A calderón multiplicative preconditioner for the combined field integral equation
Type
Article
KAUST Department
Computational Electromagnetics LaboratoryComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Physical Science and Engineering (PSE) Division
Date
2009-10Permanent link to this record
http://hdl.handle.net/10754/561446Metadata
Show full item recordAbstract
A Calderón multiplicative preconditioner (CMP) for the combined field integral equation (CFIE) is developed. Just like with previously proposed Caldern-preconditioned CFIEs, a localization procedure is employed to ensure that the equation is resonance-free. The iterative solution of the linear system of equations obtained via the CMP-based discretization of the CFIE converges rapidly regardless of the discretization density and the frequency of excitation. © 2009 IEEE.Citation
Bagci, H., Andriulli, F. P., Cools, K., Olyslager, F., & Michielssen, E. (2009). A CalderÓn Multiplicative Preconditioner for the Combined Field Integral Equation. IEEE Transactions on Antennas and Propagation, 57(10), 3387–3392. doi:10.1109/tap.2009.2029389Sponsors
Manuscript received October 17, 2008; revised January 27, 2009. First published August 07, 2009; current version published October 07, 2009. This work was supported in part by AFOSR MURI Grant F014432-051936, aimed at modeling installed antennas and their feeds, and by NSF Grant DMS 0713771.Scopus Count
Related items
Showing items related by title, author, creator and subject.
-
On the static loop modes in the marching-on-in-time solution of the time-domain electric field integral equation(IEEE Antennas and Wireless Propagation Letters, Institute of Electrical and Electronics Engineers (IEEE), 2014) [Article]When marching-on-in-time (MOT) method is applied to solve the time-domain electric field integral equation, spurious internal resonant and static loop modes are always observed in the solution. The internal resonant modes have recently been studied by the authors; this letter investigates the static loop modes. Like internal resonant modes, static loop modes, in theory, should not be observed in the MOT solution since they do not satisfy the zero initial conditions; their appearance is attributed to numerical errors. It is discussed in this letter that the dependence of spurious static loop modes on numerical errors is substantially different from that of spurious internal resonant modes. More specifically, when Rao-Wilton-Glisson functions and Lagrange interpolation functions are used as spatial and temporal basis functions, respectively, errors due to space-time discretization have no discernible impact on spurious static loop modes. Numerical experiments indeed support this discussion and demonstrate that the numerical errors due to the approximate solution of the MOT matrix system have dominant impact on spurious static loop modes in the MOT solution. © 2014 IEEE.
-
Low-frequency scaling of the standard and mixed magnetic field and Müller integral equations(IEEE Transactions on Antennas and Propagation, Institute of Electrical and Electronics Engineers (IEEE), 2014-02) [Article]The standard and mixed discretizations for the magnetic field integral equation (MFIE) and the Müller integral equation (MUIE) are investigated in the context of low-frequency (LF) scattering problems involving simply connected scatterers. It is proved that, at low frequencies, the frequency scaling of the nonsolenoidal part of the solution current can be incorrect for the standard discretization. In addition, it is proved that the frequency scaling obtained with the mixed discretization is correct. The reason for this problem in the standard discretization scheme is the absence of exact solenoidal currents in the rotated RWG finite element space. The adoption of the mixed discretization scheme eliminates this problem and leads to a well-conditioned system of linear equations that remains accurate at low frequencies. Numerical results confirm these theoretical predictions and also show that, when the frequency is lowered, a finer and finer mesh is required to keep the accuracy constant with the standard discretization. © 1963-2012 IEEE.
-
Open problems in CEM: Porting an explicit time-domain volume-integral- equation solver on GPUs with OpenACC(IEEE Antennas and Propagation Magazine, Institute of Electrical and Electronics Engineers (IEEE), 2014-04) [Article]Graphics processing units (GPUs) are gradually becoming mainstream in high-performance computing, as their capabilities for enhancing performance of a large spectrum of scientific applications to many fold when compared to multi-core CPUs have been clearly identified and proven. In this paper, implementation and performance-tuning details for porting an explicit marching-on-in-time (MOT)-based time-domain volume-integral-equation (TDVIE) solver onto GPUs are described in detail. To this end, a high-level approach, utilizing the OpenACC directive-based parallel programming model, is used to minimize two often-faced challenges in GPU programming: developer productivity and code portability. The MOT-TDVIE solver code, originally developed for CPUs, is annotated with compiler directives to port it to GPUs in a fashion similar to how OpenMP targets multi-core CPUs. In contrast to CUDA and OpenCL, where significant modifications to CPU-based codes are required, this high-level approach therefore requires minimal changes to the codes. In this work, we make use of two available OpenACC compilers, CAPS and PGI. Our experience reveals that different annotations of the code are required for each of the compilers, due to different interpretations of the fairly new standard by the compiler developers. Both versions of the OpenACC accelerated code achieved significant performance improvements, with up to 30× speedup against the sequential CPU code using recent hardware technology. Moreover, we demonstrated that the GPU-accelerated fully explicit MOT-TDVIE solver leveraged energy-consumption gains of the order of 3× against its CPU counterpart. © 2014 IEEE.