iFEM

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 40 articles )

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  1. Bi, Hai; Li, Hao; Yang, Yidu: An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem (2016)
  2. Chen, Long; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.: Multilevel methods for nonuniformly elliptic operators and fractional diffusion (2016)
  3. Cuvelier, François; Japhet, Caroline; Scarella, Gilles: An efficient way to assemble finite element matrices in vector languages (2016)
  4. Demlow, Alan; Kopteva, Natalia: Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems (2016)
  5. Garcke, Harald; Hinze, Michael; Kahle, Christian: A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow (2016)
  6. Li, Feiyan; Bi, Hai: A type of multigrid method based on the fixed-shift inverse iteration for the Steklov eigenvalue problem (2016)
  7. Lu, Peipei; Xu, Xuejun: A robust multilevel method for the time-harmonic Maxwell equation with high wave number (2016)
  8. Wang, Wansheng; Chen, Long; Zhou, Jie: Postprocessing mixed finite element methods for solving Cahn-Hilliard equation: methods and error analysis (2016)
  9. Yang, Yidu; Bi, Hai; Li, Hao; Han, Jiayu: Mixed methods for the Helmholtz transmission eigenvalues (2016)
  10. 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)
  11. Antil, Harbir; Otárola, Enrique: A FEM for an optimal control problem of fractional powers of elliptic operators (2015)
  12. Chen, Long; Wang, Ming; Zhong, Lin: Convergence analysis of triangular MAC schemes for two dimensional Stokes equations (2015)
  13. Fu, Zhixing; Gatica, Luis F.; Sayas, Francisco-javier: Algorithm 949: MATLAB tools for HDG in three dimensions (2015)
  14. Garcke, Harald; Hecht, Claudia; Hinze, Michael; Kahle, Christian: Numerical approximation of phase field based shape and topology optimization for fluids (2015)
  15. Han, Jiayu; Zhang, Zhimin; Yang, Yidu: A new adaptive mixed finite element method based on residual type a posterior error estimates for the Stokes eigenvalue problem (2015)
  16. Hateley, James C.; Wei, Huayi; Chen, Long: Fast methods for computing centroidal Voronoi tessellations (2015)
  17. Lin, Guang; Liu, Jiangguo; Sadre-Marandi, Farrah: A comparative study on the weak Galerkin, discontinuous Galerkin, and mixed finite element methods (2015)
  18. Yang, Min; Liu, Jiangguo; Lin, Yanping: Pressure recovery for weakly over-penalized discontinuous Galerkin methods for the Stokes problem (2015)
  19. Yang, Yidu; Bi, Hai; Han, Jiayu; Yu, Yuanyuan: The shifted-inverse iteration based on the multigrid discretizations for eigenvalue problems (2015)
  20. Yang, Yidu; Han, Jiayu; Bi, Hai; Yu, Yuanyuan: The lower/upper bound property of the Crouzeix-Raviart element eigenvalues on adaptive meshes (2015)

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