National Partnership for Advanced Computational Infrastructure

1
National Partnership for Advanced Computational
Infrastructure
University of California, San Diego
The Scallop Solver LibraryGreg Balls and Scott
B. Baden
Scallop is a library of solvers for elliptic
partial differential equations on regular
block-structured domains. Scallop is designed to
be scalable latency tolerant. Latency is hidden
algorithmically by taking advantage of the
locality properties of the solution. Most
iterative methods communicate frequently to
update boundary conditions. Scallop communicates
data among processors only twice first to build
a coarse approximation of the right hand side,
and second to correct the local boundary
conditions with fine grid data. The Scallop
library is built on top of the KeLP programming
system and runs on a variety of machines,
including NPACIs Blue Horizon. Scallop takes
advantage of locality of the solution. Since the
solution of an elliptic PDE is a smooth function
in the far field, far field data can be
accurately represented by a much coarser mesh.
This allows us to eliminate the need for
iterative communication updates. Only two
communication steps are required to calculate
fully resolved solutions. The first
communication step constructs a global right hand
side using information from initial local
solutions. After the coarse grid solution has
been found, processors communicate a second time
to calculate local fine grid boundary conditions.
Scallop implements its non-iterative domain
decomposition algorithm like this for each
local grid calculate_local_approximation comm
unicate_coarse_grid calculate_coarse_solution comm
unicate_fine_boundary_data for each local grid
calculate_final_solution Collaboration
Scallop is built on the KeLP programming system.
Scallop is being developed in collaboration with
the PTE/MolSci Alpha project, Adaptive
Computations Applied to Simulation of Fluids in
Biological Systems, and may be used as a solver
within that project.
Domain decomposition does not strongly affect the
solution error
Communication time does not overwhelm the total
solution time
Computation time per point is good when the
amount of work per node is reasonably large
Scallop code and further information is available
for download from http//www-cse.ucsd.edu/groups/
hpcl/scg/scallop.html