Graduate Exam Abstract
Ana Manic
Ph.D. Final
August 19, 2015, 10:00 am - 1:00 pm
ENGRG B4
Fast and Accurate Double-Higher-Order Method of Moments Accelerated by Diakoptic Domain Decomposition and Memory Efficient Parallelization for High Performance Computing Systems
Abstract: The principal objective of this
dissertation is to develop and test a
robust method based on the method
of moments (MoM) surface integral
equation (SIE) formulation for
electromagnetic analysis of dielectric
and magnetic scatterers and
antennas in the frequency domain
using double higher order (DHO)
mesh discretization. It is well known
that by using higher order basis
functions for current/field modeling in
computational electromagnetics
(CEM), significant reductions in the
number of unknowns, as well as faster
system matrix computation/solution,
can be achieved when compared to
the traditional low order modeling.
Tightly coupled with using higher
order basis functions is higher order
geometry modeling and together they
lay foundation to double higher order
(DHO) modeling. Double (geometrical
and current) higher order modeling
enables using large curved patches,
which can greatly reduce the number
of unknowns for a given problem and
enhance the accuracy and efficiency
of the computation. Element orders in
the model can also be low both in
terms of basis function order or
geometrical order, so the low-order
modeling approach is actually
included in the DHO modeling. So, a
whole range of element sizes and
shapes, geometrical orders, and
current approximation orders can be
used at the same time in a single
simulation model of a complex
structure using the high order (more
precisely, low-to-high order) CEM
technique.
The two major issues arising in the
application of the MoM-SIE numerical
methods when solving large and
computationally expensive
electromagnetic problems are: 1) fast
and accurate calculation of the system
matrix entrances arising in the MoM-
SIE formulation and 2) overall
computational and memory storage
complexity of the method. The goal of
this dissertation is to propose and
validate a solution for both of the
major method’s bottlenecks.
The accurate and fast computation of
the system matrix includes advanced
methods for numerical computation of
singular and near-singular integrals
defined on the surface mesh
elements. When the method is aimed
at analysis of both metallic and
dielectric/magnetic structures, the
singularity of the integral kernel
increases, and requires special
treatment of highly singular integrals.
Finally, this problem is even more
pronounced when higher order basis
functions are used for the
approximation of electric and
magnetic equivalent surface currents
defined on curved patches. This
dissertation presents a novel method
for numerical computation of near-
singular (potential) and near-
hypersingular (field) integrals defined
on Lagrange-type generalized curved
parametric quadrilateral surface
elements of arbitrary geometrical
orders with polynomial basis functions
of arbitrary current-approximation
orders. The integrals are evaluated
using a method based on the
singularity extraction, which consists
of analytical integration of a principal
singular part of the integrand over a
(generally not rectangular)
parallelogram whose surface is close
to the surface of the generalized
quadrilateral near the singular point
and numerical integration of the rest.
The majority of the existing extraction
techniques have been developed for
planar triangular patches involving
low-order basis functions. Few of
those have been extended to curved
patches but without really taking into
account the curvature of the surface.
The presented integration technique
considers the curvature of the patch
by extracting multiple terms in the
evaluation of the principal singular
part. Further, the theory behind the
extraction technique has been
extended to consider integrals with
higher order basis functions.
Overall computational complexity and
memory requirements of the
traditional MoM-SIE method are of the
O(N3) and O(N2), respectively, where
N is the number of unknowns. Even
though DHO modelling can reduce
number of unknowns by the order of
20, the order of computational
complexity remains the same. As the
part of this dissertation, a novel fast
scalable DHO parallel algorithm on
the DHO MoM-SIE in conjunction with
a direct solver for dense linear
systems with hierarchically
semiseparable structures (HSS) is
proposed. We are developing
asymptotically fast higher order direct
algorithms for MoM-SIE solutions
which, in a nutshell, are an algebraic
generalization to fast multipole
methods. In addition to being fast,
they offer a promise of being memory-
and communication-efficient and
amenable to extreme-scale parallel
computing. The main advantage of
the HSS algorithm is in the linear-
complexity ULV-type factorizations
(compared to the conventional LU
decomposition that has cubic
complexity). Our work uses the
recently developed new, state-of-the-
art, algorithms for solving dense and
sparse linear systems of equations
based on the HSS method. In
addition, rank revealing QR (RRQR)
decomposition for the matrix
(memory) compression. Its adaptive
nature comes from the ability to use
the stopping criteria, i.e., relative
tolerance value/minimal rank, which
allows for the method to store only the
low-rank approximation of the original
matrix that satisfies predefined
accuracy. The standard and most
accurate technique for constructing
the HSS representation of a dense
matrix implies explicit calculation of all
matrix elements, and then
compression of appropriate blocks
using the RRQR decomposition, with
an O(rN2) asymptotic cost. Once the
HSS construction is done, the other
steps are cheaper, with O(r2N) time
complexity for ULV factorization and
O(rN) for solution, respectively, where
N was previously defined and r is the
maximum numerical rank. In order to
enhance the HSS compression and
parallelization i.e. scalability of the
method, an algorithm for geometrical
preprocessing of the geometrical
mesh based on the cobblestone
distance sorting technique is utilized.
