Hi gang,
I started out writing a response to Karen's document she sent last week or the week before, then decided I needed a
better starting point from which to evaluate the proposed iMeshP interface. I came up with the attached 3 use cases. I
would encourage all to think about their iMeshP implementations in the context of these use cases, to see if their
design will enable these use cases as described. I've taken pains to avoid prescribing any iMeshP design decisions in
these use cases; if I've fallen short on any of them in this regard, please point them out. Note that some of them say
things about how the calculation is distributed over processes; this is fair game, I think, since it's how the apps
developers will approach our interface (i.e. they'll decide beforehand how they want to partition the problem over
processes).
If anybody has use case(s) which are substantially different from the space covered by those in this document, please
suggest them. The idea is to keep the number of use cases somewhat low, but to fairly represent the bulk of the space
we expect to cover with iMeshP. At some point, I imagine this document going into the repo or (heaven forbid) some sort
of paper published in the distant future.
I've written how my design will work for the first two use cases, and so far so good (though the 2nd one isn't trivial
to understand). I'm pretty sure the 3rd use case will be easier (for me), but we'll see.
I'm sending this out partly to help others get started thinking about their designs in the context of realistic use
cases, and partly to reassure Karen that I'm doing something about her message, despite the radio silence :).
- tim
--
================================================================
"You will keep in perfect peace him whose mind is
steadfast, because he trusts in you." Isaiah 26:3
Tim Tautges Argonne National Laboratory
(tautges(a)mcs.anl.gov) (telecommuting from UW-Madison)
phone: (608) 263-8485 1500 Engineering Dr.
fax: (608) 263-4499 Madison, WI 53706
iMesh, iMeshP Use Cases
The use cases below describe the PDE to be solved, and any
application-imposed constraints on the parallel solution approach.
These are meant to illustrate the use of the iMesh and iMeshP
interfaces to solve these problems.
For a given use case, describe how the constructs proposed for iMesh
and iMeshP (e.g. Process, iMesh/iMeshP Instances, iMesh/iMeshP API functions,
Partition, Part) will be used to solve the problem. While not
absolutely required, this will generally require desription of:
- the basic approach to distributing the domain and computations for
the domain across Processes
- what kind of communications are done in general, and how those
interact with iMeshP constructs
- the basic steps of the computational or time step kernel, and how
they interact with iMeshP/iMesh.
=====================
Use case 1: Solve a discretized PDE with FEM using spatial domain
decomposition
---------------------
Problem statement
Solve a function dF/dx = f(x) on a spatial domain with prescribed
boundary conditions.
===============================
Use case 2: Radiation transport
-------------------------------
Problem Statement
In this use case, the radiation flux phi(x,E,t) is computed over a
finite element grid, with flux values stored at vertices. In a very
simplified form, the implicit formulation of this equation can be
written as:
d/d(x,E,t) phi(x,E,t1) = f(S(x,E), phis(x,t0))
where
phis(x,t) = sum_E{w_E phi(x,E,t)}
is the scalar flux, a weighted sum of energy-dependent fluxes phi(x,E,t).
The discretized problem is partitioned into S spatial domains {si} and
E energy domains {ej}.
A given time step solution consists of two parts. First, across an
energy subdomain ej, the problem is solved over the spatial subdomains
si using a domain decomposition PDE solution method; the result is an
phi(v(si),ej,t0), the radiation flux for a given energy ej at each
vertex si. Second, the energy-based flux is converted to a scalar
phi(v(si),t0), by computing a weighted sum over energy subdomains ej of
the flux at each vertex, phi(v(si),ej,t0). The scalar flux is used in
computing the energy-dependent flux phi(v(si),t1) on the next time step.
===============================
Use case 3: Structural dynamics with parallel contact detection
-------------------------------
Problem Statement
Solve a structural dynamics problem:
d/dt^2 x(x,t) = f(x,t)
over a volumetric domain V with multiple connected sets V_k,
handling cases where connected sets come into contact and exert force
on each other when their boundaries collide.
Solve each time step in two phases. In the first phase, solve for new
positions x(x,t) using a standard (spatial) domain decomposition FEM,
with each process responsible for computing behavior of a spatial
subdomain. In the second phase, for all faces bounding single volume
elements (i.e. not contiguously connected to two volume elements),
given the length of the next timestep t, compute location and time of
collision of any two faces in that set. Solve this second phase by
distributing faces over processes according to spatial proximity,
based on some space-filling decomposition of the bounding box of all
volume elements (which will by definition enclose all bounding faces).
No restrictions should be placed on which process is assigned a volume
element and any of its connected boundary faces; that is, a volume and
its connected boundary faces are not required to be solved by the same
process.
