@article{YangKollmannsbergerDuesteretal.2011, author = {Yang, Zhengxiong and Kollmannsberger, Stefan and D{\"u}ster, Alexander and Ruess, Martin and Garcia, Eduardo Grande and Burgkart, Rainer and Rank, Ernst}, title = {Non-standard bone simulation: interactive numerical analysis by computational steering}, series = {Computing and Visualization in Science}, volume = {14}, journal = {Computing and Visualization in Science}, number = {5}, publisher = {Springer}, doi = {10.1007/s00791-012-0175-y}, pages = {207 -- 216}, year = {2011}, language = {en} } @article{ZanderKollmannsbergerRuessetal.2012, author = {Zander, Nils and Kollmannsberger, Stefan and Ruess, Martin and Yosibash, Z. and Rank, Ernst}, title = {The Finite Cell Method for linear thermoelasticity}, series = {Computers \& Mathematics with Applications}, volume = {64}, journal = {Computers \& Mathematics with Applications}, number = {11}, publisher = {Elsevier}, issn = {0898-1221}, doi = {10.1016/j.camwa.2012.09.002}, pages = {3527 -- 3541}, year = {2012}, language = {en} } @article{ZanderBogElhaddadetal.2014, author = {Zander, Nils and Bog, Tino and Elhaddad, Mohamed and Espinoza, R. and Hu, H. and Joly, A. and Wu, C. and Zerbe, P. and D{\"u}ster, Alexander and Kollmannsberger, Stefan and Parvizian, J. and Ruess, Martin and Schillinger, Dominik and Rank, Ernst}, title = {FCMLab: A finite cell research toolbox for MATLAB}, series = {Advances in Engineering Software}, volume = {74}, journal = {Advances in Engineering Software}, publisher = {Elsevier}, issn = {0965-9978}, doi = {10.1016/j.advengsoft.2014.04.004}, pages = {49 -- 63}, year = {2014}, language = {en} } @article{RankRuessKollmannsbergeretal.2012, author = {Rank, Ernst and Ruess, Martin and Kollmannsberger, Stefan and Schillinger, Dominik and D{\"u}ster, Alexander}, title = {Geometric modeling, isogeometric analysis and the finite cell method}, series = {Computer Methods in Applied Mechanics and Engineering}, volume = {249-252}, journal = {Computer Methods in Applied Mechanics and Engineering}, publisher = {Elsevier}, issn = {0045-7825}, doi = {10.1016/j.cma.2012.05.022}, pages = {104 -- 115}, year = {2012}, language = {de} } @article{YangRuessKollmannsbergeretal.2012, author = {Yang, Z. and Ruess, Martin and Kollmannsberger, Stefan and D{\"u}ster, Alexander and Rank, Ernst}, title = {An efficient integration technique for the voxel-based finite cell method}, series = {International Journal for Numerical Methods in Engineering}, volume = {91}, journal = {International Journal for Numerical Methods in Engineering}, number = {5}, publisher = {Wiley}, issn = {1097-0207}, doi = {10.1002/nme.4269}, pages = {457 -- 471}, year = {2012}, language = {en} } @article{KollmannsbergerOezcanBaigesetal.2015, author = {Kollmannsberger, Stefan and {\"O}zcan, Ali I. and Baiges, J. and Ruess, Martin and Rank, Ernst and Reali, A.}, title = {Parameter-free, weak imposition of Dirichlet boundary conditions and coupling of trimmed and non-conforming patches}, series = {International Journal for Numerical Methods in Engineering}, volume = {101}, journal = {International Journal for Numerical Methods in Engineering}, number = {9}, publisher = {Wiley}, issn = {1097-0207}, doi = {10.1002/nme.4817}, pages = {670 -- 699}, year = {2015}, language = {en} } @article{ZanderRuessBogetal.2017, author = {Zander, Nils and Ruess, Martin and Bog, Tino and Kollmannsberger, Stefan and Rank, Ernst}, title = {Multi-level hp -adaptivity for cohesive fracture modeling}, series = {International Journal for Numerical Methods in Engineering}, volume = {109}, journal = {International Journal for Numerical Methods in Engineering}, number = {13}, publisher = {Wiley}, issn = {1097-0207}, doi = {10.1002/nme.5340}, pages = {1723 -- 1755}, year = {2017}, language = {en} } @article{ElhaddadZanderBogetal.2018, author = {Elhaddad, Mohamed and Zander, Nils and Bog, Tino and Kudela, L{\´a}szl{\´o} and Kollmannsberger, Stefan and Kirschke, Jan and Baum, Thomas and Ruess, Martin and Rank, Ernst}, title = {Multi-level hp-finite cell method for embedded interface problems with application in biomechanics}, series = {International Journal for Numerical Methods in Biomedical Engineering}, volume = {34}, journal = {International Journal for Numerical Methods in Biomedical Engineering}, number = {4}, publisher = {Wiley}, issn = {2040-7947}, doi = {10.1002/cnm.2951}, year = {2018}, abstract = {This work presents a numerical discretization technique for solving 3-dimensional material interface problems involving complex geometry without conforming mesh generation. The finite cell method (FCM), which is a high-order fictitious domain approach, is used for the numerical approximation of the solution without a boundary-conforming mesh. Weak discontinuities at material interfaces are resolved by using separate FCM meshes for each material sub-domain and weakly enforcing the interface conditions between the different meshes. Additionally, a recently developed hierarchical hp-refinement scheme is used to locally refine the FCM meshes to resolve singularities and local solution features at the interfaces. Thereby, higher convergence rates are achievable for nonsmooth problems. A series of numerical experiments with 2- and 3-dimensional benchmark problems is presented, showing that the proposed hp-refinement scheme in conjunction with the weak enforcement of the interface conditions leads to a significant improvement of the convergence rates, even in the presence of singularities. Finally, the proposed technique is applied to simulate a vertebra-implant model. The application showcases the method's potential as an accurate simulation tool for biomechanical problems involving complex geometry, and it demonstrates its flexibility in dealing with different types of geometric description.}, language = {en} }