Hence, the MoM unknowns having
spatial locality, also exhibit the data
locality in the matrix system of
equations. To sum up, method is
validated and great performance is
achieved. Even more, the simulation
results show great scalability of the
method on more than 1000
processes.
Besides developing a fast, parallel
and robust method based on the
MoM-SIE, in order to extend
applicability of the method to the
analysis that involves inhomogeneous
anisotropic dielectric and magnetic
materials, new symmetric
hybridization of the finite element
method (FEM) and the MoM was
developed. The FEM is one of the
general numerical tools for solving
closed-region (e.g., waveguide/cavity)
problems in electromagnetics. It has
been especially effectively used in
three-dimensional (3-D) frequency-
domain modeling and analysis of
electromagnetic structures that
contain geometrical and material
complexities. In addition, as the part
of the work included in this
dissertation the DHO FEM method
was implemented primarily to support
analysis of both inhomogeneous and
anisotropic materials.
Further, numerical computation is
accelerated by applying Diakoptic
Domain Decomposition approach to
divide the original problem of interest
into smaller subsystems, analyze
subsystems independently, and then
connect them back together through
the surface equivalence theorem.
Finally, all numerical methods
described above are validated on a
variety of numerical examples and
tested across several high
performance supercomputing
platforms.
Adviser: Prof. Branislav Notaros
Co-Adviser: N/A
Non-ECE Member: Prof. Iuliana Oprea
Member 3: Prof. Steven Reising
Addional Members: Prof. Sourajeet Roy, Prof. Milan Ilic
Publications:
JOURNAL PAPERS
1) S. V. Savic, A. B. Manic, M. M. Ilic, and B. M. Notaros, “Efficient Higher Order Full-Wave Numerical Analysis of 3-D Cloaking Structures,†Plasmonics, 2012 (published online: 8 July, 2012), 10.1007/s11468-012-9410-0.
2) A. B. Manic, S. B. Manic, M. M. Ilic, and B. M. Notaros, “Large Anisotropic Inhomogeneous Higher Order Hierarchical Generalized Hexahedral Finite Elements for 3-D Electromagnetic Modeling of Scattering and Waveguide Structures,†Microwave and Optical Technology Letters, vol. 54, No. 7, July 2012, pp. 1644-1649.
3) A. B. Manic, M. Djordjevic, and B. M. Notaros, “Duffy Method for Evaluation of Weakly Singular SIE Potential Integrals over Curved Quadrilaterals with Higher Order Basis Functions,†IEEE Transactions on Antennas and Propagation, Vol. 62, No. 6, June 2014,
4) A. B. Manić, D. I. Olćan, M. M. Ilić, and B. M. Notaroš, “Diakoptic approach combining finite-element method and method of moments in analysis of inhomogeneous anisotropic dielectric and magnetic scatterers,†Electromagnetics, vol. 34, no. 3–4, pp. 222–238, 2014.
5) M. Thurai, V. N. Bringi, A. B. Manić, N. J. Šekeljić, and B. M. Notaroš, “Investigating rain drop shapes, oscillation modes, and implications for radiowave propagation,†Radio Science, vol. 49, no. 10, pp. 921-932, October 2104.
6) E. Chobanyan, N. J. Å ekeljić, A. B. Manić, M. M. Ilić, V. N. Bringi, and B. M. NotaroÅ¡, “Efficient and Accurate Computational Electromagnetics Approach to Precipitation Particle Scattering Analysis Based on Higher Order Method of Moments Integral-Equation Modelingâ€, Journal of Atmospheric and Oceanic Technology, accepted.
7) Ana B. Manić, François-Henry Rouet, Xiaoye Sherry Li, and Branislav M. Notaroš, “Efficient Scalable Parallel Higher Order Direct MoM-SIE Method with Hierarchically Semiseparable Structures for 3D Scattering, †submitted to IEEE Transactions on Antennas and Propagation.
8) Ana B. Manić, and Branislav M. Notaroš, “Fast Computation of Near-Singular and Near-Hypersingular Integrals in Higher Order Method of Moments Using Curved Quadrilateral Patches, †IEEE Transactions on Antennas and Propagation, manuscript completed, to be submitted.
