Towards a scalable domain decomposition solver for immersed boundary finite element method
Please login to view abstract download link
Immersed boundary finite element method (FEM) presents an attractive approach to simulations avoiding the generation of large body-fitted meshes. This can be tedious and challenging for complex geometries as well as for very fine adaptive meshes distributed over a parallel supercomputer. However, the price to pay are more complicated formulations for the weak enforcement of Dirichlet boundary conditions, poor conditioning of stiffness matrices, and nonstandard numerical integration at the boundary. We develop multilevel balancing domain decomposition based on constraints (BDDC) method tailored to the solution of the linear systems arising in the context of immersed boundary FEM with parallel adaptive grid refinement using Z-curves (based on the p4est library). One crucial challenge is presented by load balancing the solver since the elements cut by the domain boundary require much more time for integration, whereas these elements have the same cost during the solution of the linear system as those fully inside the domain. Another challenge is presented by fragmenting of subdomains, which has two sources: i) the partitioning strategy based on space-filling curves, and ii) extraction of the elements contributing to the stiffness matrix. Numerical results for large-scale Poisson and linear elasticity problems on complex geometries from engineering will be presented.
