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In this section, we discuss the parallel implementation of the PATCH code,
which was developed by Johnson, Wilton, and Sharp [15] to see
the similarities and the differences between the parallel PATCH code and the
ParaMoM-MPP code.
The similarities are
listed as below:
- Both are general purpose computer codes for electromagnetic
scattering from and radiation by objects of arbitrary shape. They are
based on the method of moments with a surface integral formulation in the
frequency domain. They use surface patches, which conform to surfaces and
boundaries of general shape and allow variable patch density over the
surface of the object. The basis functions for both codes are defined on pairs
of adjacent patches and give a current representation free of line and point
charges.
- Both have the following capabilities: computation of
scattering from multiple bodies, treatment of multiple intersecting
surfaces, use of symmetry planes to reduce the number of unknowns,
treatment of surfaces with lumped and distributed impedance loads, and the
capability for plane wave or voltage source excitation. The outcomes of
these two codes are the currents on the bodies, radiated fields, far
fields, and radar cross section.
- Both codes are implemented on coarse-grained MIMD distributed memory
systems. Message passing and a direct dense matrix equation solver are the main tools
for both codes. The main features of the parallel matrix fill algorithm, are:
1) looping over patches
rather than
looping over edges; 2) no communication takes place; 3) a good load balance
is achieved. LU decomposition with partial pivoting is applied to factorize the moment
matrix.
The differences between the PATCH and ParaMoM-MPP code are listed below:
- PATCH uses the popular Rao-Wilton-Glisson [14] technique with flat facets.
ParaMoM-MPP uses Wilkes' and Cha's basis function which is defined in
terms of any (set of two) arbitrary curvilinear surface coordinates and
conforms to the exact surface curvature of the parametric surface at hand.
Figure 5.31 shows the comparison of performance on a
0.4
circumference
sphere, between the popular RWG technique with flat
facets and that using ParaMoM.
The improvement in accuracy with similar
matrix size is impressive and that leads to reduction in matrix size, for a
specified error tolerance. Cha's group provides a bar chart in
Figure 5.32 showing the matrix size comparison between the RWG
code and ParaMoM 1.0, for several textbook shapes, at a 0.5 dB average
error tolerance. A better than two-to-one reduction in matrix size is
obtained with the use of curved patches.
- PATCH only uses the electric field integral equation formulation.
ParaMoM-MPP has used not only the electric field integral equation
formulation but the magnetic field integral equation and the combined field
integral equation as well.
- In matrix fill, PATCH has two redundant computations of the magnetic
vector potential and electric scalar potential for each source-field patch
pair, but ParaMoM-MPP has only an average of one redundant computation of Green's
function for each source-field patch
pair. PATCH does not precompute the arrays required by the matrix
fill.
They are computed along with the progress of the fill process. The
ParaMoM-MPP matrix fill algorithm is
much more efficient than that of PATCH.
- Compared to PATCH, ParaMoM-MPP is implemented on more architectures,
so that it has better portability.
Next: Conclusion
Up: Performance and Numerical
Previous: Numerical Results