SIAM Journal on Scientific and Statistical Computing
An energy-minimizing interpolation for robust multigrid methods
SIAM Journal on Scientific Computing
A multigrid tutorial (2nd ed.)
A multigrid tutorial (2nd ed.)
Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Multigrid
Algebraic Two-Level Preconditioners for the Schur Complement Method
SIAM Journal on Scientific Computing
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
General Constrained Energy Minimization Interpolation Mappings for AMG
SIAM Journal on Scientific Computing
A General Interpolation Strategy for Algebraic Multigrid Using Energy Minimization
SIAM Journal on Scientific Computing
| Hi-index | 0.00 |
The modeling of discontinuities arising from fracture of materials poses a number of significant computational challenges. The extended finite element method provides an attractive alternative to standard finite elements in that they do not require fine spatial resolution in the vicinity of discontinuities nor do they require repeated remeshing to properly address propagation of cracks. They do, however, give rise to linear systems requiring special care within an iterative solver method. An algebraic multigrid method is proposed that is suitable for the linear systems associated with modeling fracture via extended finite elements. The new method follows naturally from an energy minimizing algebraic multigrid framework. The key idea is the modification of the prolongator sparsity pattern to prevent interpolation across cracks. This is accomplished by accessing the standard levelset functions used during the discretization process. Numerical experiments illustrate that the resulting method converges in a fashion that is relatively insensitive to mesh resolution and to the number of cracks or their location.