Constraint interface preconditioning for topology optimization problems

The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity and size. In this work we propose a methodology which brings together existing fast algorithms, namely, interior-point for the optimization problem and a novel substructuring domain decomposition method for the ensuing large-scale linear systems. The main contribution is the choice of interface preconditioner which allows for the acceleration of the domain decomposition method, leading to performance independent of problem size.Comment: To be published in SIAM J. Sci. Com

A multigrid discretization scheme of discontinuous Galerkin method for the Steklov-Lamé eigenproblem

In this paper, for the Steklov-Lamé eigenvalue problem, we propose a multigrid discretization scheme of discontinuous Galerkin method based on the shifted-inverse iteration. Based on the existing a priori error estimates, we give the error estimates for the proposed scheme and prove that the resulting approximations can achieve the optimal convergence order when the mesh sizes fit into some relationships. Finally, we combine the multigrid scheme and adaptive procedure to present some numerical examples which indicate that our scheme are locking-free and efficient for computing Steklov-Lamé eigenvalues

A literature survey of low-rank tensor approximation techniques

During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey attempts to give a literature overview of current developments in this area, with an emphasis on function-related tensors