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Polygonal and Polyhedral Discretizations in Computational Mechanics

Gianmarco ManziniLos Alamos National Laboratory

N. Sukumar, University of California-Berkeley

Joseph Bishop, Sandia National Laboratory

The purpose of this minisymposium is to bring together researchers who develop
and apply novel discretization techniques that extend the regime of standard
finite element approaches for the solution of partial differential equations.
A few examples of such technologies are: continuous and discontinuous Galerkin
methods based on polygonal and polyhedral meshes, structure-preserving mimetic
discretizations, virtual element methods and finite element exterior calculus.
The use of polygonal and polyhedral meshes with convex and concave elements
provide greater flexibility in mesh design, and the discretizations on such
meshes afford robustness in material design simulations, capturing flow in
heterogeneous subsurface porous media, modeling of layered stratification of
faults and fractures at geological sites, and reduced mesh-sensitivity to
model complex pervasive fracture processes. These technologies have given rise
to many new opportunities in computational mechanics as well as new
mathematical challenges.  

Contributions to this minisymposium are solicited that emphasize methods
development and/or applications to problems in engineering sciences that
involve the use of polygonal and polyhedral discretizations.  While
contributions in all aspects related to these methods are invited, some of
the featured topics will include:

o Generalized barycentric coordinates for polygons and polyhedra

o Discontinuous Galerkin, nonconforming finite elements, and boundary
  element formulations on polyhedra

o Virtual element and weak Galerkin schemes for linear and higher-order

o Structure-preserving algorithms (mimetic and finite element exterior calculus)
  for multiphysics simulations

o Polygonal and polyhedral mesh generation algorithms, mesh adaptivity, and
  rapid meshing through cut-cell (carving) approaches

o Error estimates and convergence theory for polyhedral finite element

o Use of polyhedral meshes in applications such as flow simulations, material
  design and microstructural discretization, topology optimization and
  additive manufacturing, deformation of nonlinear continua, fracture,
  and computer graphics and animations