Computing Time on Massively Parallel Computer Cluster Awarded by
the National Computational Science Alliance (NCSA)
Project Title: Parallel Iterative methods for Acoustic Scattering
Start: July 2002 - Dec 2003
Grant Num: MSS020008N
SU hours: 10000.0 for Machine: IA32 Linux Cluster (platinum.ncsa.uiuc.edu)
Non-Technical Summary
Parallel iterative methods for fast solution of large-scale acoustic
radiation and scattering problems are developed using
exact Dirichlet-to-Neumann (DtN), nonreflecting boundaries.
A separable spheroidal nonreflecting boundary is used to
efficiently model unbounded regions surrounding elongated structures.
We exploit the special structure of the non-local DtN map as a low-rank update
of the system matrix to efficiently compute the matrix-by-vector products
found in Krylov subspace based iterative methods.
For the complex non-hermitian matrices resulting from the
Helmholtz equation, we use a distributed-memory parallel
BICG-STAB iterative method in conjunction with a parallel
hybrid Jacobi/SSOR preconditioner.
Domain decomposition with interface minimization was performed to ensure
optimal inter-processor communication. For the
distributed memory architectures tested, and
using the MPICH version of MPI, we show that when implemented as a
low-rank update, the non-local character of the DtN map
does not significantly decrease the scale up and
parallel efficiency versus a purely approximate local boundary condition.
This project is focused on developing and testing
efficient parallel algorithms for iterative solution of exterior
acoustic scattering problems in two and three dimensions.
When solving exterior Helmholtz problems using domain-based method
(e.g. Finite Element Method), a computational domain is defined by
truncating the
infinite domain via an arbitrary separable boundary. Accurate non-reflecting
boundary conditions have been
formulated on elliptic and spheroidal truncation boundaries,
suitable for elongated scatterers such as a submarine and a ship.
Numerical solution
of large-scale problems (i.e. wavelength is considerably smaller
than the dimensions of the scatterer) requires a large number of degrees
of freedom to capture wave patterns within the computational domain. Thus,
larger problem sizes arise at higher wavenumbers, especially
in three dimensions,
overwhelming the storage capabilities of a single computing node.
The parallel algorithm developed in this project is not intended
for massively parallel applications, as collective communication
operations are frequently required. However, this implementation
significantly reduces communication costs due to
non-locality of the non-reflecting
boundary condition, by exploiting
the outer-product structure of the boundary operator,
thus rendering a highly scalable algorithm up to approaching 100 processors.
A study performed on an NCSA system (platinum.ncsa.uiuc.edu)
for a problem size of 350,000 degrees of freedom (1 million tetrahedron)
has revealed a 98%
or better parallel efficiency when using up to 32 processors
We have now generated three-dimensional
meshes meshes of over 500,000 degrees of freedom (2.5 million
tetrahedron) and plan to increase to over 1 million degrees-of-freedom
(4 million tetrahedron) using I-DEAS.
This research is supported by NSF Award CMS 9702082.
References
Ianculescu, C., Thompson, L.L.,
``Parallel iterative methods for the Helmholtz equation with
exact nonreflecting boundaries'', Paper IMECE2002/NCA-32744,
Proc. IMECE'02, 2002 ASME International
Mechanical Engineering Congress and Exposition, New Orleans, Louisiana,
Nov. 17-22, 2002.
Ianculescu, C., Thompson, L.L.,
``Parallel iterative finite element solution methods for three-dimensional
acoustic scattering'', Paper IMECE2003-44266,
Proc. IMECE'03, 2003 ASME International
Mechanical Engineering Congress and Exposition, Washington, D.C.,
Nov. 15-21, 2003.
Ianculescu, C. and Thompson, L.L.,
``Parallel iterative solution of large-scale acoustic scattering problems
using exact non-reflecting conditions on distributed memory
computer systems'',
145th meeting of the Acoustical Society of America,
Session 3aSAb2: Structural Acoustics and Vibration: Computational Methods,
Nashville, Tennessee, April 28 -- May 2, 2003.
Abstract 3aSAb2, J. Acoust. Soc. Am., Vol. 113, No. 4, Pt. 2, April 2003,
page 2252.
Ianculescu, C., Thompson, L.L.,
``Efficient parallel iterative methods for acoustic scattering with exact
nonreflecting boundaries'', Forum Acusticum Sevilla, Spain, 2002
-L.L.Thompson
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