Research Interests

Material Point Method

The material point method (MPM) is a hybrid particle-cell method that represents continua by a number of Lagrangian elements, termed the material points. It adopts a finite element like approach on a fixed background mesh to calculate gradient terms such as the deformation gradient and to exchange information between particles. The MPM is quite attractive for solving engineering problems with large deformations.

Our group is mainly interested in the mathematical aspects of the MPM and has been working on the integration of concepts from Isogeometric Analysis.

Selected contributions

  • Wojciech T. Solowski, Martin Berzins, William M. Coombs, James E. Guilkey, Matthias Möller, Quoc Anh Tran, Tito Adibaskoro, Seyedmohammadjavad Seyedan, Roel P.W.M. Tielen, and Kenichi Soga. chapter Material Point Method: overview and challenges ahead. Advances in Applied Mechanics book series. 2020. Submitted to.
  • Pascal de Koster, Roel Tielen, Elizaveta Wobbes, and Matthias Möller. Extension of b-spline material point method for unstructured triangular grids using Powell-Sabin splines. Computational Particle Mechanics, March 2020. [ DOI | arXiv | http ]
  • Quoc-Anh Tran, Elizaveta Wobbes, Wojciech Sokowski, Matthias Möller, and Cornelis Vuik. Moving least squares reconstruction for B-spline material point method. In Proceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, Cambridge, UK, jan 2019. [ .pdf ]
  • Roel Tielen, Matthias Möller, and Kees Vuik. Efficient multigrid based solvers for b-spline mpm. In Proceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, Cambridge, UK, jan 2019. [ .pdf ]
  • Elizaveta D. Wobbes, Roel Tielen, Matthias Möller, and Cornelis Vuik. Recent developments to improve the numerical accuracy. In James Fern, Alexander Rohe, Kenichi Soga, and Eduardo Alonso, editors, The Material Point Method for Geotechnical Engineering, pages 67--88. CRC Press, jan 2019. [ DOI | http ]
  • Elizaveta Wobbes, Roel Tielen, Matthias Möller, Kees Vuik, and Vahid Galavi. Comparison between material point method and meshfree schemes derived from optimal transportation theory. In Proceedings of the Second International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, Cambridge, UK, jan 2019. [ .pdf ]
  • Elizaveta Wobbes, Matthias Möller, Vahid Galavi, and Cornelis Vuik. Conservative Taylor least squares reconstruction with application to material point methods. International Journal for Numerical Methods in Engineering, 117(3):271--290, oct 2018. [ DOI | http ]
  • Elizaveta Wobbes, Matthias Möller, Vahid Galavi, and Cornelis Vuik. Taylor least squares reconstruction technique for material point methods. In Proceedings of the 6th European Conference on Computational Mechanics (ECCM 6) and the 7th European Conference on Computational Fluid Dynamics (ECFD 7), Glasgow, UK, jun 2018. ECCOMAS. (pdf).
  • Pascal de Koster. Towards a material point method with Powell-Sabin spline basis functions, 2018. [ http ]
  • Roel Tielen, Elizaveta Wobbes, Matthias Möller, and Lars Beuth. A high order material point method. Procedia Engineering, 175:265--272, 2017. [ DOI | http ]
  • Roel P.W.M Tielen. High-order material point method, 2016. [ http ]