Speaker
Description
We prove the convergence of the multigrid method for parameter-dependent symmetric positive definite linear systems. We present the smoothing and approximation properties for such problems and prove the smoothing property for the parameter-dependent damped Richardson as well as the parameter-dependent damped Jacobi method.
Our theoretical results require a parameter-dependent representation of the operator, the solution, the right-hand side, the smoother as well as the prolongation and restriction. We use tensor formats to derive such a representation for linear systems with affine-linear operators. For the parameter-dependent damped Jacobi method, we derive an approximation using exponential sums and prove the smoothing property for this representation.
In numerical experiments, we observe that the convergence behavior of the multigrid method with the damped Jacobi smoother in the parameter-dependent case seems to be grid size independent.
