In this paper we present a family of scalable preconditioners for matrices arising in the
discretization of H(div) problems using the lowest order Raviart--Thomas finite elements. Our …

This work introduces nodal auxiliary space preconditioners for discretizations of mixed-
dimensional partial differential equations. We first consider the continuous setting and …

A block-diagonal preconditioner with the minimal residual method and an approximate block-
factorization preconditioner with the generalized minimal residual method are developed for …

Over the last few decades, developing efficient iterative methods for solving discretized
partial differential equations (PDEs) has been a topic of intensive research. Though these …

We present a parallel algebraic multigrid (AMG) algorithm for the implicit solution of the
Darcy problem discretized by the discontinuous Galerkin (DG) method that scales optimally …

This thesis is concerned with multilevel methods for the efficient solution of partial differential
equations in the field of scientific computing. Further, emphasis is put on an extensive study …

We are interested in positivity preserving spatial discretizations applicable to arbitrary order
mixed finite element spatial discretizations of the radiative diffusion equations. Though not …

We propose an auxiliary space method for the solution of the indefinite problem arising from
mixed method finite element discretizations of scalar elliptic problems. The proposed …

This paper gives an overview of some recent works by the author and collaborators on
numerical methods for partial differential equations. One focus is on the development and …

Persevering symmetric solutions, even in the under-converged limit, is important to the
robustness of production simulation codes. We explore the symmetry preservation in both a …