Technologies and Tools for High-Performance Distributed Computing

1
Scalable Solvers
In support of SciDAC fusion, astophysical,
combustion, and other simulations, TOPS is
creating a new generation of solvers for PDE
field problems.
How SciDAC apps engage TOPS solvers
PDE solver software is strategic to SciDAC

• Directly (now)
• Apps code sets up own discretization, possibly
  built on a grid made up of distributed objects
  from PETSc (like M3D)
• Apps code calls a TOPS solver, possibly with
  explicit matrix elements, or in a Jacobian-free
  mode
• Through APDEC or TSTT (coming in 2003)
• Apps code calls on Chombo, Overture, Trellis,
  etc., to express its PDEs with an automatically
  adapted discretization
• Through componentization (coming later)
• Apps code, discretization frameworks, TOPS
  solvers are all peer components interacting in a
  Common Component Architecture framework
• Benefits to apps
• With solver, get stability analysis and
  sensitivity analysis functionality

• Many DOE mission-critical systems are modeled by
  PDEs
• Finite-dimensional models of PDEs must be large
  for accuracy
• Qualitative insight is not enough (Hamming
  notwithstanding)
• Simulations must resolve policy controversies
• Advances in algorithms are at least as important
  as advances in hardware, in supporting simulation
• Easily demonstrated for PDEs in the period
  19452000
• Continuous problems provide exploitable hierarchy
  of approximation models, creating hope for
  optimal algorithms
• Software lags both hardware and algorithms

Keyword, key challenge Optimal
Early TOPS partners
TOPS has many application partners, including the
Center for Extended Magnetohydrodynamic Modeling
(CEMM, left), the Center for Magnetic
Reconnection Studies (CMRS, below left), and the
Terascale Supernovae Initiative (TSI, below
right). For CEMM, TOPSs scalable linear solvers
power linear solvers inside an operator-split
time integration of tokamak dynamics. For CMRS,
TOPS has developed a fully implicit nonlinear
capability, permitting accurate implicit time
stepping that exceeds the Courant stability limit
for an explicit method. For TSI, TOPS is
extending TSIs 1D operator-split solvers to 2D
and 3D operator-split and nonlinearly implicit,
both.

• Convergence rate nearly independent of
  discretization parameters
• Multilevel schemes for linear and nonlinear
  problems
• Newton-like schemes for quadratic convergence of
  nonlinear problems
• Convergence rate as independent as possible of
  physical parameters
• Continuation schemes
• Asymptotics-induced, operator-split
  preconditioning

time
size, procs
Algebraic multigrid (AMG) above, shows perfect
iteration scaling, above, in contrast to additive
Schwarz (ASM), but still needs performance work
to achieve temporal scaling, below, on CEMM
fusion code, M3D
iters
size, procs
Interoperability TOPS brings together and will
make interoperable some of the most popular
solver software toolkits in the DOE, such as
Hypre, PETSc, and SUNDIALS. TOPS solvers will
also interoperate with APDEC and TSTT codes.
Multiple interfaces TOPSs conceptual interfaces
(from Hypre, below) allow users to access its
multilevel solvers from data structures close to
the applications. TOPSs interface to automatic
differentiation tools (through PETSc, below
right) provides rapid nonlinear solution and
optimization, all matrix-free.
for more information ...
http//www.tops-scidac.org