BOOK CHAPTER
1) B. M. Notaros, M. M. Ilic, S. V. Savic, and A. B. Manic, “Construction, Modeling, and Analysis of Transformation-Based Metamaterial Invisibility Cloaks,†accepted for publication in The Annual Reviews in Plasmonics, 2015.
PEER-REVIEWED CONFERENCE PAPERS AND ABSTRACTS
1) A. B. Manic, M. Djordjevic, E. Smith, and B. M. Notaros, “Numerical Computation of Singular Integrals in Higher Order Method of Moments Using Curved Quadrilateral Patches,†Proc. 2013 USNC-URSI National Radio Science Meeting, January 9-12, 2013, Boulder, Colorado.
2) A. B. Manic, M. M. Ilic, and B. M. Notaros, “Symmetric Coupling of Finite Element Method and Method of Moments Using Higher Order Elements,†2012 IEEE Antennas and Propagation Society International Symposium Digest, July 8-14, 2012, Chicago, Illinois.
3) A. B. Manic, D. I. Olcan, M. M. Ilic, and B. M. Notaros, “FEM-MoM-Diakoptic Analysis of Scatterers with Anisotropic Inhomogeneities Using Hierarchical Vector Bases on Large Curved Elements,†invited paper, Special Session “Advances in Vector Bases for CEM,†11th International Workshop on Finite Elements for Microwave Engineering – FEM2012, June 4-6, 2012, Estes Park, Colorado.
4) A. B. Manic, M. M. Ilic, and B. M. Notaros, “Symmetric and Nonsymmetric FEM-MoM Techniques Using Higher Order Hierarchical Vector Basis Functions and Curved Parametric Elements,†invited paper, Special Session “Advances in Hybrid Methods and Multiphysics Problems,†11th International Workshop on Finite Elements for Microwave Engineering –FEM2012, June 4-6, 2012, Estes Park, Colorado.
5) A. B. Manic, S. B. Manic, S. V. Savic, M. M. Ilic, and B. M. Notaros, “Efficient Electromagnetic Analysis Using Electrically Large Curved p-Refined Hierarchical Anisotropic Inhomogeneous Finite Elements,†Proc. 2012 USNC-URSI National Radio Science Meeting, January 4-7, 2012, Boulder, Colorado.
6) A. B. Manic, D. I. Olcan, M. M. Ilic, and B. M. Notaros, “Diakoptic FEM-MoM Analysis Using Explicit Connection between Field and Current Bases,†2013 IEEE Antennas and Propagation Society International Symposium Digest, July 7-12, 2013, Lake Buena Vista, Florida.
7) E. Chobanyan, N. J. Sekeljic, A. B. Manic, M. M. Ilic, and B. M. Notaros, “Atmospheric Particle Scattering Computation Using Higher Order MoM-SIE Method,†2013 IEEE Antennas and Propagation Society International Symposium Digest, July 7-12, 2013, Lake Buena Vista, Florida.
8) N. J. Sekeljic, A. B. Manic, M. M. Ilic, and B. M. Notaros, “Transient Analysis of 3D Waveguides Using Double-Higher Time-Domain Finite Element Method,†2013 IEEE Antennas and Propagation Society International Symposium Digest, July 7-12, 2013, Lake Buena Vista, Florida.
9) M. Thurai, V. N. Bringi, A. B. Manic, and B. M. Notaros, “Ongoing Investigations of Rain Drop Shapes and Oscillation Modes,†Proc. URSI Commission F Triennial Open Symposium on Radiowave Propagation & Remote Sensing, April 30-May 3, 2013, Ottawa, Canada.
10) Ana Manic, Elene Chobanyan, Milan Ilic, and Branislav Notaros, “Parallelization of Double Higher Order FEM and MoM Techniques,†2014 IEEE Antennas and Propagation Society International Symposium Digest, July 6-11, 2014, Memphis, Tennessee.
11) Nada Sekeljic, Ana Manic, Elene Chobanyan, Merhala Thurai, V. N. Bringi, and Branislav Notaros, “Electromagnetic Scattering by Oscillating Rain Drops of Asymmetric Shapes,†2014 IEEE Antennas and Propagation Society International Symposium Digest, July 6-11, 2014, Memphis, Tennessee.
12) B. M. Notaros, M. M. Ilic, D. I. Olcan, M. Djordjevic, A. B. Manic, and E. Chobanyan, “Hybrid Higher Order Num
Program of Study:
ECE 536
ECE 512
ECE 742
MATH 652
ECE 540
ECE 742
ECE 641
ECE 642
