Algebraic multigrid theory: The symmetric case
Applied Mathematics and Computation - Second Copper Mountain conference on Multigrid methods Copper Mountain, Colorado
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
Multigrid optimization in applications
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
Algebraic Multigrid Based on Element Interpolation (AMGe)
SIAM Journal on Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
On the utilization of edge matrices in algebraic multigrid
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
| Hi-index | 0.00 |
The paper deals with a fast computational method for discretized optimal shape design problems governed by 2---dimensional magnetostatics. We discretize the underlying state problem using linear Lagrange triangular finite elements and in the optimization we eliminate the state problem for each shape design. The shape to be optimized is the interface between the ferromagnetic and air domain. The novelty of our approach is that shape perturbations do not affect grid nodal displacements, which is the case of the traditional moving---grid approach, but they are rather mapped to the coefficient function of the underlying magnetostatic operator. The advantage is that there is no additional restriction for the shape perturbations on fine discretizations. However, this approach often leads to a decay of the finite element convergence rate, which we discuss. The computational efficiency of our method relies on an algebraic multigrid solver for the state problem, which is also described in the paper. At the end we present numerical results.