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 76 articles )

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  1. Broersen, D.; Dahmen, W.; Stevenson, R. P.: On the stability of DPG formulations of transport equations (2018)
  2. Hofherr, Florian; Karrasch, Daniel: Lagrangian transport through surfaces in compressible flows (2018)
  3. Hou, Tianliang; Chen, Luoping; Yang, Yin: Two-grid methods for expanded mixed finite element approximations of semi-linear parabolic integro-differential equations (2018)
  4. Huang, Jian; Chen, Long; Rui, Hongxing: Multigrid methods for a mixed finite element method of the Darcy-Forchheimer model (2018)
  5. Li, Hao; Yang, Yidu: $C^0\mathrmIPG$ adaptive algorithms for the biharmonic eigenvalue problem (2018)
  6. Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran: The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes (2018)
  7. Song, Xiaoliang; Chen, Bo; Yu, Bo: An efficient duality-based approach for PDE-constrained sparse optimization (2018)
  8. Chen, Long; Wei, Huayi; Wen, Min: An interface-fitted mesh generator and virtual element methods for elliptic interface problems (2017)
  9. Chen, Luoping; Zheng, Bin; Lin, Guang; Voulgarakis, Nikolaos: A two-level stochastic collocation method for semilinear elliptic equations with random coefficients (2017)
  10. Demlow, Alan: Convergence and quasi-optimality of adaptive finite element methods for harmonic forms (2017)
  11. Faugeras, Blaise; Heumann, Holger: FEM-BEM coupling methods for tokamak plasma axisymmetric free-boundary equilibrium computations in unbounded domains (2017)
  12. Heumann, Holger; Rapetti, Francesca: A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries (2017)
  13. Hintermüller, Michael; Hinze, Michael; Kahle, Christian; Keil, Tobias: Fully adaptive and integrated numerical methods for the simulation and control of variable density multiphase flows governed by diffuse interface models (2017)
  14. Wu, Jinbiao; Zheng, Hui: Uniform convergence of multigrid methods for adaptive meshes (2017)
  15. Wu, Shuonan; Gong, Shihua; Xu, Jinchao: Interior penalty mixed finite element methods of any order in any dimension for linear elasticity with strongly symmetric stress tensor (2017)
  16. Yang, Yidu; Bi, Hai; Li, Hao; Han, Jiayu: A $C^0 \mathrmIPG$ method and its error estimates for the Helmholtz transmission eigenvalue problem (2017)
  17. Zhang, Xuping; Zhang, Jintao; Yu, Bo: Symmetric homotopy method for discretized elliptic equations with cubic and quintic nonlinearities (2017)
  18. Bi, Hai; Li, Hao; Yang, Yidu: An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem (2016)
  19. Chen, Long; Nochetto, Ricardo H.; Otárola, Enrique; Salgado, Abner J.: Multilevel methods for nonuniformly elliptic operators and fractional diffusion (2016)
  20. Cockburn, Bernardo; Demlow, Alan: Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces (2016)

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