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 83 articles )

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  1. Broersen, D.; Dahmen, W.; Stevenson, R. P.: On the stability of DPG formulations of transport equations (2018)
  2. Chen, Long; Hu, Jun; Huang, Xuehai: Multigrid methods for Hellan-Herrmann-Johnson mixed method of Kirchhoff plate bending problems (2018)
  3. Froyland, Gary; Junge, Oliver: Robust FEM-based extraction of finite-time coherent sets using scattered, sparse, and incomplete trajectories (2018)
  4. Hofherr, Florian; Karrasch, Daniel: Lagrangian transport through surfaces in compressible flows (2018)
  5. Hou, Tianliang; Chen, Luoping; Yang, Yin: Two-grid methods for expanded mixed finite element approximations of semi-linear parabolic integro-differential equations (2018)
  6. Huang, Jian; Chen, Long; Rui, Hongxing: Multigrid methods for a mixed finite element method of the Darcy-Forchheimer model (2018)
  7. Li, Hao; Yang, Yidu: An adaptive $C^0$IPG method for the Helmholtz transmission eigenvalue problem (2018)
  8. Li, Hao; Yang, Yidu: $C^0\mathrmIPG$ adaptive algorithms for the biharmonic eigenvalue problem (2018)
  9. Li, Qi; Mei, Liquan; You, Bo: A second-order, uniquely solvable, energy stable BDF numerical scheme for the phase field crystal model (2018)
  10. Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran: The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes (2018)
  11. Song, Xiaoliang; Chen, Bo; Yu, Bo: An efficient duality-based approach for PDE-constrained sparse optimization (2018)
  12. Wang, Fei; Wei, Huayi: Virtual element method for simplified friction problem (2018)
  13. Wang, Gang; He, Yinnian; Yang, Jinjin: Weak Galerkin finite element methods for the simulation of single-phase flow in fractured porous media (2018)
  14. Chen, Long; Wei, Huayi; Wen, Min: An interface-fitted mesh generator and virtual element methods for elliptic interface problems (2017)
  15. Chen, Luoping; Zheng, Bin; Lin, Guang; Voulgarakis, Nikolaos: A two-level stochastic collocation method for semilinear elliptic equations with random coefficients (2017)
  16. Demlow, Alan: Convergence and quasi-optimality of adaptive finite element methods for harmonic forms (2017)
  17. Faugeras, Blaise; Heumann, Holger: FEM-BEM coupling methods for tokamak plasma axisymmetric free-boundary equilibrium computations in unbounded domains (2017)
  18. Guo, Hailong; Zhang, Zhimin; Zhao, Ren: Superconvergent two-grid methods for elliptic eigenvalue problems (2017)
  19. Heumann, Holger; Rapetti, Francesca: A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries (2017)
  20. 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)

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