| NSF Org: |
CCF Division of Computing and Communication Foundations |
| Recipient: |
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| Initial Amendment Date: | August 30, 2010 |
| Latest Amendment Date: | May 4, 2012 |
| Award Number: | 1018516 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Jack S. Snoeyink
CCF Division of Computing and Communication Foundations CSE Directorate for Computer and Information Science and Engineering |
| Start Date: | September 1, 2010 |
| End Date: | August 31, 2015 (Estimated) |
| Total Intended Award Amount: | $496,335.00 |
| Total Awarded Amount to Date: | $512,335.00 |
| Funds Obligated to Date: |
FY 2012 = $16,000.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
426 AUDITORIUM RD RM 2 EAST LANSING MI US 48824-2600 (517)355-5040 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
426 AUDITORIUM RD RM 2 EAST LANSING MI US 48824-2600 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): |
Algorithmic Foundations, NUM, SYMBOL, & ALGEBRA COMPUT |
| Primary Program Source: |
01001213DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.070 |
ABSTRACT
This proposal seeks to answer a growing engineering need: the development of robust computationally efficient methods to analyze transient radiation and scattering from electrically large multiscale objects. The proposed work can be categorized into two interrelated areas: (i) building parallel transient potential evaluators for computing interactions between random non-uniform source/observer pairs wherein separation between two points ranges from a millionth to a thousand of the minimum wavelength; (ii) development of parallel time domain higher-order integral equation solvers that include these potential integrators. The four-fold objectives of this proposal are as follows: (i) rigorous methods that can be integrated with the plane wave time domain (PWTD) algorithm to extend its applicability to the quasi-static regime; (ii) windowed operators that will morph PWTD with beams; (iii) parallel, multiscale, fast potential evaluators that include the above developments; and (iv) integration of these into time domain integral equation solvers. To realize these objectives, advances will be made on two fronts: (i) numerical methods to effect these operations with a proper understanding of error bounds and the means to control them; and (ii) parallel algorithms that are provably scalable.
The design and analysis of realistic devices is the holy grail of any computational endeavor. The same is true of Maxwell solvers. As Maxwell's equations form the foundation to a wide array of modern technology, methods developed to efficiently and accurately solve these equations can have wide ranging impact. To date, simulation tools have been complementary to, but have not supplanted experiments. The principal challenge has been bottlenecks posed by complex structural topologies with fine features, embedded in electrically large structures. Our goal-to enable the analysis of field deployable systems-will be realized by making advances in both the underlying numerics and parallel algorithms. These, in turn, will enable transition of this technology from tens of processors to thousands and tens of thousands of processors. Methods developed will yield a robust, accurate, and adaptable code that can be widely adopted in multiple domains in electromagnetics, acoustics, plasma dynamics, etc. To ensure dissemination, the PIs will work with practitioners in industry as well as with the Michigan Center for Industrial and Applied Mathematics. Existing channels in recruitment at MSU and ISU will be utilized to encourage participation by women and minorities. Undergraduate students will be involved through senior design projects and potentially through REU supplements. Additionally, a post-doctoral scholar will be mentored in all aspects necessary to be a successful academic.
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
Electromagnetics is a critical driver in the modern world that is rooted in technology. It finds application in areas as diverse as GPS, communications, circuits, optics, remote sensing, sensors, and so on. As a result, methods to understand and thereby exploit the field structure for design of devices is of great demand, and computational electromagnetics plays a key role in this endeavor. The research pursued during the course of the project focused on a set of challenging problems in computational electromagnetics. These are (a) develop robust and stable transient integral equation solvers, (b) develop acceleration methods that are robust across different scale in time and space, (c) develop parallel algorithms for solution of time domain integral equations. In addition to the above tasks and pursuant to our holistic goal of creating the a robust simulation electromagnetic tool, we sought to develop solution techniques that were mesh agnostic and exploited the latest advances in computer graphics. In addition to these intellectual advances, we have had (3 students) who were partially supported by this award, who have won awards at conferences, and are now leading computational electromagnetic software development in leading industry and government laboratories. Finally, we have published about 16 journal papers and countless conference papers based on our work. The specific problems that we have addressed during the course of the project are described in detail next.
A: Stabilization techniques for time domain integral equations; The state of art of time domain integral equation (TDIE) solvers has grown by leaps and bounds. Advances have been made in (i) the development of accelerators that can be retrofitted with these solvers and (ii) understanding the stability properties of the electric field integral equation. As is well known, time domain electric field integral equation solvers have been notoriously difficult to stabilize. Research into methods for understanding and prescribing remedies have been on the uptick. The most recent of these efforts are (i) Lubich quadrature and (ii) exact integration. In this work, we re-examine the solution to this equation using (i) the undifferentiated form of the TDEFIE and (ii) a separable approximation to the spatio-temporal convolution. The proposed method renders the spatial integrand over the source and observer domains is smooth and integrable. As several numerical results will demonstrate, the proposed scheme yields stable results for long simulation times and a variety of targets, both of which have proven extremely challenging in the past.
B: Extension to higher order in both space and time: Stability of time domain integral equation (TDIE) solvers has remained an elusive goal for many years. Advancement of this research has largely progressed on four fronts: (1) Exact integration, (2) Lubich quadrature, (3) smooth temporal basis functions, and (4) Space-time separation of convolutions with the retarded potential. The latter method was explored in our earlier work. This method's efficacy in stabilizing solutions to the time domain electric field integral equation (TD-EFIE) was demonstrated on first order surface descriptions (flat elements) in tandem with 0th order functions as the temporal basis. In this work, we develop the methodology necessary to extend to higher order surface descriptions as well as to enable its use with higher order basis functions in both space and time. A number of results are presented that demonstrate convergence in time.
C: Acceleration across length scales: For a long time, the challenges to transient simulation arose in two fronts, late time stability and CPU/memory bottlenecks. A solution to the latter was presented by the PI in 1998 w...
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