghafouri, H.: A novel discontinuous Galerkin model for two-phase flow in porous media using an improved IMPES method (2016)
  11. Li, Feiyan; Bi, Hai: A type of multigrid method based on the fixed-shift inverse iteration for the Steklov eigenvalue problem (2016)
  12. Liu, Jie: A second-order changing-connectivity ALE scheme and its application to FSI with large convection of fluids and near contact of structures (2016)
  13. Lu, Peipei; Xu, Xuejun: A robust multilevel method for the time-harmonic Maxwell equation with high wave number (2016)
  14. Mungkasi, Sudi: Adaptive finite volume method for the shallow water equations on triangular grids (2016)
  15. Wang, Wansheng; Chen, Long; Zhou, Jie: Postprocessing mixed finite element methods for solving Cahn-Hilliard equation: methods and error analysis (2016)
  16. Yang, Yidu; Bi, Hai; Li, Hao; Han, Jiayu: Mixed methods for the Helmholtz transmission eigenvalues (2016)
  17. Zheng, Bin; Chen, Luoping; Hu, Xiaozhe; Chen, Long; Nochetto, Ricardo H.; Xu, Jinchao: Fast multilevel solvers for a class of discrete fourth order parabolic problems (2016)
  18. Antil, Harbir; Otárola, Enrique: A FEM for an optimal control problem of fractional powers of elliptic operators (2015)
  19. Chen, Long; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.: A PDE approach to fractional diffusion: a posteriori error analysis (2015)
  20. Chen, Long; Wang, Ming; Zhong, Lin: Convergence analysis of triangular MAC schemes for two dimensional Stokes equations (2015)

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