Workshop will begin 9:00 AM Tuesday and end by 3:15 PM Saturday.
Participants should plan to attend the entire workshop.
The numerical solution of partial differential equations (PDE)
is a fundamental task in science and engineering. The goal of
the workshop is to bring together a spectrum of scientists at
the forefront of the research in the numerical solution of PDEs
to discuss compatible spatial discretizations. We define compatible
spatial discretizations as those that inherit or mimic fundamental
properties of the PDE such as topology, conservation, symmetries,
and positivity structures and maximum principles. A wide variety
of discretization methods applied across a wide range of scientific
and engineering applications have been designed to or found
to inherit or mimic instrinsic spatial structure and reproduce
fundamental properties of the solution of the continuous PDE
model at the finite dimensional level. A profusion of such methods
and concepts relevant to understanding them have been developed
and explored: mixed finite element methods, mimetic finite differences,
support operator methods, control volume methods, discrete differential
forms, Whitney forms, conservative differencing, discrete Hodge
operators, discrete Helmholtz decomposition, finite integration
techniques, staggered grid and dual grid methods, etc. This
workshop seeks to foster communication among the diverse groups
of researchers designing, applying, and studying such methods
as well as researchers involved in practical solution of large
scale problems that may benefit from advancements in such discretizations;
to help elucidate the relations between the different methods
and concepts; and to generally advance our understanding in
the area of compatible spatial discretization methods for PDE.
Particular points of emphasis will include:
Identification of intrinsic properties of PDE models that
are critical for the fidelity of numerical simulations.
Identification and design of compatible spatial discretizations
of PDEs, their classification, analysis, and relations.
Relationships between different compatible spatial discretization
methods and concepts which have been developed;
Impact of compatible spatial discretizations upon physical
fidelity, verification and validation of simulations, especially
in large-scale, multiphysics settings.
How solvers address the demands placed upon them by compatible