Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multigrid and saddle-point preconditioners for unfitted finite element
  modelling of inclusions   In this work, we consider the modeling of inclusions in the material using an
unfitted finite element method. In the unfitted methods, structured background
meshes are used and only the underlying finite element space is modified to
incorporate the discontinuities, such as inclusions. Hence, the unfitted
methods provide a more flexible framework for modeling the materials with
multiple inclusions. We employ the method of Lagrange multipliers for enforcing
the interface conditions between the inclusions and matrix, this gives rise to
the linear system of equations of saddle point type. We utilize the Uzawa
method for solving the saddle point system and propose preconditioning
strategies for primal and dual systems.
  For the dual systems, we review and compare the preconditioning strategies
that are developed for FETI and SIMPLE methods. While for the primal system, we
employ a tailored multigrid method specifically developed for the unfitted
meshes. Lastly, the comparison between the proposed preconditioners is made
through several numerical experiments.

36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
18
The categories of this paper are: econ
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat