BDDC by a frontal solver and the stress computation in a hip joint replacement

A parallel implementation of the Balancing Domain Decomposition based on Constraints (BDDC) method using the frontal solver is employed to solve systems of linear equations from finite element analysis, and incorporated into a standard finite element system for engineering analysis by linear elasticity. Results of computation of stress in a hip replacement are presented. The part is made of titanium and loaded by the weight of human body. The performance of BDDC with added constraints by averages and with added corners is compared.

[1]  Andrea Toselli,et al.  Domain decomposition methods : algorithms and theory , 2005 .

[2]  Patrick R. Amestoy,et al.  Multifrontal parallel distributed symmetric and unsymmetric solvers , 2000 .

[3]  Jan Mandel,et al.  BDDC and FETI-DP under minimalist assumptions , 2007, Computing.

[4]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[5]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[6]  Pavel Burda,et al.  Face-based selection of corners in 3D substructuring , 2009, Math. Comput. Simul..

[7]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[8]  Susanne C. Brenner,et al.  BDDC and FETI-DP without matrices or vectors , 2007 .

[9]  Olof B. Widlund,et al.  DUAL-PRIMAL FETI METHODS FOR THREE-DIMENSIONAL ELLIPTIC PROBLEMS WITH HETEROGENEOUS COEFFICIENTS , 2022 .

[10]  Z. Bittnar,et al.  Static load balancing applied to Schur complement method , 2007 .

[11]  Olof B. Widlund,et al.  FETI‐DP, BDDC, and block Cholesky methods , 2006 .

[12]  J. Mandel,et al.  An algebraic theory for primal and dual substructuring methods by constraints , 2005 .

[13]  C. Farhat,et al.  A scalable dual-primal domain decomposition method , 2000, Numer. Linear Algebra Appl..

[14]  Clark R. Dohrmann,et al.  Convergence of a balancing domain decomposition by constraints and energy minimization , 2002, Numer. Linear Algebra Appl..

[15]  CLARK R. DOHRMANN,et al.  A Preconditioner for Substructuring Based on Constrained Energy Minimization , 2003, SIAM J. Sci. Comput..

[16]  Bruce M. Irons,et al.  A frontal solution program for finite element analysis , 1970 .